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We numerically investigate thermochemically-driven convection in a spherical shell at a high Ekman number for a range of Rayleigh numbers, Prandtl numbers and buoyancy ratios. Rotating convection displays a nearly axisymmetric large-scale structure and appears mostly unaffected by the nature (thermal or chemical) of the driving buoyancy source. We observe both precession directions, prograde and retrograde, of convection structures and identify a snap-through transition between the prograde and retrograde flows in the parameter space spanned by the Rayleigh and Prandtl numbers. Equatorially wall-attached and spiralling columnar convection structures, which typically emerge in rapidly rotating shells, are not observed. [ABSTRACT FROM AUTHOR]

A time-resolved experimental investigation was undertaken on the temperature evolution of Rayleigh–Bénard convection (RBC) in a slender convection cell with aspect ratio of Γ = 0.1. Experiments were conducted for Rayleigh numbers of R a = 5.3 × 10 7 , 7.6 × 10 7 , and 9.5 × 10 7 and Prandtl number of P r ≈ 6 within the non-Oberbeck–Boussinesq (NOB) condition with a temperature difference variation in the range of 30 ° C ≤ Δ T ≤ 40 ° C. Measurement of the temperature was by applying time-resolved two-color planar laser-induced fluorescence over the initial 2400 s. Experimental observations showed that the lateral confinement of the convection cell leads to the development of a single large-scale thermal plume instead of multiple plumes. Results showed that contrary to expectations, lateral confinement was found to be ineffective in suppressing temperature oscillations near thermal boundaries. Results also indicated that for R a = 5.3 × 10 7 , 7.6 × 10 7 , the temperature oscillations had a frequency of f ≈ 0.028 Hz similar to the frequency of the oscillations in Oberbeck–Boussinesq (OB) RBC. For R a = 9.5 × 10 7 , however, it was found that the frequency of the oscillations was much lower than the OB RBC with a relatively wide range of the oscillations in the vicinity of f ≈ 0.006 Hz. It is also found that the lateral confinement and formation of singular high-energy thermal plumes leads to an increase in the nonsymmetrical temperature distribution of NOB RBC with a bimodal distribution of the temperature field, deviating significantly from the Gaussian distribution temperature field found in OB RBC. [ABSTRACT FROM AUTHOR]

We investigate the boundary layer characteristics within annular centrifugal Rayleigh–Bénard convection (ACRBC) considering a Rayleigh number R a ∈ [ 10 8 , 10 11 ] , a Prandtl number Pr = 10.7, and an inverse Rossby number R o − 1 = 16. Our study is based on the temperature and velocity data obtained from direct numerical simulations. Different from the flow over a flat plate, the ACRBC system bifurcates into three regions: the plume-impacting regions, plume-ejecting regions, and plume-sweeping regions, and all three regions are moving with the zonal flow. Our focus is primarily on the temperature dynamics within the plume-sweeping region, where the wind of large-scale circulation shears the boundary. We determine the transient thermal boundary layer thickness over time using the slope method, relying on the temperature curve's orientation relative to the wall. Notably, the probability density function distribution of the thermal boundary layer thickness is reminiscent of traditional RBC systems, albeit with a more extended exponential tail. Employing a dynamic frame based on time resampling, we discern that the temperature boundary layer traits align with the Prandtl–Blasius boundary layer theory. In conclusion, we show that the exponential decay index for the thermal boundary layer thickness harmonizes with the system's heat transfer scaling law. It is found that the ratio between the inner and outer boundary layer thickness remains stable, providing theoretical guidance for the design and control of the internal flow field of high-speed rotating machinery. [ABSTRACT FROM AUTHOR]

Microorganisms inhabit various natural environments and thrive in diverse ecosystems, including freshwater and marine bodies. Many of these microorganisms can swim and have a higher density than water, generating a vertical stratification of cell concentration that may lead to instability due to the buoyancy force. Biothermal convection refers to the convective motion that arises due to the combined effect of up-swimming microorganism and thermal gradients in a fluid medium. In the present work we investigate the onset of biothermal convection in a horizontal layer of cold water in the presence of the density inversion. This previously unexplored issue holds significance due to its potential applications in both natural and industrial contexts. We applied linear stability analysis to determine the critical thresholds at which instability initiates. To confirm these stability findings, we conducted numerical simulations using the finite volume method and compared them with the available experimental results in the case of penetrative convection. The critical threshold is shown to depend essentially upon the value of the density inversion parameter and the thermal Rayleigh number. Additionally, the linear stability analysis suggests the possible occurrence of Hopf bifurcations at the onset of motion. Article Highlights: Biothermal convection stability depends on both the thermal Rayleigh number and the density inversion parameter. The temperature stratification can either stabilize or destabilize, depending on the density inversion parameter. An increase in the thermal Rayleigh number can introduces wave number transitions. [ABSTRACT FROM AUTHOR]

Bionanofluids containing biological nanoparticles suspended in base fluids exhibit altered dynamics due to coupled effects between the nanoparticles and fluid properties. More efficient cooling can enhance medical technology performance, reduce energy usage, and provide safer, more sustainable healthcare solutions. This work overcomes previous research limitations by elucidating the combined impacts of microorganisms and couple stress properties on the behavior of water-based bionanofluids containing copper nanoparticles, under inclined magnetic fields. Governing equations for momentum, energy, concentration, and microorganisms are transformed into ordinary differential equations (ODEs) via similarity methods. The resulting ODE system is then solved semi-analytically using the Homotopy Analysis Method, revealing distinct profile behaviors. Additionally, quantitative indicators including skin friction for different values of M, λ,β, and Nr increased by 7.19%, 62.81%, 31.27%, and 21.32% respectively. Similarly Nusselt number for different values Qe , Ec, and Df decrease by 3.502 %, 2.5705%, and 2.447% respectively. Furthermore, Sherwood Numbers for different values of Sc, Kc, increased by 16.41%, and 4.133% respectively. Finally, Microorganisms for different values of Lb, Pe, and σ1 increase by 2.934%, 2.61%, and 1.172% respectively.

The effect of time-periodic two-frequency rotation modulation on Rayleigh–Bénard convection in water with either AA7072 or AA7075 nanoparticles is investigated. The single-phase description of the Khanafer–Vafai–Lightstone model is used for modeling the nanoliquids. An asymptotic expansion procedure is adopted in the case of the linear stability to obtain the correction (due to modulation) to the Rayleigh number at marginal stability of unmodulated convection. A nonlinear regime of convection is considered with a nonautonomous generalized Lorenz model as the governing equation. The method of multiscales is then employed to obtain the coupled nonautonomous Ginzburg–Landau equations with cubic nonlinearity from the Lorenz model. These equations are presented in the phase-amplitude form and the amplitude is used to quantify the heat transport. The modulation amplitude is considered to be small (of order less than unity) and moderate frequencies of modulation are considered. We found that there is a threshold frequency beyond which the system behavior reverses. At frequencies below the threshold, the mean Nusselt number increases with an increase in the amplitude of modulation while an opposite influence is seen for values above the threshold. Such a behavior is a consequence of what is analogously seen in the case of the critical Rayleigh number. The influence of two-frequency modulation is more pronounced on the results of the linear and nonlinear regimes compared to that of the single-frequency one. The heat transport is enhanced due to the presence of dilute concentration of suspended nanoparticles (either AA7072 or AA7075 nanoalloys) in water. The influence of nanoparticles is to modify the threshold values generating chaos but it does not qualitatively alter the dynamical behavior of the system. The plots of Lyapunov exponents reveal that there is no possibility of hyper-chaos in the generalized Lorenz model when there is a rotational modulation. [ABSTRACT FROM AUTHOR]

