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The interaction between droplets and a liquid pool is a widely observed fluid phenomenon with significant relevance to various industrial applications. This study numerically investigates the impact of both a single droplet and two successive droplets on a liquid pool with a fixed thickness. Particular emphasis was focused on the evolution of cavity depth and width during the deformation process. For single droplet impacts, the cavity depth exhibits linear growth with time in the early stage, consistent with predictions based on energy balance. This growth is independent of the Weber number (We) within the explored range of 96 < We < 345. Similarly, the cavity width shows weak dependence on the Weber number during early development, deviating and reaching a maximum width at later times. The maximum cavity width follows a power-law relationship with the Weber number, with a 0.5 exponent. In the case of successive droplet impacts with small initial separation, cavity depth also evolves linearly with time in the early stage but over an extended period. This prolonged growth is attributed to droplet merging, resulting in an effectively larger merged droplet. However, for successive droplets with large separation, the two linear growth stages exhibit intermittent interruptions due to the second impact occurring at a later time. The variation in cavity width due to different initial spacings between two successive droplets still exhibits similarity until a larger spacing causes a change in the rate of cavity width development. [ABSTRACT FROM AUTHOR]

In this paper, we introduce WindFormer, an innovative transformer-based model engineered for short-term wind speed forecasting, leveraging multivariate time series data. Unlike traditional approaches, WindFormer excels in processing diverse meteorological features—temperature, humidity, and power—to intricately map their spatiotemporal interdependencies with wind speeds. Utilizing a novel unsupervised pre-training strategy, WindFormer initially learns from vast volumes of unlabeled data to capture generalized feature representations. This foundation enhances the subsequent fine-tuning phase on labeled wind speed data, in which our model demonstrates exceptional predictive accuracy. Empirical evaluations across various public datasets illustrate that WindFormer markedly surpasses both conventional statistical models and contemporary deep learning techniques. The model not only achieves superior accuracy in forecasting wind speeds but also reveals a significant enhancement in handling complex spatiotemporal data dynamics. These advancements facilitate more effective wind farm management and power grid scheduling, making a substantial impact on operational efficiencies and renewable energy utilization. Our findings confirm the robustness of WindFormer in a real-world setting, underscoring its potential as a pivotal tool in meteorological and energy sectors. The integration of unsupervised pre-training with multi-task fine-tuning establishes a new benchmark for short-term wind speed prediction. [ABSTRACT FROM AUTHOR]

Transport of exhaled droplets and aerosol suspension is a main route for the transmission of highly infectious respiratory diseases. A poorly ventilated room, where human body heat drives the flow and the pathogen motion, is one such paradigmatic situation with an elevated risk of viral transmission. Here, we report a numerical study on human body heat-driven buoyancy convection in a slender rectangular geometry with the geometric size of 12 × 1 × 3 m3. Using large-scale three-dimensional simulations, we reveal how different spacings between human body heat sources can potentially spread pathogenic species between occupants in a room. Morphological transition in airflow takes place as the distance between human heat sources is varied, which shapes distinct patterns of disease transmission: For sufficiently large distance, individual buoyant plume creates a natural barrier, forming buoyant jets that block suspension spread between occupants. Thermal plumes exhibit significant individual effects. However, for small distances, a collective effect emerges and thermal plumes condense into superstructure, facilitating long-distance suspension transport via crossing between convection rolls. In addition, we quantify the impact of morphological transition on the transport of viral particles by introducing tracer particles. The quantitative analysis shows that under certain critical distances, the infection risk becomes significantly elevated due to this transition and collective behavior. Our findings highlight the importance of reasonable social distancing to reduce indoor cross-transmission of viral particles between people and provide new insights into the hidden transitional behavior of pathogen transmission in indoor environments. [ABSTRACT FROM AUTHOR]

