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Central supermassive black holes are found in most massive galaxies. However, their origin is still poorly understood. Observations of quasars show that many supermassive black holes existed less than 700 million years after the Big Bang. To explain the existence of such black holes with masses comparable to the stellar mass of the host galaxy, just 500 million years after the Big Bang, it is probably necessary to assume that they originated from heavy seeds. In an ekpyrotic universe, a hot Big Bang occurs as a result of the collision of two branes. Quantum fluctuations create ripples on the brane surfaces, leading to spatial variations in the timing of collisions, thereby creating density perturbations that can facilitate the formation of massive black hole seeds. I hypothesize that perhaps Rayleigh–Bénard–Marangoni-type convection in the extra dimension is a more efficient source of macroscopic density perturbations than quantum fluctuations. [ABSTRACT FROM AUTHOR]

Radiative natural convection is of vital importance in the process of energy storage, power generation, and thermal storage technology. As the attenuation coefficients of many heat transfer media in these fields are high enough to be considered as optically thick media, like nanofluids or molten salts in concentrated solar power or phase change thermal storage, Rosseland approximation is commonly used. In this paper, we delve into the impact of thermal radiation on the Rayleigh-Bénard (RB) convection. Theoretical analysis has been conducted by modifying the Grossmann-Lohse (GL) model. Based on turbulent dissipation theory, the corresponding scaling laws in four main regimes are proposed. Direct numerical simulation (DNS) was also performed, revealing that radiation exerts a notable influence on both flow and heat transfer, particularly on the formation of large-scale circulation. By comparing with DNS results, it is found that due to the presence of radiation, the modified Nu scaling law in small Pr range of the GL model is more suitable for predicting the transport characteristics of optical thick media with large Pr. The maximum deviation between the results of DNS and prediction model is about 10%, suggesting the summarized scaling law can effectively predict the Nu of radiative RB convection. [ABSTRACT FROM AUTHOR]

The joint effect of rectangular-type roughness and horizontal vibration on two-dimensional (2D) turbulent Rayleigh–Bénard convection (RBC) is investigated by using the thermal lattice Boltzmann method (LBM) in this article. The present work focuses on the Nusselt number and plume dynamics of the convection in the range of dimensionless vibration frequency 0 ≤ ω* ≤ 1000 and the range of dimensionless roughness height 0 ≤ h* ≤ 0.05. The Rayleigh number is 108 and Prandtl number is 4.38. Our numerical results indicate that the relationship between the Nusselt number and roughness height is mostly proportional, and the relationship between the Nusselt number and the vibration frequency is exponential. It is further found that heat transfer enhances by 3.06 times under the joint effect of horizontal vibration and rectangular roughness on turbulent RBC. It provides significant physical insight into the mechanism of cooperative heat transfer enhancement. [ABSTRACT FROM AUTHOR]

This study emphasizes the two-dimensional incompressible flow of Williamson nanofluid caused by an inclined, infinite, expanding/contracting cylinder that is inclined at an angle with the horizontal axis. The focus is on the behavior of non-Newtonian fluid on the flow, heat, and mass transfer during the process. The properties of the fluid are modeled using a set of partial differential equations in association with the characterizing parameters obtained during the presentation of non-dimensional form. The problem is solved numerically using the shooting-based Runge–Kutta fourth-order technique. The results are shown graphically for the behavior of the several contributing parameters. The effect of various pertaining parameters is analyzed henceforth. The physical quantities of interest are also discussed in the tables. The study provides useful insight into the behavior of the fluid, i.e. suction/injection shows opposite behavior on the fluid velocity profiles where suction decelerates the profile and injection enhances it significantly. [ABSTRACT FROM AUTHOR]

The effect of an internal heat source linearly dependent on the solid fraction on the onset of convection in a composite air‐porous channel with vertical throughflow has been analyzed. We considered boundaries to be insulating to temperature perturbations. The governing equation that satisfies the air‐porous configuration is analyzed by the normal mode approach, solved by the regular perturbation technique for linear stability, and the critical internal Darcy–Rayleigh number for the onset of stationary convection has been derived. The paper aims to analyze the effects of parameters like heat source size, depth ratio, Darcy number, throughflow direction, solid fraction, and Prandtl number on stationary convection in a composite air‐porous configuration. Understanding these influences can illuminate thermal behaviors in intricate systems and inform applications in heat transfer and fluid dynamics. The observed stability configuration decreases monotonically due to increasing the effect of the depth ratio and solid fraction at any direction and velocity of the throughflow. The thermal and vertical velocity profiles and the results obtained during the analysis have been presented graphically. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a practical strategy to accelerate Newton's method in the vicinity of singular points. We present an adaptive safeguarding scheme with a tunable parameter, which we call adaptive γ-safeguarding, that one can use in tandem with Anderson acceleration to improve the performance of Newton's method when solving problems at or near singular points. The key features of adaptive γ-safeguarding are that it converges locally for singular problems, and it can detect nonsingular problems automatically, in which case the Newton-Anderson iterates are scaled towards a standard Newton step. The result is a flexible algorithm that performs well for singular and nonsingular problems, and can recover convergence from both standard Newton and Newton-Anderson with the right parameter choice. This leads to faster local convergence compared to both Newton's method, and Newton-Anderson without safeguarding, with effectively no additional computational cost. We demonstrate three strategies one can use when implementing Newton-Anderson and γ-safeguarded Newton-Anderson to solve parameterdependent problems near singular points. For our benchmark problems, we take two parameter-dependent incompressible flow systems: flow in a channel and Rayleigh-Bénard convection. [ABSTRACT FROM AUTHOR]