Advancing our understanding of astrophysical turbulence is bottlenecked by the limited resolution of numerical simulations that may not fully sample scales in the inertial range. Machine-learning (ML) techniques have demonstrated promise in upscaling resolution in both image analysis and numerical simulations (i.e., superresolution). Here we employ and further develop a physics-constrained convolutional neural network ML model called "MeshFreeFlowNet" (MFFN) for superresolution studies of turbulent systems. The model is trained on both the simulation images and the evaluated partial differential equations (PDEs), making it sensitive to the underlying physics of a particular fluid system. We develop a framework for 2D turbulent Rayleigh–Bénard convection generated with the Dedalus code by modifying the MFFN architecture to include the full set of simulation PDEs and the boundary conditions. Our training set includes fully developed turbulence sampling Rayleigh numbers (Ra) of Ra = 106–1010. We evaluate the success of the learned simulations by comparing the power spectra of the direct Dedalus simulation to the predicted model output and compare both ground-truth and predicted power spectral inertial range scalings to theoretical predictions. We find that the updated network performs well at all Ra studied here in recovering large-scale information, including the inertial range slopes. The superresolution prediction is overly dissipative at smaller scales than that of the inertial range in all cases, but the smaller scales are better recovered in more turbulent than laminar regimes. This is likely because more turbulent systems have a rich variety of structures at many length scales compared to laminar flows. [ABSTRACT FROM AUTHOR]

Buoyancy-assisted upward MHD flows and dynamical behaviors of flow channel insert (FCI) in the dual-coolant lead-lithium (DCLL) blanket are studied numerically. Based on our internally developed and validated solver, the dynamical behaviors of magneto-thermo-fluid-structure coupled multiphysical field are investigated. A large amplitude, low frequency, and quasiperiodic unsteady reverse flow at high Re (31000), high G r (3.5 × 1 0 11 ), and moderate magnetic field (0.7~1.7T) is found in the DCLL blanket. This intricate phenomenon has been discovered for the first time, representing a combination of separate experimental results from Melnikov et al. (2016) and Khanal and Lei (2012). In our study of this large amplitude, low frequency, and quasiperiodic unsteady reverse flows, the importance of the cold helium gas to the instability of fluid flow in the bulk region and the thermal conductivity of the FCI to convection structure and instability are first found and recognized. Additionally, we take into account the effects of the temperature field and flow field on structural deformation and mechanical behavior of FCI, and we have discovered several intriguing phenomena, such as (1) the stability of fluid flow in the bulk region depends on the strength of the heat source, the magnitude of the magnetic field, and thermal conductivity of FCI; (2) the instability and periodicity of the fluid flow are primarily related to the unsteady reverse flow, which rises up and falls down periodically in the bulk region; (3) the physical mechanism of unsteady flow influenced by reverse flow, pressure drop, and Lorentz force has been concluded. It has been discovered that the breakdown of a reverse flow vortex causes a rapid reduction in pressure drop. (4) To avoid this phenomenon in engineering, a phase map of unsteady and steady flows in the DCLL blanket has been created. (5) The quasiperiodic characteristics of solid (flow channel insert) affected by flow are found and analyzed. [ABSTRACT FROM AUTHOR]

The present work focuses on the effect of rough horizontal boundaries on the heat transfer in rotating Rayleigh-Bénard convection. We measure the non-dimensional heat transfer, the Nusselt number Nu, for various strengths of the buoyancy forcing characterized by the Rayleigh number Ra (105 <~ Ra <~ 5 × 108), and rotation rates characterized by the Ekman number E (1.4 × 10-5 <~ E <~ 7.6 × 10-4) for aspect ratios G = 1, 2.8 and 6.7. Similar to rotating convection with smooth horizontal boundaries, the so-called rotationally constrained (RC), rotation-affected (RA) and rotation-unaffected (RuA) regimes of heat transfer seem to persist for rough horizontal boundaries. However, the transition from the RC regime to RA regime occurs at a lower Rayleigh number for rough boundaries. For all experiments with rough boundaries in this study, the thermal and Ekman boundary layers are in a perturbed state, leading to a significant enhancement in the heat transfer as compared with that for smooth walls. However, the enhancement in heat transfer due to wall roughness is observed to attain a maximum in the RC regime. We perform companion direct numerical simulations of rotating convection over smooth walls to suggest a phenomenology explaining this observation. We propose that the heat transfer enhancement due to wall roughness reaches a maximum when the strength and coherence of the columnar structures are both significant, which enables efficient vertical transport of the additional thermal anomalies generated by the roughness at the top and bottom walls. [ABSTRACT FROM AUTHOR]

In this paper, we have studied the criteria for the onset of instability in the Rayleigh-Bénard convection problem, by considering a fluid layer confined between two infinitely extended rough boundaries, which are subjected to mixed-type thermal boundary conditions, physically representing the imperfectly conducting boundaries. The rough boundaries are assumed to be shallow porous layers with different pore size, properties, and permeabilities. Mathematically, it is given by the Saffman type boundary condition. Therefore, we have two generalized forms of boundary conditions, one for the flow field and the other for the thermal field. The two limiting cases of the mixed-type thermal boundary condition correspond to a perfectly conducting boundary and to a perfectly insulating boundary, whereas the two limiting cases of the hydrodynamic boundary condition correspond to a no-slip condition and to a free-surface condition, depending upon the limiting values of the parameters involved in these two generalized boundary conditions. The linear and nonlinear energy stability analyses are performed, and the existence of the region of subcritical instability is checked. Through the principle of exchange of stability analysis, it is found that the instability occurs only in the stationary mode. The adiabatic boundary condition is found to be more restrictive than the isothermal boundary condition. Under given conditions, the instability is observed to be occurring in the infinite wavelength mode for the case of adiabatic boundaries. In the present work, the effect of temperature and pressure dependent viscosity on the stability of the system has been shown and found to be of destabilizing nature. However, the roughness of the boundaries is found to be of stabilizing nature. [ABSTRACT FROM AUTHOR]

Approximate streamsurfaces of a three-dimensional velocity field have recently been constructed as isosurfaces of the closest first integral of the velocity field. Such approximate streamsurfaces enable effective and efficient visualization of vortical regions in three-dimensional flows. Here we propose a variational construction of these approximate streamsurfaces to remove the limitation of Fourier series representation of the first integral in earlier work. Specifically, we use finite-element methods to solve a partial differential equation that describes the best approximate first integral for a given velocity field. We use several examples to demonstrate the power of our approach for three-dimensional flows in domains with arbitrary geometries and boundary conditions. These include generalized axisymmetric flows in the domains of a sphere (spherical vortex), a cylinder (cylindrical vortex) and a hollow cylinder (Taylor–Couette flow) as benchmark studies for various computational domains, non-integrable periodic flows (ABC and Euler flows) and Rayleigh–Bénard convection flows. We also illustrate the use of the variational construction in extracting momentum barriers in Rayleigh–Bénard convection. [ABSTRACT FROM AUTHOR]

We present a formulation of proper orthogonal decomposition (POD) producing a velocity–temperature basis optimized with respect to an H1 dissipation norm. This decomposition is applied, along with a conventional POD optimized with respect to an L2 energy norm, to a dataset generated from a direct numerical simulation of Rayleigh–Bénard convection in a cubic cell (Ra = 10 7 , Pr = 0.707). The dataset is enriched using symmetries of the cell, and we formally link symmetrization to degeneracies and to the separation of the POD bases into subspaces with distinct symmetries. We compare the two decompositions, demonstrating that each of the 20 lowest dissipation modes is analogous to one of the 20 lowest energy modes. Reordering of modes between the decompositions is limited, although a corner mode known to be crucial for reorientations of the large-scale circulation is promoted in the dissipation decomposition, indicating suitability of the dissipation decomposition for capturing dynamically important structures. Dissipation modes are shown to exhibit enhanced activity in boundary layers. Reconstructing kinetic and thermal energy, viscous and thermal dissipation, and convective heat flux, we show that the dissipation decomposition improves overall convergence of each quantity in the boundary layer. Asymptotic convergence rates are nearly constant among the quantities reconstructed globally using the dissipation decomposition, indicating that a range of dynamically relevant scales is efficiently captured. We discuss the implications of the findings for using the dissipation decomposition in modeling and argue that the H1 norm allows for a better modal representation of the flow dynamics. [ABSTRACT FROM AUTHOR]