Practical extreme ultraviolet (EUV) sources yield the desired 13.5 nm radiation but also generate debris, significantly limiting the lifespan of the collector mirror in lithography. In this study, we explore the role of buffer gas in transporting debris particles within an EUV source vessel using direct numerical simulations. Our study involves a 2 × 1 × 1m3 rectangular cavity with an injecting jet flow subjected to sideward outlet. Debris particles are introduced into the cavity with specified initial velocities, simulating a spherical radiating pattern with particle diameters ranging from 0.1 to 1 μm. Varying the inflow velocity (from 1 to 50 m/s) of the buffer gas reveals a morphological transition in the flow field. At low inflow velocities, the flow remains steady, whereas higher inflow velocities induce the formation of clustered corner rolls. Upon reaching sufficiently high inflow velocities, the jet flow can penetrate the entire cavity, impacting the end wall. Interestingly, the resulting recirculation flow leads to the spontaneous formation of spiraling outflow. The distinct flow structures at various inflow velocities lead to distinct patterns of particle transport. For low-speed gas, it is efficient in expelling all particles smaller than 0.4 μm, while for high-speed gas, those fine particles accumulate near the end wall and are challenging to be extracted. Our findings highlight the significance of controlling flow conditions for effective debris particle transport and clearance in diverse applications especially in EUV source vessels. [ABSTRACT FROM AUTHOR]

This study investigates the effect of vibration on the flow structure transitions in thermal vibrational convection (TVC) systems, which occur when a fluid layer with a temperature gradient is excited by vibration. Direct numerical simulation (DNS) of TVC in a two-dimensional enclosed square box is performed over a range of dimensionless vibration amplitudes $0.001 \le a \le 0.3$ and angular frequencies $10^{2} \le \omega \le 10^{7}$ , with a fixed Prandtl number of 4.38. The flow visualisation shows the transition behaviour of flow structure upon the varying frequency, characterising three distinct regimes, which are the periodic-circulation regime, columnar regime and columnar-broken regime. Different statistical properties are distinguished from the temperature and velocity fluctuations at the boundary layer and mid-height. Upon transition into the columnar regime, columnar thermal coherent structures are formed, in contrast to the periodic oscillating circulation. These columns are contributed by the merging of thermal plumes near the boundary layer, and the resultant thermal updrafts remain at almost fixed lateral position, leading to a decrease in fluctuations. We further find that the critical point of this transition can be described nicely by the vibrational Rayleigh number ${{Ra}}_{vib}$. As the frequency continues to increase, entering the so-called columnar-broken regime, the columnar structures are broken, and eventually the flow state becomes a large-scale circulation (LSC), characterised by a sudden increase in fluctuations. Finally, a phase diagram is constructed to summarise the flow structure transition over a wide range of vibration amplitude and frequency parameters. [ABSTRACT FROM AUTHOR]

We experimentally study the heat transfer and flow characteristics of thermal convection in a rectangular cell with built-in lattice channels. The working fluid used is water with a Prandtl number of 5.5, and the Rayleigh number ranges from 2.5 × 10 8 to 6.9 × 10 9 . Three proposed models with different channel sizes and positions and the classical Rayleigh–Bénard convection (RBC) are studied, and the heat transfer and flow structure characteristics are analyzed using measured temperature signals. The first model included two short channels placed near the top and bottom plates, which disrupt the mixing zone and enhance heat transport. The second model involves relatively long channels positioned at the center of the cell, but far from the thermal boundary layer, resulting in a more coherent bulk flow that also enhances heat transport. For these two configurations, the heat transfer enhancement rate is approximately 20% compared to standard RBC. The third model uses long lattice channels that almost touches the top and bottom plates. This configuration results in a maximum heat transfer enhancement of about 138% due to the organized boundary layer and bulk flow induced by lattice channels. The presence of channels also results in a two-order smaller standard deviation of temperature, indicating a significant reduction in fluctuations. However, the average temperatures in the center of some channels were significantly different from the mean system temperature, suggesting the existence of cold or hot fluid flow through the channel. Our experimental results show that the inclusion of channels with appropriate lengths and positions can effectively regulate the flow near the boundary layer and in the bulk, leading to significant enhancements in heat transfer. [ABSTRACT FROM AUTHOR]