We present a hydrodynamic model for nonisothermal, incompressible binary fluids that incorporates buoyancy effects using the Boussinesq approximation. This model adheres to the generalized Onsager principle, ensuring both volume preservation for each fluid phase and a positive entropy production rate under thermodynamically consistent boundary conditions, maintaining overall thermodynamic consistency. We then develop a set of second-order numerical algorithms that preserve both volume and entropy production rates to solve the model in finite domains, subject to physically appropriate boundary conditions. By implementing an efficient adaptive time-stepping strategy, we perform several numerical simulations that validate the accuracy and second-order convergence of the schemes. These simulations successfully capture Rayleigh-Bénard convection in binary fluids and the interfacial dynamics between immiscible fluids under the influence of temperature gradients, buoyancy, and interfacial forces, demonstrating the accuracy and practical utility of the model and the numerical methods. [ABSTRACT FROM AUTHOR]

This study investigates the impact of an inclined magnetic field (MHD) on entropy generation in double diffusive natural convective flow in a wavy enclosure filled with a non-Newtonian Casson fluid. The Galerkin Finite Element Method (GFEM) is employed to numerically solve the standard formulation, utilizing quadratic polynomials for momentum interpolation and a linear interpolating function for model approximation. The discretized system is resolved using Newton's approach and PARDISO's matrix factorization. Through simulations of varying ranges of Rayleigh numbers (1 e 3 ≤ Ra ≤ 1 e 5 ) , Casson parameter (0.1 ≤ β ≤ 10) , Hartmann numbers (0 ≤ Ha ≤ 40) , Lewis numbers (0.1 ≤ Le ≤ 5) , and inclined angle gamma (0 ≤ γ ≤ 60 o ) , the study provides valuable insights into the behavior of double diffusive natural convection in the wavy enclosure. Isotherms, iso-concentration contours, and streamlines are analyzed to assess different input distributions, and the study presents graphical representations and tabular data on heat transfer, mass transfer rate, and entropy production. [ABSTRACT FROM AUTHOR]

In this article, two-dimensional (2-D) Rayleigh–Bénard (RB) convection with isothermal-adiabatic boundary conditions is simulated by using the double distribution function approach of lattice Boltzmann method. The effects of isothermal-adiabatic boundary on the flow and the heat transfer characteristics in the RB system under instability, transition and turbulence are discussed in detail. The effect of the isothermal-adiabatic boundary on the scaling of Nusselt (Nu) number as a function of Rayleigh (Ra) number is analyzed. The 0.3 scaling is observed in the mixed boundary system when the Ra number is in the range of 107–108. The scaling is well consistent with that in the RB system with uniform boundaries. A comparison of the influence on the root mean square of Nu number between uniform isothermal boundary and isothermal-adiabatic boundary demonstrates that in both "transition" region and "turbulence" region, the intensity of the fluctuation of average Nu number at uniform isothermal boundary is higher than that at the isothermal-adiabatic boundary. The comparison of the fluctuation of the average Nu number between "transition" region and "turbulence" region shows that the isothermal-adiabatic boundary has a better suppression effect on the fluctuation of heat transfer in the "transition" region. The supression is related to ratio of the scale of plume and the "heat source core." When the scales are comparable, the fluctuation of average Nu number will be significantly suppressed. Flow field and temperature field further show the plumes are generated at these "heat source cores," which effectively supports the "heat source core" assumption. [ABSTRACT FROM AUTHOR]

We consider the Oberbeck–Boussinesq approximation driven by an inhomogeneous temperature distribution on the boundary of a bounded fluid domain. The relevant boundary conditions are perturbed by a non–local term arising in the incompressible limit of the Navier–Stokes–Fourier system. The long time behaviour of the resulting initial/boundary value problem is investigated. [ABSTRACT FROM AUTHOR]