Understanding turbulent thermal convection is essential for modeling many natural phenomena. This study investigates the spatiotemporal dynamics of the vortical structures in the mid-plane of turbulent Rayleigh–Bénard convection in SF6 via experiments. For this, a Rayleigh–Bénard cell of aspect ratio 10 is placed inside a pressure vessel and pressurized up to 1, 1.5, and 2.5 bar in order to reach Rayleigh numbers of Ra = 9.4 × 10 5 , 2.0 × 10 6 , and 5.5 × 10 6 , respectively. For all three cases, the Prandtl number is Pr = 0.79 and Δ T ≈ 7 K. Then, stereoscopic particle image velocimetry is conducted to measure the three velocity components in the horizontal-mid-plane for 5.78 × 10 3 free fall times. For the given aspect ratio, the flow is no longer dominated by the side walls of the cell and turbulent superstructures that show a two-dimensional repetitive organization form. These superstructures show diverse shapes with faster dissipation rates as Ra increases. Out-of-plane vortices are the main feature of the flow. As Ra increases, the number of these vortices also increases, and their size shrinks. However, their total number is almost constant for each Ra through the measurement period. Furthermore, their occurrence is random and does not depend on whether the flow is upward-heated, downward-cooled, or horizontally directed. Vortex tracking was applied to measure lifetime, displacement, and traveled distance of these structures. The relation between lifetime and traveled distance is rather linear. Interestingly, in the vortex centers, the out-of-plane momentum transport is larger in comparison to the bulk flow. Therefore, these vortices will play a major role in the heat transport in such flows. [ABSTRACT FROM AUTHOR]

We present an experimental study on the large-scale circulation (LSC) and temperature oscillation in the flattened cylindrical turbulent Rayleigh–Bénard Convection cell with aspect ratio Γ = 2. The Prandtl number is maintained at Pr = 5.7, and the Rayleigh number Ra ranges from 8.0 × 10 7 to 6.5 × 10 8 . The strength and the orientation of the LSC are measured through the multi-point temperature signal at the mid-height of the convection cell. Our findings reveal that the single roll form of the LSC consistently dominates the flow, with its orientation confined to a narrower azimuthal range compared to the slender cell (e.g., Γ = 1 cell). Differing from the diffusion process observed in the Γ = 1 cell, the azimuthal motion of the LSC in the Γ = 2 cell exhibits a superdiffusion process. The mean square change of the strength of the LSC displays multiple regimes, with the scaling exponent of the first regime being 2, indicating ballistic motion within the short time interval. The scaling exponent of the second regime is 0.5 (0.2) for a leveled (tilted) cell, signifying a subdiffusion motion. Moreover, the temperature oscillations in the Γ = 2 cell differ significantly from those reported in a Γ = 1 cell, and it is found that the temperature oscillation exits everywhere at the mid-height of the cell. Furthermore, at the mid-height of the cell, the orientation and strength of the LSC exhibit prominent oscillations with characteristic frequencies of f0 and 2 f 0 , respectively, which are absent in Γ = 1 and 1/2 cells. These behaviors can be well-explained by the motion of the vortex center. [ABSTRACT FROM AUTHOR]

We report an experimental study about the effect of an obstructed centre on heat transport and flow reversal by inserting an adiabatic cylinder at the centre of a quasi-two-dimensional Rayleigh-Bénard convection cell. The experiments are carried out in a Rayleigh number (Ra) range of 2 × 107 = Ra = 2 × 109 and at a Prandtl number (Pr) of 5.7. It is found that for low Ra, the obstructed centre leads to a heat transfer enhancement of up to 21%, while as Ra increases, the magnitude of the heat transfer enhancement decreases and the heat transfer efficiency (Nu) eventually converges to that of the unobstructed normal cell. Particle image velocimetry measurements show that the heat transfer enhancement originates from the change in flow topology due to the presence of the cylindrical obstruction. In the low-Ra regime the presence of the obstruction promotes the transition of the flow topology from the four-roll state to the abnormal single-roll state then to the normal single-roll state with increasing obstruction size. While in the high-Ra regime, the flow is always in the single-roll state regardless of the obstruction size, although the flow becomes more coherent with the size of the obstruction. We also found that in the presence of the cylindrical obstruction, the stability of the corner vortices is significantly reduced, leading to a large reduction in the frequency of flow reversals. [ABSTRACT FROM AUTHOR]

The interior oceans of several icy moons are considered as affected by rotation. Observations suggest a larger heat transport around the poles than at the equator. Rotating Rayleigh‐Bénard convection (RRBC) in planar configuration can show an enhanced heat transport compared to the non‐rotating case within this "rotation‐affected" regime. We investigate the potential for such a (polar) heat transport enhancement in these subglacial oceans by direct numerical simulations of RRBC in spherical geometry for Ra = 106 and 0.7 ≤ Pr ≤ 4.38. We find an enhancement up to 28% in the "polar tangent cylinder," which is globally compensated by a reduced heat transport at low latitudes. As a result, the polar heat transport can exceed the equatorial by up to 50%. The enhancement is mostly insensitive to different radial gravity profiles, but decreases for thinner shells. In general, polar heat transport and its enhancement in spherical RRBC follow the same principles as in planar RRBC. Plain Language Summary: The icy moons of Jupiter and Saturn like for example, Europa, Titan, or Enceladus are believed to have a water ocean beneath their ice crust. Several of them show phenomena in their polar regions like active geysers or a thinner crust than at the equator, all of which might be related to a larger heat transport around the poles from the underlying ocean. We simulate the flow dynamics and currents in these subglacial ocean by high‐fidelity simulations, though still at less extreme parameters than in reality, to study the heat transport and provide a possible explanation of such a "polar heat transport enhancement." We find that the heat transport around the poles can be up to 50% larger than around the equator, and that the believed properties of the icy moons and their oceans would allow polar heat transport enhancement. Therefore, our results may help to improve the understanding of ocean currents and latitudinal variations in the oceanic heat transport and crustal thickness on icy moons. Key Points: The polar heat transport in spherical rotating Rayleigh‐Bénard convection experiences an enhancement by rotationThe influence of rotation differs at low latitudes: the heat flux is reduced and compensates the polar enhancement on the global averageIn combination, this strengthens the latitudinal variation between polar and equatorial heat flux for Prandtl numbers larger than unity [ABSTRACT FROM AUTHOR]

Supergranule aggregation, i.e. the gradual aggregation of convection cells to horizontally extended networks of flow structures, is a unique feature of constant heat flux-driven turbulent convection. In the present study, we address the question if this mechanism of self-organisation of the flow is present for any fluid. Therefore, we analyse three-dimensional Rayleigh-Bénard convection at a fixed Rayleigh number Ra ≈ 2.0 x 105 across 4 orders of Prandtl numbers Pr ∈ [10-2, 10²] by means of direct numerical simulations in horizontally extended periodic domains with aspect ratio Γ = 60. Our study confirms the omnipresence of the mechanism of supergranule aggregation for the entire range of investigated fluids. Moreover, we analyse the effect of Pr on the global heat and momentum transport, and clarify the role of a potential stable stratification in the bulk of the fluid layer. The ubiquity of the investigated mechanism of flow self-organisation underlines its relevance for pattern formation in geophysical and astrophysical convection flows, the latter of which are often driven by prescribed heat fluxes. [ABSTRACT FROM AUTHOR]

Direct numerical simulations have been conducted to investigate turbulent Rayleigh- Bénard convection (RBC) of liquid metal in a cuboid vessel with aspect ratio Γ = 5 under an imposed horizontal magnetic field. Flows with Prandtl number Pr = 0.033, Rayleigh numbers ranging up to Ra ≤ 107, and Chandrasekhar numbers up to Q ≤ 9 x 106 are considered. For weak magnetic fields, our findings reveal that a previously undiscovered decreasing region precedes the enhancement of heat transfer and kinetic energy. For moderate magnetic fields, we have reproduced the reversals of the large-scale flow, which are considered a reorganization process of the roll-like structures that were reported experimentally by Yanagisawa et al. (Phys. Rev. E, vol. 83, 2011, 036307). Nevertheless, the proposed approach of skewed-varicose instability has been substantiated as insufficient to elucidate fundamentally the phenomenon of flow reversal, an occurrence bearing a striking resemblance to the large-scale intermittency observed in magnetic channel flows. As we increase the magnetic field strength further, we observe that the energy dissipation of the system comes primarily from the viscous dissipation within the boundary layer. Consequently, the dependence of Reynolds number Re on Q approaches a scaling as RePr/Ra2/3 ~ Q-1/3. At the same time, we find the law for the cutoff frequency that separates large quasi-two-dimensional scales from small three-dimensional ones in RBC flow, which scales with the interaction parameter as ~N1/3. [ABSTRACT FROM AUTHOR]