The vortex dynamics of a supersonic flow past an impulsively started circular cylinder are studied numerically. A well-developed high-order finite difference method is adopted to solve the two-dimensional Navier–Stokes equations. In particular, Ma = 1.1 and Re = 2.2 × 104 are selected to report the vortex evolution process. The results confirm that the α-, β-, sub-α-, and sub-β-phenomena observed in incompressible flow in the separated region do exist in the supersonic regime. In addition, the influence of Mach number and Reynolds number on the vortex is also studied, and the vortex changes are compared at Ma = 1.1, 1.7 and Re = 1 × 104, 2 × 104, 2.5 × 104, 3 × 104, 5 × 104, and 1 × 105. [ABSTRACT FROM AUTHOR]

Thermal convection in nature and industrial applications usually encounters time-varying internal heating (IH); however, the effect of temporal modulation on temperature responses and heat fluxes of the system has been rarely explored. Here, we numerically studied the IH convection with a temporally periodic heating source. We conducted direct numerical simulations over Rayleigh number (Ra) range 10 5 ≤ R a ≤ 10 9 at fixed Prandtl number Pr = 1 with dimensionless modulation frequency 4 × 10 − 5 ≤ f ≤ 10 − 1 and amplitude fixed at Ω = 1. We first find that the introduction of periodic modulation has a slight effect on the heat transport over the individual plates and flow strength except for the lowest Ra. We then focus on the characteristics of the amplitude A and phase lag Δ ϕ of the globally averaged temperature response to the periodic modulation. Three regimes of the phase response are identified: (i) in-phase regime, where synchronous response is found at small frequencies with the vanished phase lag Δ ϕ and A keeping at constant value; (ii) transition regime, where both Δ ϕ and A decrease with increasing f for moderate frequencies; and (iii) half anti-phase regime, where Δ ϕ attains the minimal value − π / 2. We also find that the transition behavior between three regimes can be well described using the normalization of the Ra-dependent critical frequency with the scaling R a − 0.30 . To explain the regime transition, we further theoretically deduce an analytical solution for A and Δ ϕ , which agrees well with the numerical results. This solution can explain why f R a 0.30 gives a good description of the transition behavior. Our present findings provide a fundamental understanding of the underlying mechanism of temporal modulation on IH systems and have substantial implications for the investigation of convective system with periodic heating source. [ABSTRACT FROM AUTHOR]

The flow past a cylinder near a plane wall for small gap ratios (G / D = 0.1 , 0.3 , and 0.9) and fixed ReD = 1000 is numerically studied. The fundamental flow features are characterized by the instantaneous and mean fields. Then, the dynamics of cylinder-wake/boundary-layer interaction are revealed by the turbulent momentum transport and kinetic energy production. The turbulent fluctuations caused by the secondary vortex (SV) (at G / D = 0.3 , 0.9) and the novel tertiary vortex (TV) (at G / D = 0.9) can be observed in the distributions of Reynolds stresses. For G / D = 0.1 and G / D = 0.3 , the wake/boundary-layer interaction is dominated by ejection and sweep events, which are related to the generation of the hairpin vortex. These two bursting events lead to the momentum transport between the high- and low-speed sides. For G / D = 0.9 , the ejection event is not found in the interaction region because the head of the hairpin vortex is entrained into the wake. The upper roller (RU) helps to transport high-momentum fluid toward the wall in this case, although it does not take part in the interaction directly. The shedding of RU, the lower roller (RL), SV (at G / D = 0.3 and 0.9), and KH (Kelvin–Helmholtz) vortex (at G / D = 0.1) and the generation of the hairpin vortex are crucial to turbulent kinetic energy (TKE) production. The RU, KH vortex, and SV transfer ⟨ u ′ u ′ ⟩ out to ⟨ v ′ v ′ ⟩ and ⟨ w ′ w ′ ⟩ resulting redistribution of the TKE. While RL, surviving for a shorter time, transfers ⟨ v ′ v ′ ⟩ out to ⟨ u ′ u ′ ⟩ and ⟨ w ′ w ′ ⟩ , helping explain why it disappears quickly, TV only transfers out ⟨ v ′ v ′ ⟩ out to ⟨ u ′ u ′ ⟩ , and its TKE comes from other terms rather than the production term. The redistribution of TKE due to the generation of the hairpin vortex can result in the slower growth rate of the secondary disturbance growth stage, promoting the wall boundary layer transition. [ABSTRACT FROM AUTHOR]