Liquid crystals, which have both liquid and solid properties, inevitably exhibit fluctuations. Some frustrated liquid-crystalline phases with a hierarchical structure, such as cybotactic nematic, modulated smectic, and bicontinuous cubic phases, are fascinating fluctuation-induced phases. In addition to these equilibrium phases, a pattern formation that is a nonequilibrium order through fluctuation is one of the most attractive research areas in soft matter. In this review, the studies on producing these fluctuation-induced orders in liquid crystals are described. Liquid-crystalline supermolecules in which several mesogens are connected via a flexible spacer have been designed. They have not only a characteristic shape but also an intra-molecular dynamic order. The supermolecules induce the fluctuations in layer structures at a molecular level, producing from the frustrated hierarchical to dynamic dissipative structures. In addition to reviewing molecular design for the hierarchical structures, the pattern propagation in a smectic phase is discussed based on the rotation of smectic blocks through Rayleigh–Bénard convection. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, the statistical properties of the kinetic εu and thermal εθ dissipation rates in two-dimensional (2D) turbulent Rayleigh–Bénard convection (RBC) are studied by using the thermal lattice Boltzmann method (LBM). A series of direct numerical simulations (DNS) are implemented in a square cell with the unit aspect ratio for the Rayleigh number Ra = 108 and Prandtl number Pr = 4.38. The roughness height h* and vary the vibration frequency ω* from 0 to 1000 are fixed in the vibrational RBC with rough plates to explore their effect on the kinetic and thermal dissipation rates. The global features indicate that the εu and εθ are more intense in the regions with high gradients of velocity and temperature, which is in good agreement with the previous work. The scalings of Nu∼ω*0.55±0.1 and Re∼0.59±0.2 are proposed between the ensemble averaged Nusselt number Nu and Reynolds number Re. The probability density functions (PDFs) of both logarithmic kinetic dissipation rate lg εu and thermal dissipation rate lg εθ are not conformed to the log-normal distributions. Through the analysis of the time-averaged εu and εθ vertical profiles, it is further demonstrated that the local dissipation rates from the boundary layer region are still the major contribution in the vibrational RBC with rough plates. [ABSTRACT FROM AUTHOR]

The present work investigates the combined effect of varying gravity and heat flux direction with respect to gravity on the melting dynamics of Phase Change Material. Similar conditions are relevant to applications in space, at different space infrastructures, such as orbiting satellites, as well as various extraterrestrial surface assets, landers, and rovers. The numerical simulations are performed to study the melting dynamics of a paraffin-based phase change material with Prandtl number Pr ≈ 71 and Stefan number Ste ≈ 0.33 inside a differentially heated square enclosure. The mathematical model employs a control volume-based enthalpy porosity approach to simulate the melting process inside enclosure. The direction of the incoming heat flux relative to the gravity vector is defined in terms of an orientation angle, which is varying circularly with a step of 45°, whereas the gravity level is ranging from the terrestrial surface value g to 0.2 g to analyze the melting process over a wide range of Rayleigh number 100 ≤ Ra ≤ 107. The study provides a detailed insight into the attributes of heat transfer, flow dynamics, and energy storage, along with a quantitative analysis of the transition between various melting regimes and temporal fluctuations in the performance parameters. The findings demonstrate that the mutual orientation between the directions of incoming heat flux and gravity, as well as the value of the latter, significantly affect features of the convective motion in the liquid phase, as well as the entire thermally driven heat transfer within the domain. In particular, for the oppositely directed gravity and heat flux, the melted fluid closely resembles Rayleigh-Bénard convection with the presence of multicellular flow structures, while at other orientation angles, except for a co-directed gravity and heat flux case, a circular convective motion of the melted fluid takes place. The results of numerical simulations reveal declining melting rates as the mutual orientation of gravity and heat flux changes from opposite to co-directed and vice versa. The low gravity conditions delay the onset of convection-driven melting, reducing the melting rate significantly. • Effect of heat flux direction and varied gravity on PCM melting dynamics is studied. • Paraffin-based PCM (Pr ≈ 71, Ste ≈ 0.33) filled inside square enclosure is investigated. • Study considers orientation angle range (0 ° to 315 °) and gravity level (0.2g to g). • A detailed analysis of thermal, flow, and energy storage attributes is presented. • Results reveal details useful for designing thermal control for space applications. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive experimental investigation aimed at elucidating the influence of magnetic fields, nanoparticle concentration, and the presence of polymer on Rayleigh–Benard convection in yield stress nanofluids. The test fluid comprises Ultrez 30 polymeric powder and Iron oxide nanoparticles. Herschel–Bulkley's model is applied to capture the rheological behaviour. The concentration of both Ultrez 30 polymeric gel and Iron oxide nanoparticles varies from 0.05 % to 0.10 %. The in-house developed experimental set-up is exposed to the magnetic field in the 0 mT to 100 mT range. Without a magnetic field, heat transfer increases with the elevation of nanoparticle fraction in the fluid. However, in the presence of a magnetic field, the convection effect weakens as the nanoparticle concentration rises. Furthermore, an optimised artificial neural network (ANN) model featuring a single hidden layer with nine hidden neurons is presented to predict the Nusselt number. [ABSTRACT FROM AUTHOR]

The electrothermoconvection in a rotating dielectric fluid layer heated from below (or above) is studied analytically using linear stability theory. First, we derive the necessary conditions for oscillatory motion when the fluid layer is heated from below and from above. Then as a consequence, sufficient conditions for the validity of the exchange principle are derived for the two configurations in terms of the parameters of the systems alone. The results hold for free boundaries for all wave numbers and for rigid boundaries with some restrictions. Further, the results for electrothermoconvection without rotation, rotatory Rayleigh–Bénard convection and Rayleigh–Bénard convection are also obtained as special cases which validate the existing results. To the best of author's knowledge such results are not reported in the literature as far as the domain of electrothermoconvection studies is concerned. [ABSTRACT FROM AUTHOR]