The present work presents a stable proper orthogonal decomposition (POD)-Galerkin based reduced-order model (ROM) for two-dimensional Rayleigh–Bénard convection in a square geometry for three Rayleigh numbers: 10 4 (steady state), 3 × 10 5 (periodic), and 6 × 10 6 (chaotic). Stability is obtained through a particular (staggered-grid) full-order model (FOM) discretization that leads to a ROM that is pressure-free and has skew-symmetric (energy-conserving) convective terms. This yields long-time stable solutions without requiring stabilizing mechanisms, even outside the training data range. The ROM's stability is validated for the different test cases by investigating the Nusselt and Reynolds number time series and the mean and variance of the vertical temperature profile. In general, these quantities converge to the FOM when increasing the number of modes, and turn out to be a good measure of accuracy. However, for the chaotic case, convergence with increasing numbers of modes is relatively difficult and a high number of modes is required to resolve the low-energy structures that are important for the global dynamics. [ABSTRACT FROM AUTHOR]

Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a structure-preserving and thermodynamically consistent finite element method and time-stepping scheme for heat conducting viscous fluids, with general state equations. The method is deduced by discretizing a variational formulation for nonequilibrium thermodynamics that extends Hamilton's principle for fluids to systems with irreversible processes. The resulting scheme preserves the balance of energy and mass to machine precision, as well as the second law of thermodynamics, both at the spatially and temporally discrete levels. The method is shown to apply both with insulated and prescribed heat flux boundary conditions, as well as with prescribed temperature boundary conditions. We illustrate the properties of the scheme with the Rayleigh–Bénard thermal convection. While the focus is on heat conducting viscous fluids, the proposed discrete variational framework paves the way to a systematic construction of thermodynamically consistent discretizations of continuum systems. [ABSTRACT FROM AUTHOR]

The traditional approach of using the Monin–Obukhov similarity theory (MOST) to model near-surface processes in large-eddy simulations (LESs) can lead to significant errors in natural convection. In this study, we propose an alternative approach based on feedforward neural networks (FNNs) trained on output from direct numerical simulation (DNS). To evaluate the performance, we conduct both a priori and a posteriori tests. In the a priori (offline) tests, we compare the statistics of the surface shear stress and heat flux, computed from filtered DNS input variables, to the stress and flux obtained from the filtered DNS. Additionally, we investigate the importance of various input features using the Shapley additive explanations value and the conditional average of the filter grid cells. In the a posteriori (online) tests, we implement the trained models in the System for Atmospheric Modeling (SAM) LES and compare the LES-generated surface shear stress and heat flux with those in the DNS. Our findings reveal that vertical velocity, a traditionally overlooked flow quantity, is one of the most important input features for determining the wall fluxes. Increasing the number of input features improves the a priori test results but does not always improve the model performance in the a posteriori tests because of the differences in input variables between the LES and DNS. Last, we show that physics-aware FNN models trained with logarithmic and scaled parameters can well extrapolate to more intense convection scenarios than in the training dataset, whereas those trained with primitive flow quantities cannot. Significance Statement: The traditional near-surface turbulence model, based on a shear-dominated boundary layer flow, does not represent near-surface turbulence in natural convection. Using a feedforward neural network (FNN), we can construct a more accurate model that better represents the near-surface turbulence in various flows and reveals previously overlooked controlling factors and process interactions. Our study shows that the FNN-generated models outperform the traditional model and highlight the importance of the near-surface vertical velocity. Furthermore, the physics-aware FNN models exhibit the potential to extrapolate to convective flows of various intensities beyond the range of the training dataset, suggesting their broader applicability for more accurate modeling of near-surface turbulence. [ABSTRACT FROM AUTHOR]

In this work, we perform direct numerical simulations of Rayleigh–Bénard convection in a two-dimensional confined square cell for Rayleigh numbers (Ra) from 109 to 1013 and a Prandtl number (Pr) of 0.7. In contrast to a previous study in a periodic box conducted by Zhu et al. [Phys. Rev. Lett. 120, 144502 (2018)], our simulations apply two adiabatic sidewalls. In particular, boundary layer structures near the heating plates are examined using both mean velocity and temperature profiles in the impacting, shearing, and ejecting regions of the plumes. After an appropriate normalization using the wall units, the friction Reynolds numbers of our simulations exceed the critical value of 200 and follow R e τ ∼ R a 0.323 , and we also observe the logarithmic mean velocity profiles (with the slope κ v ≈ 0.35) in the shearing regions and logarithmic mean temperature profiles (with the slope κ θ ≈ 2) in the ejecting regions. These logarithmic behaviors indicate that both the thermal and momentum boundary layers may have entered the fully developed turbulent state. However, for the Nusselt number (Nu), our data still follow the trend of classical 1/3 scaling, differing from the ultimate state reported before but agreeing with the three-dimensional results obtained by Iyer et al. [PNAS 117, 14 (2020)] for confined cells. [ABSTRACT FROM AUTHOR]

Although natural convection is frequently encountered in various chemical processes, Rayleigh number (Ra) cannot be defined fully in shear‐thinning fluid systems. In particular, the velocity scale, which is necessary to estimate the effective viscosity of the system, should be discussed carefully. Thus, in this study, the representative velocity scale of Rayleigh‐Bénard (RB) convection, which is a typical example of natural convection, with shear‐thinning fluids was investigated based on the velocity fields obtained using computational fluid dynamics. Numerical simulations revealed that the critical temperature difference at which RB convection starts to fully develop decreases with an increase in the shear‐thinning property. The shear‐thinning property also induced subcritical bifurcation. In addition, the velocity scale of convection increases with an increase in the shear‐thinning property. Thus, the shear‐thinning property is considered to accelerate convection. Compared with several types of velocity scales used by other researchers, significant deviations from the actual scale were observed. Therefore, a new type of velocity scale, including the buoyant to viscous force ratio, arbitrary parameter, and thermal diffusivity, was proposed. The proposed velocity scale allowed an approximate estimation of the actual velocity scale. Although further investigation of the validity is necessary with varying geometries and rheological parameters, this velocity scale will be useful for controlling RB convection with Newtonian/shear‐thinning fluids. [ABSTRACT FROM AUTHOR]

This work studies two-dimensional fixed-flux Rayleigh–Bénard convection with periodic boundary conditions in both horizontal and vertical directions and analyses its dynamics using numerical continuation, secondary instability analysis and direct numerical simulation. The fixed-flux constraint leads to time-independent elevator modes with a well-defined amplitude. Secondary instability of these modes leads to tilted elevator modes accompanied by horizontal shear flow. For Pr = 1, where Pr is the Prandtl number, a subsequent subcritical Hopf bifurcation leads to hysteresis behaviour between this state and a time-dependent direction-reversing state, followed by a global bifurcation leading to modulated travelling waves without flow reversal. Single-mode equations reproduce this moderate Rayleigh number behaviour well. At high Rayleigh numbers, chaotic behaviour dominated by modulated travelling waves appears. These transitions are characteristic of high wavenumber elevator modes since the vertical wavenumber of the secondary instability is linearly proportional to the horizontal wavenumber of the elevator mode. At a low Pr, relaxation oscillations between the conduction state and the elevator mode appear, followed by quasi-periodic and chaotic behaviour as the Rayleigh number increases. In the high Pr regime, the large-scale shear weakens, and the flow shows bursting behaviour that can lead to significantly increased heat transport or even intermittent stable stratification. [ABSTRACT FROM AUTHOR]

Coherent structures are characterized in high‐resolution simulations of three atmospheric boundary layers: dry convection, marine cumulus, and stratocumulus. Based on radioactive‐decaying tracers emitted at different altitudes (surface, top of well‐mixed layer, and cloud top), an object‐oriented methodology allows individual characterization of coherent tridimensional plumes within the flow. Each boundary layer shows updraft structures surrounded by subsiding shells that have similar thermodynamical characteristics. Well‐mixed downdrafts are located relatively close to updrafts and entrain dry, warm air from the free troposphere. While updrafts primarily carry the majority of heat and moisture within well‐mixed layers, accounting for 62‐70% of the total resolved flux, it is noteworthy that well‐mixed downdrafts also contibute a significant portion, ranging from 14% to 35%. Identified in all boundary layers, these subsiding structures are triggered by air mass convergence linked to updrafts' divergence and are thus part of an overturning circulation in well‐mixed layers. Close to the surface, downdrafts' divergence constrain updrafts' locations and thus shape a mesoscale cellular organization with cell sizes scaling with the boundary‐layer height (aspect ratio of around 2). Active cumulus formation does not strongly perturb the spatial organization of the sub‐cloud well‐mixed layer. The stratocumulus‐topped boundary layer also shares similarities with the overturning circulation despite having condensation and cloud‐radiation diabatic effects within the mixed layer. However, the visible mesoscale organization of stratocumulus shows larger cells than the boundary‐layer depth (aspect ratio >$$ > $$10) that suggest deviations from the clear‐sky conceptual view. The boundary‐layer decoupling influences mass fluxes of coherent structures and thus potentially plays a role in shaping the spatial organization. Since well‐mixed downdrafts contribute to a significant part of resolved flux of heat and moisture, our results suggest that downdraft properties in well‐mixed layers should be represented at the subgrid scale in climate models through non‐local mass‐flux parametrizations. [ABSTRACT FROM AUTHOR]

Using curvature and torsion to describe Lagrangian trajectories gives a full description of these as well as an insight into small and large time scales as temporal derivatives up to order 3 are involved. One might expect that the statistics of these observables depend on the geometry of the flow. Therefore, we calculated curvature and torsion probability density functions (PDFs) of experimental Lagrangian trajectories processed using the Shake-the-Box algorithm of turbulent von Kármán flow, Rayleigh–Bénard convection and a zero-pressure-gradient turbulent boundary layer over a flat plate. The results for the von Kármán flow compare well with experimental results for the curvature PDF and results obtained by numerical simulations of homogeneous and isotropic turbulence for the torsion PDF. Results for Rayleigh–Bénard convection agree with those measured for von Kármán flow, while results for the logarithmic layer within the boundary layer differ slightly. We provide a potential explanation for the latter. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry or tracer particle trajectories, we introduce the curvature vector. We connect its statistics with those of velocity fluctuations and demonstrate that strong large-scale motion in a given spatial direction results in meandering rather than helical trajectories. [ABSTRACT FROM AUTHOR]

We explore the mechanisms of heat transfer in a turbulent constant heat flux-driven Rayleigh–Bénard convection flow, which exhibits a hierarchy of flow structures from granules to supergranules. Our computational framework makes use of time-dependent flow networks. These are based on trajectories of Lagrangian tracer particles that are advected in the flow. We identify coherent sets in the Lagrangian frame of reference as those sets of trajectories that stay closely together for an extended time span under the action of the turbulent flow. Depending on the choice of the measure of coherence, sets with different characteristics are detected. First, the application of a recently proposed evolutionary spectral clustering scheme allows us to extract granular coherent features that are shown to contribute significantly less to the global heat transfer than their spatial complements. Moreover, splits and mergers of these (leaking) coherent sets leave spectral footprints. Second, trajectories which exhibit a small node degree in the corresponding network represent objectively highly coherent flow structures and can be related to supergranules as the other stage of the present flow hierarchy. We demonstrate that the supergranular flow structures play a key role in the vertical heat transport and that they exhibit a greater spatial extension than the granular structures obtained from spectral clustering. [Display omitted] • Evolving networks are built from Lagrangian trajectories in flux-driven convection. • Evolutionary spectral clustering extracts smaller coherent sets related to granules. • The local node degree detects large-scale coherent sets related to supergranules. [ABSTRACT FROM AUTHOR]

Collisional growth of cloud droplets is an essential yet uncertain process for drizzle and precipitation formation. To improve the quantitative understanding of this key component of cloud‐aerosol‐turbulence interactions, observational studies of collision‐coalescence in a controlled laboratory environment are needed. In an existing convection‐cloud chamber (the Pi Chamber), collisional growth is limited by low liquid water content and short droplet residence times. In this work, we use numerical simulations to explore various configurations of a convection‐cloud chamber that may intensify collision‐coalescence. We employ a large‐eddy simulation (LES) model with a size‐resolved (bin) cloud microphysics scheme to explore how cloud properties and the intensity of collision‐coalescence are affected by the chamber size and aspect ratio, surface roughness, side‐wall wetness, side‐wall temperature arrangement, and aerosol injection rate. Simulations without condensation and evaporation within the domain are first performed to explore the turbulence dynamics and wall fluxes. The LES wall fluxes are used to modify the Scalar Flux‐budget Model, which is then applied to demonstrate the need for non‐uniform side‐wall temperature (two side walls as warm as the bottom and the two others as cold as the top) to maintain high supersaturation in a tall chamber. The results of LES with full cloud microphysics reveal that collision‐coalescence is greatly enhanced by employing a taller chamber with saturated side walls, non‐uniform side‐wall temperature, and rough surfaces. For the conditions explored, although lowering the aerosol injection rate broadens the droplet size distribution, favoring collision‐coalescence, the reduced droplet number concentration decreases the frequency of collisions. Plain Language Summary: A convection‐cloud chamber is useful in understanding how turbulence affects the interaction between aerosols and cloud droplets. The current convection‐cloud chamber (the Pi Chamber) is likely too small to explore how turbulence affects the collision‐coalescence among cloud droplets. To see whether collisional growth may be observable in a larger cloud chamber, we use numerical simulations to model the cloud droplet size distributions under several different configurations of the cloud chamber. The results suggest that the likelihood of detectable collisional growth increases significantly in a tall chamber with two warm and two cold saturated side walls and rough wall surfaces. Key Points: Collision‐coalescence effects on a steady‐state droplet size distribution are stronger in a taller chamberWet side walls are essential for maintaining cloud liquid water in a chamber with a low width‐to‐height aspect ratioRougher surfaces increase surface heat and moisture fluxes, leading to larger liquid water content that promotes collision‐coalescence [ABSTRACT FROM AUTHOR]

This study investigates the modulation by inertial nonisothermal particles in two-dimensional Rayleigh–Bénard (RB) convection with non-Oberbeck–Boussinesq effects due to a large temperature difference. Direct numerical simulations combined with a Lagrangian point-particle method are performed for 1 × 10 6 ≤ R a ≤ 1 × 10 8 and 6.1 × 10 − 3 ≤ S t f ≤ 1.2 , where the Rayleigh number Ra and Stokes number Stf measure the vigor of convection and particle response time, respectively. The typical aspect ratio Γ = 1 is of primary concern. We find that a horizontally arranged double-roll flow pattern prevails at intermediate Stokes numbers with optimal heat transfer efficiency, which has never been reported before. Compared to the single-phase cases, the heat transfer efficiency is enhanced by a factor of two or three. For micro Stokes numbers, unlike cases in the Oberbeck–Boussinesq limit where the addition of particles causes a small amount of flow structure changes, in this study, it is observed that a tiny volume load of particles could actually induce significant flow oscillations or trigger fluid instability for R a = 10 6 ; conversely, for medium Rayleigh numbers (R a = 10 7 ), it is found that flow reversal is slightly suppressed by small particles. For intermediate Stokes numbers, where particle–fluid couplings are strongest and a wealth of new phenomena emerge, special attention is paid. Considering different aspect ratios, after the addition of particles, it is found that closed RB systems tend to contain an even number of convection rolls rather than odd ones. Quantitatively, heat transfer also improves significantly for various aspect ratios for intermediate Stokes numbers. Subsequent investigations reveal that the narrowing of the horizontal size of convection rolls cannot fully explain the significant enhancement; instead, it should also be attributed to strong couplings between particles and fluid dynamics. Moreover, it is found that both momentum and thermal couplings play crucial roles in enhancing heat transfer efficiency. [ABSTRACT FROM AUTHOR]