Numerical simulations of turbulent moist Rayleigh–Bénard convection driving CCN activation and droplet growth in the laboratory Pi chamber are discussed. Supersaturation fluctuations come from isobaric mixing of warm and humid air rising from the lower boundary with colder air featuring lower water vapor concentrations descending from the upper boundary. Lagrangian particle–based microphysics is used to represent the growth of haze CCN and cloud droplets with kinetic, solute, and surface tension effects included. Dry CCN spectra in the range between 2- and 200-nm radii from field observations are considered. Increasing the total CCN concentration from pristine to polluted conditions results in an increase in the droplet concentration and reduction in the mean droplet radius and spectral width. These are in agreement with Pi chamber observations and numerical simulations, as well as with numerous past studies of CCN cloud-base activation in natural clouds. The key result is that a relatively small fraction of the available CCN is activated in the Pi chamber fluctuating supersaturations, from about a half in the pristine case to only a 10th in the polluted case. The activation fraction as a function of the dry CCN radius is similar in all simulations, close to zero at the CCN small end, increasing to a maximum at CCN radius around 50 nm, and decreasing to close to zero at the large CCN end. This is explained as too small supersaturations to activate small CCN as in natural clouds and insufficient time to allow large CCN reaching the critical radius. Significance Statement: Impact of turbulence on the formation and growth of cloud droplets is an important cloud physics problem. Laboratory experiments in the Michigan Technological University cloud chamber provide key insights into this problem. Numerical simulations of cloud chamber processes discussed in this paper complement laboratory experiments by providing insights difficult or impossible to obtain in the laboratory. The study contrasts the formation and growth of cloud droplets in the laboratory cloud chamber with processes taking place in natural clouds. The differences documented in this paper pose questions concerning the impact of turbulence on the formation and growth of cloud droplets as a result of interactions of clouds with their environment. [ABSTRACT FROM AUTHOR]

There is growing interest in discovering interpretable, closed‐form equations for subgrid‐scale (SGS) closures/parameterizations of complex processes in Earth systems. Here, we apply a common equation‐discovery technique with expansive libraries to learn closures from filtered direct numerical simulations of 2D turbulence and Rayleigh‐Bénard convection (RBC). Across common filters (e.g., Gaussian, box), we robustly discover closures of the same form for momentum and heat fluxes. These closures depend on nonlinear combinations of gradients of filtered variables, with constants that are independent of the fluid/flow properties and only depend on filter type/size. We show that these closures are the nonlinear gradient model (NGM), which is derivable analytically using Taylor‐series. Indeed, we suggest that with common (physics‐free) equation‐discovery algorithms, for many common systems/physics, discovered closures are consistent with the leading term of the Taylor‐series (except when cutoff filters are used). Like previous studies, we find that large‐eddy simulations with NGM closures are unstable, despite significant similarities between the true and NGM‐predicted fluxes (correlations >0.95). We identify two shortcomings as reasons for these instabilities: in 2D, NGM produces zero kinetic energy transfer between resolved and subgrid scales, lacking both diffusion and backscattering. In RBC, potential energy backscattering is poorly predicted. Moreover, we show that SGS fluxes diagnosed from data, presumed the "truth" for discovery, depend on filtering procedures and are not unique. Accordingly, to learn accurate, stable closures in future work, we propose several ideas around using physics‐informed libraries, loss functions, and metrics. These findings are relevant to closure modeling of any multi‐scale system. Plain Language Summary: Even in state‐of‐the‐art climate models, the effects of many important small‐scale processes cannot be directly simulated due to limited computing power. Thus, these effects are represented using functions called parameterizations. However, many of the current physics‐based parameterizations have major shortcomings, leading to biases and uncertainties in the models' predictions. Recently, there has been substantial interest in learning such parameterizations directly from short but very high‐resolution simulations. Most studies have focused on using deep neural networks, which while leading to successful parameterizations in some cases, are hard to interpret and explain. A few more recent studies have focused on another class of machine‐learning methods that discover equations. This approach has resulted in fully interpretable but unsuccessful parameterizations that produce unphysical results. Here, using widely used test cases, we (a) explain the reasons for these unphysical results, (b) connect the discovered equations to well‐known mathematically derived parameterizations, and (c) present ideas for learning successful parameterizations using equation‐discovery methods. Our main finding is that the common loss functions that match patterns representing effects of small‐scale processes are not enough, as important physical phenomena are not properly learned. Based on this, we have proposed a number of physics‐aware metrics and loss functions for future work. Key Points: Subgrid‐scale momentum/heat flux closures discovered using common algorithms are the analytically derivable nonlinear gradient model (NGM)In 2D turbulence/convection, NGM leads to unstable online simulations due to its inability to fully capture key inter‐scale energy transfersWe suggest that physics‐informed loss functions, libraries, metrics, and sparsity selections are needed to discover accurate/stable closures [ABSTRACT FROM AUTHOR]