We studied the evolution of flow structures and large-scale circulations (LSC) in Rayleigh–Bénard convection (RBC) using liquid carbon dioxide as the working medium. In this experiment, a transparent sapphire pressure vessel with observable internal flow was designed, and different temperature differences were applied between the upper and the lower surfaces of the fluid to obtain different Rayleigh numbers (Ra). We employed proper orthogonal decomposition and reconstruction to extract internal flow structures from the shadowgraphy images. We used optical flow techniques to acquire the velocity field of the flow, and we reconstructed the temperature field inside the supercritical fluid using the relationship between shadowgraphy images and refractive index. It is clearly observed that the RBC begins to produce different flow structures under a small temperature difference of 0.4 °C. As the number of Ra increases, the number and the speed of plumes increase, and the morphology of plumes gradually becomes elongated. When Ra exceeds a certain critical value, an LSC structure appears in the flow field, and the plumes translate laterally with the large-scale circulation, and the disorder of the vortex structure in the central flow region increases significantly. Three typical flow structures were observed: (1) single plume, (2) thermal boundary layer traveling waves, and (3) Rayleigh–Taylor instability waves. We believe that the traveling wave structure is the precursor to the single plume. The temperature field analysis of the three structures was carried out, and the velocity of the typical plume was calculated by the optical flow method. It was found that LSC transitioned from oval to square shape with the increase in Ra, and the internal plume Reynolds number slowly increased with the increase in Ra. By the in-depth study of the thermal turbulence characteristics and the coherent structure evolution law of RBC, this paper provides experimental support for revealing the mechanism of enhanced heat transfer in energy system with a liquid CO2 working fluid. [ABSTRACT FROM AUTHOR]

We present global and local statistical properties of turbulent Rayleigh–Bénard (RB) convection at low Prandtl numbers in this work. A series of high resolution two-dimensional (2D) direct numerical simulations are carried out in a square box for the Prandtl number ranges 0.005 ≤ P r ≤ 0.07 and 0.01 ≤ P r ≤ 0.15 at Rayleigh numbers R a = 10 7 and R a = 10 8 , respectively. The global heat and momentum transport expressed as Nusselt number Nu and Reynolds number Re are found to scale as N u ∼ P r 0.14 and R e ∼ P r − 0.82 for R a = 10 7 , and N u ∼ P r 0.11 R e ∼ P r − 0.93 for R a = 10 8 . The local velocity fluctuation at the cell center shows larger amplitudes at lowered Pr, indicating a stronger turbulence in the bulk. The magnitudes of kinetic and thermal energy dissipation rates in the bulk also increase with the decreasing of Pr, due to the intensified velocity gradient and larger thermal diffusivity, respectively. In the cell central region, probability density functions (PDFs) of velocity show a bimodal distribution, and it approaches the Gaussian distribution at higher Pr, while the PDFs of temperature display a stretched exponential shape with intermittent behavior. The kinetic energy spectra further reveal that the velocity cascade follows the Bolgiano–Obukhov scaling in the bulk of the convective flow. [ABSTRACT FROM AUTHOR]

The linear instability and the nonlinear stability analyses have been performed to examine the combined impact of a uniform vertical throughflow and a depth-dependent viscosity on bidispersive porous convection using the Darcy theory with a single temperature field. The validity of the principle of exchange of stability is proved. The eigenvalue problems resulting from both linear instability and nonlinear stability analyses with variable coefficients are numerically solved using the Chebyshev pseudo-spectral method. The equivalence of linear instability and nonlinear stability boundaries is established in the absence of throughflow, while in its presence, the subcritical instability is shown to be evident. The stability of the system is independent of the direction of throughflow in the case of constant viscosity, whereas upflow is found to be more stabilizing than downflow when the viscosity is varying with depth. While the viscosity parameter offers a destabilizing influence on the onset of convection in the absence of throughflow, it imparts both stabilizing and destabilizing effects on the same in its presence. The influence of the ratio of permeabilities and the interphase momentum transfer parameter is to make the system more stable. The findings of a mono-disperse porous medium are presented as a specific case within the broader context of this investigation. [ABSTRACT FROM AUTHOR]

In this article, we report on numerical simulations of laminar Rayleigh–Bénard convection of air in cuboids. We provide numerical evidence of the existence of multiple steady states when the aspect ratio of the cuboid is sufficiently large. In our simulations, the Rayleigh number is fixed at R a = 1.7 × 10 4 . The gas in the cube is initially at rest but subject to random small-amplitude velocity perturbations and an adverse temperature gradient. When the flow domain is a cube, i.e., the aspect ratio is equal to unity, there is only one steady state. This state is characterized by the development of a single convective roll and by a symmetric normalized temperature profile with respect to the mid-height. On the contrary, when the aspect ratio is equal to 2, there are five different steady states. Only one of them exhibits a symmetric temperature profile and flow structure. The other four steady states are characterized by two-roll configurations and asymmetric temperature profiles. [ABSTRACT FROM AUTHOR]

The onset of oscillatory Benard-Marangoni convection in a horizontal fluid layer with internal heat generation and a deformable free surface is studied using an analytical technique employing the classical linear stability theory. We consider the case when both the Rayleigh number and Marangoni number are linearly dependent. We obtained the analytical result for the expansion of the Rayleigh number in the limit of a very short wave. We found that the internal heat generation factor influences the leading order of Rayleigh number.

Both spatially-averaged kinetic energy K and influx-averaged Nusselt number Nuinflux are numerically investigated concerning the three-dimensional thermal convection in a cubic cavity heated from a bottom wall and chilled from its opposite top wall. Nuinflux represents the total influx of heat normalised by an area. Assuming incompressible fluid with a Prandtl number of 7.1 (water) in a Rayleigh-number range of 1.0×104– 1.0×105, the authors solve the three-dimensional Navier-Stokes equations with the Boussinesq approximation, using the finite difference method. As a result, in the Rayleigh-number range, hysteresis effects appear accompanying various steady flow structures. Hence, there can exist multiple values of K and multiple values of Nuinflux for the same Ra due to the different steady flow structures. As Rayleigh number gradually increases or decreases, there exist four stable branches. On the branches, the authors reveal the relation between K and flow structure and the relation between Nuinflux and flow structure. Besides, a steady flow structure becomes oscillatory on one branch, as Rayleigh number gradually increases.

Rotational effects are investigated in Newtonian ferromagnetic liquids with linear stability modified by temperature and magnetic field. When thermorheological and magnetorheological effects are taken into account, the fluid's rheological behaviour becomes more complex. Thermorheological effects deal with viscosity changes in relation to temperature, whereas magnetorheological effects deal with viscosity changes in reaction to an applied magnetic field. Understanding the interplay between these effects and thermal convection sheds light on how connected these processes are. In idealized boundary conditions, the convective thresholds are expressed explicitly using the Galerkin technique. In the case of free-free and rigid upper-free boundaries, the exchange of stability principle is demonstrated, and corresponding results are presented. The oscillatory convection is not a preferable mode of instability for ferromagnetic liquids with Prandtl numbers more than one. In addition, rotational and ferromagnetic parameters are discussed in relation to system instability. Results reveals that an increase in Taylor number has a stabilizing effect on the system. Increasing magnetic buoyancy number, results in destabilizing effects on the system. Ferroconvection is not affected due to the nonlinearity of non-magnetic parameter. The results obtained agree truly with those of limiting cases.