Three-dimensional direct numerical simulations of rotating Rayleigh–Bénard convection in the planar geometry with no-slip top and bottom and periodic lateral boundary conditions are performed for a broad parameter range with the Rayleigh number spanning in $5\times 10^{6}\leq Ra \leq 5\times 10^{13}$ , Ekman number within $5\times 10^{-9}\leq Ek \leq 5\times 10^{-5}$ and Prandtl number $Pr=1$. The thermal and Ekman boundary layer (BL) statistics, temperature drop within the thermal BL, interior temperature gradient and scaling behaviours of the heat and momentum transports (reflected in the Nusselt $Nu$ and Reynolds numbers $Re$) as well as the convective length scale are investigated across various flow regimes. The global and local momentum transports are examined via the $Re$ scaling derived from the classical theoretical balances of viscous–Archimedean–Coriolis (VAC) and Coriolis–inertial–Archimedean (CIA) forces. The VAC-based $Re$ scaling is shown to agree well with the data in the cellular and columnar regimes, where the characteristic convective length scales as the onset length scale ${\sim } Ek^{1/3}$ , while the CIA-based $Re$ scaling and the inertia length scale $\sim (ReEk)^{1/2}$ work well in the geostrophic turbulence regime for $Ek\leq 1.5\times 10^{-8}$. The examinations of $Nu$ , global and local $Re$ , and convective length scale as well as the temperature drop within the thermal BL and its thickness scaling behaviours, indicate that for extreme parameters of $Ek\leq 1.5\times 10^{-8}$ and $80\lesssim RaEk^{4/3}\lesssim 200$ , we have reached the diffusion-free geostrophic turbulence regime. [ABSTRACT FROM AUTHOR]

This paper studies the global regularity problem for the 2D micropolar Rayleigh–Bénard convection system with velocity zero dissipation, micro‐rotation velocity Laplace dissipation, and temperature critical diffusion. By introducing a combined quantity and using the technique of Littlewood–Paley decomposition, we establish the global regularity result of solutions to this system. [ABSTRACT FROM AUTHOR]

In this paper, the effect of Coulomb and dielectric forces on the onset of Rayleigh-Bénard convection (RBC) in a dielectric liquid layer contained between two parallel electrode plates has been numerically investigated. Two different operating conditions have been considered in electrohydrodynamic (EHD) conduction: ohmic and saturation, and variations in the physical properties of the dielectric fluid with temperature. The electric equations and the state equations based on the Boussinesq approximation are integrated in the framework of OpenFOAM buoyantBoussinesqPimpleFoam program. The results show that in the ohmic regime, the combined effect of Coulomb and dielectric forces promotes the onset of RBC flow, while in the saturation state, the inhibition of RBC flow by Coulomb force is more significant. The value of the critical Rayleigh number Ra decreases with increasing electric Reynolds number ReE in the ohmic regime, whereas in the saturation state, the critical Ra increases with increasing ReE. In the saturation regime, the flow field always has a steady flow in the range of parameters considered. However, the onset of the RBC flow promoted by the dielectric force is more pronounced in the ohmic state. Due to the presence of the dielectric force, the flow field exhibits periodic oscillatory flow at low electric Reynolds numbers for the range of parameters considered. [ABSTRACT FROM AUTHOR]

In this paper, we present numerical and experimental results on helicity oscillations in a liquid-metal Rayleigh–Bénard convection cell with an aspect ratio of 0.5. While the numerical simulations use the finite volume library OpenFOAM, the experimental results are obtained by means of contactless inductive flow tomography. We find that helicity oscillations occur during transitions of flow states with different roll numbers that are characterized by significant changes in the Reynolds number. However, helicity oscillations are also observed when the number of rolls is constant and the Reynolds number is changing only very slowly. Notably, the helicity oscillations observed during the transient double-roll state exhibit characteristics remarkably similar to those associated with the Tayler instability, which points to a rather generic and universal character of this phenomenon. Helicity oscillations are also discussed as a possible mechanism for synchronizing the solar dynamo by tidal forces of the orbiting planets. [ABSTRACT FROM AUTHOR]

Precise estimation of the thermal updraft environment is important for the effective exploration of wind resources in long-endurance drones. Nevertheless, previous regression algorithms exhibit limitations in accurately evaluating updrafts under new operating conditions, and traditional airborne wind measurement methods are constrained by narrow ranges and sparse spatial sampling. This study addresses these challenges by harnessing continuous temperature data acquired via infrared sensors. The proposed methodology employs a data-driven deep operator network (DeepONet) to map the temperature field to the velocity field. Numerical simulations of two-dimensional Rayleigh–Bénard convection are conducted to simulate sensing measurements under various Rayleigh number R a , used as both training and testing datasets. For the DeepONet framework, a convolutional neural network (CNN) structure is employed as the branch network to extract features from the temperature field. Simultaneously, a fully connected neural network (FNN) is adopted as the trunk network, encoding input functions from fixed sensors. In order to assess the estimation performance in new environments, the training data are under operating conditions within the range of R a = 3 × 10 7 – 6 × 10 7 , and the testing data are under other unknown operating conditions. By compared to the conventional FNN network and the standard DeepONet framework, the DeepONet(CNN) in this study manifests a significant enhancement in estimation performance, demonstrating improvements ranging from 20% to 40% under unknown operating conditions. [ABSTRACT FROM AUTHOR]

In the present study, we numerically investigate the effect of Prandtl number on the heat transfer mechanism in turbulent Rayleigh–Bénard convection inside a cubical box endowed with conical roughness elements. The Rayleigh number is kept fixed at R a = 10 8 , while the Prandtl number (Pr) varies from 1 to 50. In contrast to the monotonic increasing trend of the Nusselt number (N u ∼ P r 0.27 ) in the two-dimensional (2D) roughness explored previously [Sharma et al., "Influence of Prandtl number in turbulent Rayleigh-Bénard convection over rough surfaces," Phys. Rev. Fluids 7, 104609 (2022)], it assumes an invariant behavior (∼ P r 0.012 ) for three dimensional (3D), though it is approximately 50% higher than its smooth counterpart. Flow intensity, measured in terms of Reynolds number (Re), drops with increasing Pr showing consistently lower magnitude for the 3D configuration. The addition of roughness elements is observed to disrupt the preferred orientation of large-scale circulation (LSC). The effect is predominant for lower Pr, where the roughness interferes most with the natural bias of LSC toward the diagonal planes of the cubical box. The analysis of plume statistics reveals that both coverage and intensity of plumes are augmented for the roughened cell. Increased homogeneity in the flow at higher Pr is reflected by the emergence of a more pronounced and distinguishable peak in probability density functions of temperature and velocity. Temporal spectra and variance data substantiate augmented intensity of fluctuations in the rough cell, while behavioral differences in the flow at different Pr are elucidated by using cross correlation of vertical velocity and temperature fluctuations. [ABSTRACT FROM AUTHOR]

Owing to the importance of non-Fourier heat flux model in several natural and engineering processes, the convection of binary viscoelastic fluid in a vertical channel with non-Fourier heat flux model is investigated. The linear Oldroyd-B constitutive equation is used to model viscoelasticity. The presence of the basic flow in the vertical y-direction makes the problem challenging compared with the case in Rayleigh–Bénard convection. We use the Chebyshev collocation method to explore the instability characteristics of the linear Oldroyd-B fluid under a wide variety of physical parameters. Results show that the non-Fourier effect and relaxation time contribute to destabilize the system for oscillatory convection. The retardation time can inhibit the instability of the convective system. In the absence of the non-Fourier effect, the vertical fluid layer cannot support oscillatory motions. Oscillatory motion is possible, and the neutral stability curve branches when the non-Fourier effect is taken into account in the fluid. In addition, a new interesting phenomenon can be found: under the coupling action of viscoelastic fluids and the non-Fourier effect, the neutral stability curve would change from single to two branches and then to a single branch with the increase in relaxation time. [ABSTRACT FROM AUTHOR]

In this study, we investigate the spatiotemporal instability of double-diffusive convection with and without a Couette flow, focusing mainly on the characters of transverse rolls. In the absence of shear, double-diffusive convection is always absolutely unstable even in the oscillatory instability regime, which is different from other flows that can also take the form of oscillatory convection. In the pure diffusive convection, before the transition from the oscillatory instability to steady instability, a saddle shift phenomenon is observed, which is related to the subcritical bifurcation of the steady branch. The presence of shear breaks the symmetry of oscillatory instability and along the neutral stability curve the spatiotemporal evolution of disturbance is determined by the competition between the shear intensity and the phase speed of oscillatory eigenmode traveling upstream. Therefore, as the shear intensity increases a transition from the absolute instability to the convective instability is expected, whereas as buoyancy strengthens the absolute instability eventually sets in again. On the other hand, the spatiotemporal instability of the sheared fingering convection is similar to the sheared Rayleigh–Bénard convection, in which the flow always undergoes a transition from the convective instability to absolute instability. In this case, increasing the Prandtl number or decreasing the diffusivity ratio between the two components, the region of convective instability expands due to the increasing viscous dissipation caused by the shear flow. [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.

This paper examines turbulent Rayleigh-Bénard convection in a two-dimensional square cavity with partially isothermal conducting plates on the horizontal walls. The study reveals that controlling the relative locations of the partially isothermal plates can accelerate or completely suppress the reversals of large-scale circulation. The heat transfer efficiency, which is characterised by the time-averaged Nusselt number, is generally higher than that of the traditional Rayleigh-Bénard convection, and can be further enhanced when the reversal is fully suppressed. The reversal in our cases is mainly caused by the competition between the two alternately growing 'corner' vortices, fed by the detaching plumes from the hot/cold plates. This differs from those reported in traditional Rayleigh-Bénard convection. Fourier mode decomposition of the kinetic energy, reflecting the diverse contributors, in the reversing cases further emphasises the distinction between the current system and traditional Rayleigh-Bénard convection. In addition, multiple states were observed where the conducting plates were positioned at specific relative locations and had different initial conditions. It has been observed that the difference in Nusselt numbers between the anticlockwise and clockwise states increases linearly with the distance between the upper cold and lower hot plates. Moreover, the analysis of the buoyancy moment and the stability of the primary roll structure suggests that the higher heat transfer efficiency between the two states is strongly linked to a more stable primary roll structure. This study presents a new approach for controlling flow reversal and improving heat transfer efficiency by modifying the non-global conducting boundary and initial conditions. [ABSTRACT FROM AUTHOR]