Abstract Collisional growth of cloud droplets is an essential yet uncertain process for drizzle and precipitation formation. To improve the quantitative understanding of this key component of cloud‐aerosol‐turbulence interactions, observational studies of collision‐coalescence in a controlled laboratory environment are needed. In an existing convection‐cloud chamber (the Pi Chamber), collisional growth is limited by low liquid water content and short droplet residence times. In this work, we use numerical simulations to explore various configurations of a convection‐cloud chamber that may intensify collision‐coalescence. We employ a large‐eddy simulation (LES) model with a size‐resolved (bin) cloud microphysics scheme to explore how cloud properties and the intensity of collision‐coalescence are affected by the chamber size and aspect ratio, surface roughness, side‐wall wetness, side‐wall temperature arrangement, and aerosol injection rate. Simulations without condensation and evaporation within the domain are first performed to explore the turbulence dynamics and wall fluxes. The LES wall fluxes are used to modify the Scalar Flux‐budget Model, which is then applied to demonstrate the need for non‐uniform side‐wall temperature (two side walls as warm as the bottom and the two others as cold as the top) to maintain high supersaturation in a tall chamber. The results of LES with full cloud microphysics reveal that collision‐coalescence is greatly enhanced by employing a taller chamber with saturated side walls, non‐uniform side‐wall temperature, and rough surfaces. For the conditions explored, although lowering the aerosol injection rate broadens the droplet size distribution, favoring collision‐coalescence, the reduced droplet number concentration decreases the frequency of collisions.

Two-dimensional horizontally periodic Rayleigh-Bénard convection between stress-free boundaries displays two distinct types of states, depending on the initial conditions. Roll states are composed of pairs of counter-rotating convection rolls. Windy states are dominated by strong horizontal wind (also called zonal flow) that is vertically sheared, precludes convection rolls and suppresses heat transport. Windy states occur only when the Rayleigh number Ra is sufficiently above the onset of convection. At intermediate Ra values, windy states can be induced by suitable initial conditions, but they undergo a transition to roll states after finite lifetimes. At larger Ra values, where windy states have been observed for the full duration of simulations, it is unknown whether they represent chaotic attractors or only metastable states that would eventually undergo a transition to roll states. We study this question using direct numerical simulations of a fluid with a Prandtl number of 10 in a layer whose horizontal period is eight times its height. At each of seven Ra values between 9 x 106 and 2.25 x 106 we have carried out 200 or more simulations, all from initial conditions leading to windy convection with finite lifetimes. The lifetime statistics at each Ra indicate a memoryless process with survival probability decreasing exponentially in time. The mean lifetimes grow with Ra approximately as Ra4. This analysis provides no Ra value at which windy convection becomes stable; it might remain metastable at larger Ra with extremely long lifetimes. [ABSTRACT FROM AUTHOR]

The measurement of the transport of scalar quantities within flows is oftentimes laborious, difficult or even unfeasible. On the other hand, velocity measurement techniques are very advanced and give high-resolution, high-fidelity experimental data. Hence, we explore the capabilities of a deep learning model to predict the scalar quantity, in our case temperature, from measured velocity data. Our method is purely data-driven and based on the u-net architecture and, therefore, well-suited for planar experimental data. We demonstrate the applicability of the u-net on experimental temperature and velocity data, measured in large aspect ratio Rayleigh–Bénard convection at Pr = 7.1 and Ra = 2 × 10 5 , 4 × 10 5 , 7 × 10 5 . We conduct a hyper-parameter optimization and ablation study to ensure appropriate training convergence and test different architectural variations for the u-net. We test two application scenarios that are of interest to experimentalists. One, in which the u-net is trained with data of the same experimental run and one in which the u-net is trained on data of different Ra . Our analysis shows that the u-net can predict temperature fields similar to the measurement data and preserves typical spatial structure sizes. Moreover, the analysis of the heat transfer associated with the temperature showed good agreement when the u-net is trained with data of the same experimental run. The relative difference between measured and reconstructed local heat transfer of the system characterized by the Nusselt number Nu is between 0.3 and 14.1% depending on Ra . We conclude that deep learning has the potential to supplement measurements and can partially alleviate the expense of additional measurement of the scalar quantity. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the convection instability in phase-change Rayleigh–Bénard convection systems at a finite Stefan number, where a pure solid substance confined between two horizontal walls is isothermally heated from below in order to induce melting, assuming no heat conduction in the solid phase. By establishing a connection between the heat transfer behaviors in the conduction and convection melting regimes through the jump events in the temporal evolution of the heat flux and the melted liquid fraction, two criteria (the critical average fluid temperature θ ¯ f c and the critical melted liquid fraction f l c ) are derived to characterize the convection onset. In contrast to the conventional instability analysis, the derivation in the present work is much more convenient and removes the limitation of a vanishing Stefan number (Ste → 0). The two obtained criteria are successfully validated by the data available in the literature, together with the numerical simulations conducted in this paper. The validations revealed that the proposed θ ¯ f c and f l c work well at a finite Ste and that f l c is slightly less accurate than θ ¯ f c , due to the error inherited from the employed scaling law describing the convective heat flux. With the relation between the effective and global parameters, f l c is further converted into the commonly used critical effective Rayleigh number by R a ec = R a f l c 3 , which is found depending on Ste only, being the same as the criterion of θ ¯ f c , while its precision is less satisfying due to amplified error from the cubic power operation of f l c 3 . [ABSTRACT FROM AUTHOR]

The problem of ferroconvection in a viscoelastic fluid layer is studied with the aim to investigate oscillatory motions. In this article, a stability analysis for both linear and nonlinear systems is carried out. In the linear stability analysis, the expressions for steady and oscillatory Rayleigh numbers are obtained and the effects of magnetic as well as viscoelastic parameters on the onset of viscoelastic ferromagnetic convection are investigated numerically. From the analysis, we found that the magnetic number (M1), the stress relaxation time (λ1) and the nonlinearity of magnetization (M3) have destabilizing influences on the onset of ferroconvection, whereas the strain retardation time (λ2) has stabilizing influence. In the weakly nonlinear stability analysis, the formula for heat transfer rate in terms of the Nusselt number is derived for oscillatory convection. From the analyses, we found that for increasing values of the magnetic number, stress relaxation time and nonlinearity of magnetization, the heat transfer rate rises, whereas it decreases for larger values of the strain retardation time. Moreover, the pitchfork bifurcation analysis yields that in order to reach the stable positions, the value of amplitude increases as the stress relaxation time increases, whereas a reverse trend is observed for the strain retardation time. [ABSTRACT FROM AUTHOR]

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh–Bénard convection in a reduced Rayleigh number range $1.3\le Ra/Ra_{c}\le 83.1$. Under slow rotations ($Ra\approx 80\,Ra_{c}$), the vortices are distributed randomly, which is manifested by the size distribution of the Voronoi cells of the vortex centres being a standard $\varGamma$ distribution. The vortices exhibit Brownian-type horizontal motion in the parameter range $Ra\gtrsim 10\,Ra_{c}$. The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ($4\,Ra_{c}\le Ra\lesssim 10\,Ra_{c}$), the centrifugal force leads to radial vortex motions, i.e. warm cyclones (cold anticyclones) moving towards (outwards from) the rotation axis. The horizontal scale of the vortices decreases with decreasing $Ra/Ra_c$ , and the size distribution of their Voronoi cells deviates from the $\varGamma$ distribution. In the rapidly rotating regime ($1.6\,Ra_{c}\le Ra\le 4\,Ra_{c}$), the vortices are densely distributed. The hydrodynamic interaction of neighbouring vortices results in the formation of vortex clusters. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the outward motion of the strong anticyclones, and the radial velocity of the anticyclones is enhanced. The radial mobility of isolated vortices, scaled by their vorticity strength, is shown to be a simple power function of the Froude number. For all flow regimes studied, we show that the number of vortices with a lifespan greater than $t$ decreases exponentially as $\exp ({-t/{\tau }})$ for large time, where $\tau$ represents the characteristic lifetime of long-lived vortices. [ABSTRACT FROM AUTHOR]