Predicting the heat flux through a horizontal layer of fluid confined between a hot bottom plate and a cold top one has always spurred theoretical, numerical and experimental work on Rayleigh–Bénard convection. Customarily, the Nusselt number (the heat flux in non-dimensional form) has been modelled in the form of one or several power-laws of three parameters, the Rayleigh, Prandtl and Reynolds numbers. Quantifying the large-scale flow that spontaneously develops in a turbulent Rayleigh–Bénard cell, the Reynolds number, unlike the Rayleigh and Prandtl numbers, is not a control parameter strictly speaking and, depending on the model, is sought as another power-law or introduced as an external input. Whereas balancing the different transport mechanisms can predict the exponents in these power laws, experimental and numerical results are required to adjust the various prefactors. The early and simple model of Malkus (1954) and Howard (1966) assumed that the value of the Nusselt number could be directly deduced from the marginal stability of the two sheared thermal boundary layers along the upper and lower plates, interacting via the large-scale flow. Maintaining this simplicity, this work shows that in the classical regime of turbulent convection, considering the linear critical conditions of absolute (as opposed to convective) thermo-convective instabilities alleviates the flaws of the original model. Revisiting available Direct Numerical Simulations from which a Reynolds number can be unambiguously extracted, the present approach then yields the Nusselt number as a function of the Rayleigh and Prandtl numbers agreeing well with the numerical results. [ABSTRACT FROM AUTHOR]

Various velocity measurements techniques for fluid dynamics experiments have been developed over the last four decades. These include Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV), both of which rely on imaging the flow with passive particles. While these techniques now allow for an accurate determination of velocity fields at high particle densities, they still suffer from significant inaccuracies when it comes to measurements near boundaries, due to smaller particle concentrations and imaging difficulties in these regions. To improve such measurements, we developed a correction technique for measured velocity fields. Using a PTV approach, we reconstructed the 3D velocity field from an experimental setup designed to study Rayleigh–Bénard convection in a tank. We corrected the obtained velocity field to ensure its accurate, rigid boundary conditions corresponding to the tank walls, while keeping the flow divergence-free. We then assessed the quality of the corrected velocity fields by comparing them with the outputs of 3D numerical simulations that reproduced the precise experimental conditions. The experimentally obtained divergence-free velocity fields with exact boundary conditions compare well with the results of the numerical simulations, which validates our approach. Using synthetic images, we estimated that our corrected fields are in better agreement with numerical simulations (Pearson coefficient R = 0.96 ) than the raw measured fields (Pearson coefficient R = 0.91 ). We find that at high Reynolds numbers, our results can be described by scaling laws that are consistent with previous results from the literature. The correction technique could be useful for a wide range of fluid dynamics experiments where accurate measurements near the walls are needed. These include the advection of passive tracers, where the boundary conditions need to be exact, or turbulence measurements, where the flow gradient at the walls must be precisely determined. [ABSTRACT FROM AUTHOR]

The fully nonlinear equations of gas dynamics are solved in the framework of a numerical approach in order to study the stability of the steady mode of Rayleigh-Bénard convection in compressible, viscous and heat-conducting gases encapsulated in containers with no-slip boundaries and isothermal top and bottom walls. An initial linear temperature profile is assumed. A map of the possible convective modes is presented assuming the height of the region and the value of the temperature gradient as influential parameters. For a relatively small height, isobaric convection is found to take place, which is taken over by an adiabatic mode when the height exceeds the critical value, or by a super-adiabatic mode in case of a relatively high temperature gradient. In the adiabatic mode, convective flow develops due to adiabatic processes given a stable initial stratification. An analytic formula for the critical height of the region is derived taking into account and neglecting the dependence of the gas viscosity on the temperature. Moreover, an analytic formula is obtained for the upper boundary of the region of applicability of the Boussinesq approximation for incompressible gases. These models for compressible gases are relevant to practical situations such as the study of convective flows in spatially extended gas mixtures when dealing with safety issues related to hydrocarbons stored in gas stations. A dangerous situation arises when the tank is almost empty but some hydrocarbon is left at the bottom of the tank. In the presence of convective flows, the vaporized fuel is mixed with the oxidizer (air) forming a gas-vapor medium. However, if the volumetric concentration of fuel vapor (hydrocarbon) is in the interval between the lower and upper concentration limits of ignition, then the gas-vapor mixture becomes explosive and any accidental spark is sufficient to cause an emergency. [ABSTRACT FROM AUTHOR]

We report an experimental study of the formation and evolution of laminar thermal structures generated by a small heat source, with a focus on their correlation to the thermal boundary layer and effects of heating time $t_{heat}$. The experiments are performed over the flux Rayleigh number ($Ra_f$) range $2.1\times 10^6 \leq Ra_f \leq 3.6\times 10^{7}$ and the Prandtl number ($Pr$) range $28.6 \leq Pr \leq 904.7$. The corresponding Rayleigh number ($Ra= t_{heat}\,Ra_{f}/\tau _0\,Pr$) range is $900 \leq Ra \leq 4\times 10^{4}$ , where $\tau _0$ is a diffusion time scale. For thermal structures generated by continuous heating (i.e. starting plumes), their formation process exists three characteristic times that are well reflected by changes in the thermal boundary layer thickness. These characteristic times, denoted as $t_{emit}$ , $t_{recover}$ and $t_{static}$ , correspond to the moments when the plume emission begins and completes, and when the thermal boundary layer becomes quasi-static, respectively. Their $Ra_f$ – $Pr$ dependencies are found to be $t_{emit}/\tau _0\sim Ra_f^{-0.41}\,Pr^{0.41}$ , $t_{recover}/\tau _0\sim Ra_f^{-0.48}\,Pr^{0.48}$ and $t_{static}/\tau _0\sim Ra_f^{-0.49}\,Pr^{0.33}$ , respectively. Thermal structures generated by finite $t_{heat}$ exhibit similar evolution dynamics once $t_{heat} \ge t_{emit}$ , with the accelerating stage behaving like starting plumes and the decay stage like thermals (i.e. a finite amount of buoyant fluids). It is further found that their maximum rising velocity experiences a transition in the $Ra$ -dependence from $Ra$ to $(Ra\ln Ra)^{0.5}$ at $Ra \simeq 6000$ ; and their maximum acceleration reaches the value of starting plumes at $t_{heat}\simeq t_{recover}$ , and remains unchanged for larger $t_{heat}$. In particular, the maximum rising velocity for the cases with $t_{heat} = t_{recover}$ follows a scaling relation $Ra_f^{0.37}\,Pr^{-0.37}$ , in contrast to the relation $Ra_f^{0.48}\,Pr^{-0.48}$ for starting plumes. This study provides a more comprehensive understanding of laminar thermal structures, which are relevant to a range of processes in nature and laboratory systems such as Rayleigh–Bénard convection. [ABSTRACT FROM AUTHOR]

The geostrophic turbulence in rapidly rotating thermal convection exhibits characteristics shared by many highly turbulent geophysical and astrophysical flows. In this regime, the convective length and velocity scales and heat flux are all diffusion-free, i.e. independent of the viscosity and thermal diffusivity. Our direct numerical simulations (DNS) of rotating Rayleigh–Bénard convection in domains with no-slip top and bottom and periodic lateral boundary conditions for a fluid with the Prandtl number $Pr=1$ and extreme buoyancy and rotation parameters (the Rayleigh number up to $Ra=3\times 10^{13}$ and the Ekman number down to $Ek=5\times 10^{-9}$) indeed demonstrate all these diffusion-free scaling relations, in particular, that the dimensionless convective heat transport scales with the supercriticality parameter $\widetilde {Ra}\equiv Ra\, Ek^{4/3}$ as $Nu-1\propto \widetilde {Ra}^{3/2}$ , where $Nu$ is the Nusselt number. We further derive and verify in the DNS that with the decreasing $\widetilde {Ra}$ , the geostrophic turbulence regime undergoes a transition into another geostrophic regime, the convective heat transport in this regime is characterized by a very steep $\widetilde {Ra}$ -dependence, $Nu-1\propto \widetilde {Ra}^{3}$. [ABSTRACT FROM AUTHOR]

We report a home-built velocity-gradient-tensor-resolved particle image velocimetry (VGTR-PIV) system which spatio-temporally resolves all components of the velocity gradient tensor. This technique is applied to the paradigmatic turbulent Rayleigh–Bénard convection system in a cylindrical cell at three representative positions, i.e. centre, side and bottom regions. The VGTR-PIV system allows us to directly measure, for the first time, the spatio-temporally resolved energy dissipation rate and enstrophy in turbulent thermal convection. In the experiment, the Rayleigh number $Ra$ varied in the range $2 \times 10^8 \leqslant Ra \leqslant 8 \times 10^9$ and the Prandtl number $Pr$ was fixed at $Pr = 4.34$. Compared with the fully resolved energy dissipation rate $\varepsilon$ , the pseudo-dissipation provides the best estimate within $3\,\%$ , the planar (two-dimensional) surrogate has a larger relative error and the one-dimensional surrogate leads to the largest error. The power-law scalings of the time-averaged energy dissipation rate with the Rayleigh number follow $\langle \varepsilon _c \rangle _t / (\nu ^3 H^{-4}) = 9.86 \times 10^{-6} Ra^{1.54 \pm 0.02}$ , $\langle \varepsilon _s \rangle _t / (\nu ^3 H^{-4}) = 9.26 \times 10^{-3} Ra^{1.25 \pm 0.02}$ and $\langle \varepsilon _b \rangle _t / (\nu ^3 H^{-4}) = 2.70 \times 10^{-2} Ra^{1.23 \pm 0.02}$ in the centre, side and bottom regions, respectively where $\nu$ is dynamic viscosity and $H$ is cell height. These scaling relations, along with our earlier measured time-averaged energy dissipation rate at the bottom wall surface $\langle \varepsilon _w \rangle _t / (\nu ^3 H^{-4}) = 9.65 \times 10^{-2} Ra^{1.25 \pm 0.02}$ (J. Fluid Mech. , vol. 947, 2022, A15), provide important constraints against which theoretical models may be tested. For the centre and side locations in the convection cell, the probability density functions (p.d.f.s) of the energy dissipation rate and enstrophy both follow a stretched exponential distribution. For the bottom region, the p.d.f.s of dissipation and enstrophy exhibit a stretched exponential distribution outside the viscous boundary layer and an exponential distribution inside the viscous boundary layer. It is also found that extreme events with high dissipation are the most intermittent in the side region, whereas the bottom region is less intermittent than the cell centre. [ABSTRACT FROM AUTHOR]

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]

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]