In this paper we report on an experimental study focusing on the manifestation and dynamics of the large-scale circulation (LSC) in turbulent liquid metal convection. The experiments are performed inside a cylinder of aspect ratio $\varGamma = 0.5$ filled with the ternary alloy GaInSn, which has a Prandtl number of $Pr = 0.03$. The large-scale flow structures are classified and characterized at Rayleigh numbers of ${Ra} = 9.33 \times 10^6, 5.31 \times 10^7$ and $6.02 \times 10^8$ by means of the contactless inductive flow tomography which enables the full reconstruction of the three-dimensional (3-D) flow structures in the entire convection cell. This is complemented with the multi-thermal-probe method for capturing the azimuthal temperature variation induced by the LSC at the sidewall. We use proper orthogonal decomposition (POD) to identify the dominating modes of the turbulent convection. The analysis reveals that a single-roll structure of the LSC alternates in short succession with double-roll structures or a three-roll structure. This is accompanied by dramatic fluctuations of the Reynolds number, whose instantaneous values can deviate by more than 50 % from the time-average value. No coherent oscillations are observed, whereas a correlation analysis indicates a residual contribution of the torsion and sloshing modes. Results of the POD analysis suggest a stabilization of the single-roll LSC with increasing $Ra$ at the expense of flow structures with multiple rolls. Moreover, the relative lifetime of all identified flow states, measured in units of free-fall times, increases with rising $Ra$. [ABSTRACT FROM AUTHOR]

In this study, we performed a set of experiments of the thermal plume on an open cylinder heated from below and a simple scaling analysis. The flow structure of the plume was visualized using the shadowgraph technique, and the temperature at specific points was measured using a thermistor. Transient plumes in a developing stage, an equilibrating stage and a fully developed stage were described. The new scaling laws of the stem radius and the velocity of the rising plume were presented, which are different from those on a two-dimensional heated plate due to the cylindrical effect and agree with experimental results. In the fully developed stage, there is a transition route of the plume from a steady to chaotic state with an increase in the Rayleigh number, which involves a series of bifurcations. A reverse bifurcation from a periodic (Ra  = 1.17 × 106) back to a steady (Ra  = 1.30 × 106) state has been observed in the experiment, which is referred to as the period bubbling bifurcation. Thus, the present experimental results validate the previous numerical results presented by Zhang et al. (Phys. Fluids , vol. 33 (6), 2021, 064110). The bifurcation diagram, spectral analysis and attractor are used to characterize the transitional plume. In addition, the heat and mass transfer have also been quantified. [ABSTRACT FROM AUTHOR]

Naturally flows have been the scope of the scientific research for centuries, Rayleigh-Benard convection being one of the leading. Many researchers have considered the flow patterns, boundary conditions, various cavities, nanofluids, theoretically, numerically, and experimentally. The flow was investigated in atmosphere and in nanofluids, in air, water, molten metals, non-Newtonian fluids. Almost all research focuses on 2-D or 3-D analysis of flow in laterally unlimited enclosures, as parallel plates or coaxial cylinders. In technical practice, only limited enclosures exist. This paper presents numerical and real experimental results for the test chamber with ratio 4×2×1 in x-, y-, and zdirection, respectfully. The measurements were taken at fifteen different positions on the faces of the tank. Probes used are PT100 elements. As the chamber is limited in all directions, the results have shown strong influence of the lateral walls. The results are compared with the those obtained by IR camera. Various fluids were tested, and results for motor oil will be presented. [ABSTRACT FROM AUTHOR]

The pseudopotential models are very convenient, flexible and robust for practical purposes of two-phase dynamics, but the presence of spurious velocities is inevitable due to the limited discretization of gradient terms, and large amount of intermolecular forces at the interface of liquid and gas phases. The existence of such velocities, in addition to creating counterfeit flows, causes errors in obtaining the temperature field and solving the energy equation. Here, two models (Li (Phys Rev 89(5):053022, 2014) and Kupershtokh (Phys Rev E 98(2):023308, 2018)) are examined to show their capability in weakening and reducing the temperature parasites arising from the spurious velocities. Results are presented for a stationary droplet, which show the good performance of the exact difference method in reducing the parasitic temperatures. Also, the Marangoni phenomenon is simulated to validate the solution of the temperature field in the two-phase flow, which expresses the movement of droplet caused by the surface tension gradient. For more complicated problem, the Rayleigh–Bénard convection is simulated and effects of density ratio, Rayleigh number, and contact angle on the average wall Nusselt number and the average temperature of the droplet and vapor phases are investigated. The results of this work show the capability of the improved passive scalar method in simulating the two-phase heat transfer problems. [ABSTRACT FROM AUTHOR]

We discuss the effects of nonhomogeneous magnetic fields in liquid metal flows in two different configurations. In the first configuration, we briefly report the impact of fringing magnetic fields in a turbulent Rayleigh–Bénard convection setup, where it was shown that the global heat transport decreases with an increase of fringe‐width. The convective motion in regions of strong magnetic fields is confined near the sidewalls. In the second configuration, we numerically study the effects of an oscillating magnetic obstacle with different frequencies of oscillation on liquid metal flow in a duct. The Reynolds number is low such that the wake of the stationary magnetic obstacle is steady. The transverse oscillation of the magnet creates a sinusoidal time‐dependent wake reminiscent of the vortex shedding behind solid obstacles. We examine the behavior of the streamwise and spanwise components of the Lorentz forces as well as the work done by the magnets on the fluid. The frequency of the oscillation of the streamwise component of Lorentz force is twice that of the spanwise component as in the case of lift and drag on solid cylindrical obstacles. The total drag force and the energy transferred from the magnets to the fluid show a nonmonotonic dependence on the frequency of oscillation of the magnetic obstacle indicative of a resonant excitation of the sinusoidal vortex shedding. [ABSTRACT FROM AUTHOR]

Despite the widespread popularity of the Bhatnagar–Gross–Krook lattice Boltzmann (BGK-LB) model due to its simplicity and efficiency, its application in heat transfer involving non-Newtonian fluids (NNFs) has been limited by inherent constraints. This paper proposes a numerically stable BGK-LB model for the thermal flow of NNFs. The modified model incorporates the local shear rate into the equilibrium distribution function of the velocity field and addresses the numerical instability problems encountered in the traditional BGK-LB model under low viscosity conditions by introducing an additional parameter. In addition, a temperature evolution equation that can accurately recover the convective diffusion equation is adopted. The accuracy of the current method is validated by performing simulations of Rayleigh–Bénard convection (RBC) in a square cavity filled with Newtonian fluids and NNFs. Subsequently, simulations are conducted to investigate the behavior of RBC in power-law fluids. The analysis focuses on examining the impact of the Rayleigh number (Ra = 5 × 10³ − 105 ) and the power-law index (n = 0.8–1.3) on the convective structure and heat transfer characteristics while maintaining a fixed Prandtl number (Pr = 7) and aspect ratio (L/H = 2). It is discovered that, for a given n value, the convection intensity and heat transfer rate increase with increasing Ra, which is supported by the increasing trend of the mean Nusselt number (Nu) with Ra. Furthermore, compared to NFs, pseudo-plastic fluids display a higher Nu value due to an augmented heat transfer rate, while dilatant fluids exhibit a lower Nu value owing to a diminished heat transfer rate. [ABSTRACT FROM AUTHOR]

Using direct numerical simulations, we investigate the effect of surface roughness on the statistics of fluctuations in a 2D rectangular cell of aspect ratio Γ = 2 with air as the working fluid. We consider roughly two decades of Rayleigh number, 10 8 ≤ Ra ≤ 4.64 × 10 9 , with three roughness configurations of R1, R2, and R3 characterized by their maximum heights of 5%, 10%, and 20% of the cell height, respectively. We show that roughened cells trigger stronger fluctuations, which further gets augmented with increasing Ra. Vertical variations of velocity and temperature fluctuations show different trends. While the temperature fluctuation becomes homogeneous in the bulk, it exhibits strong inhomogeneous vertical velocity fluctuations. The comparison of global heat flux with smooth case shows a significant increment beyond R a = 2.15 × 10 8 . Surface roughness impacts local heat flux through augmented plumes, which is qualitatively ascertained by instantaneous temperature field. Furthermore, probability distribution functions reveal no particular trend for the taller roughness configurations, though the magnitude is amplified. Through identification of plumes and background regions, we show their behavior as a function of Ra for different rough cases. Finally, we decompose the shear production into its three components (based on the nature of mechanical forces) to understand the energy interaction between the mean flow and fluctuating flow field. [ABSTRACT FROM AUTHOR]