In this paper, we report that reversals of the large-scale circulation in two-dimensional Rayleigh–Bénard (RB) convection can be suppressed by imposing sinusoidally distributed heating to the bottom plate. We examine how the frequency of flow reversals depends on the dimensionless wavenumber $k$ of the spatial temperature modulation with various modulation amplitude $A$. For sufficiently large $k$ , the flow reversal frequency is close to that in the standard RB convection under uniform heating. However, when $k$ decreases, the frequency of flow reversal gradually becomes lower and can even be largely reduced. Furthermore, we examine the growth of the corner roll and the global flow structure based on Fourier mode decomposition, and reveal that the size of the corner roll diminishes as the wavenumber decreases. The reason is that the regions occupied by the cold phase can absorb heat from the hot plumes and thus lower their temperature, which reduces the corner roll's kinetic energy input provided by the buoyancy force, and weakens the feeding process of the corner rolls. This results in the locking of the corner roll into a smaller region near the corner, making it harder for a reversal to occur. Using the concept of horizontal convection caused by non-uniform heating, we find a relevant parameter $k/A$ to describe briefly how the reversal frequency depends on wavenumber and modulation amplitude. The present work provides a new way to control the flow reversals in RB convection through modifying temperature boundary conditions. [ABSTRACT FROM AUTHOR]

Vertical convection (VC) under the action of vertical vibration in a square cavity has been investigated using direct numerical simulation. The simulations are conducted with Prandtl number Pr fixed at 4.38 and Rayleigh number Ra ranging from 10 8 to 10 10 . To examine the influence of vertical vibration, the dimensionless vibration frequency is varied in the range of 0 ≤ ω ≤ 1000 and a small dimensionless amplitude is fixed at a = 1.52 × 10 − 3 . First, for low vibration frequency, trivial results are obtained where flow structures and the scalings of Nu and Re resemble that of the standard VC cases. In contrast, when the vibration frequency ω increases beyond a critical value ω * , a strong shearing effect from vibration leads to abundant eruptions of thermal plumes from sidewalls, and thus a laminar-turbulent transition of the bulk flow. As a result, heat-transport is greatly enhanced and the scaling exponent β of N u ∼ R a β substantially increases in such the vibration-dominated regime. In specific, the scaling relations obtained transit from N u ∼ R a 0.25 and R e ∼ R a 0.37 at ω = 0 in the laminar regime to N u ∼ R a 0.42 and R e ∼ R a 0.52 at ω ≳ 300 in the turbulent regime. Analysis of the mean flow field shows that the vibration thins the thermal boundary layer and enhances the thermal dissipation rate in the bulk region. Furthermore, we found that the trend of Nu and Re can be well described by the vibrational Rayleigh number R a vib . In particular, Nu is insensitive to R a vib for R a vib ≤ R a vib * , whereas N u (ω) / N u (0) ∼ (R a vib / R a vib *) 0.42 for R a vib > R a vib * , where the critical vibrational Rayleigh number exhibits a scaling relation R a vib * ∼ R a 0.68 obtained from numerical results. [ABSTRACT FROM AUTHOR]

We investigate the flow characteristics and kinetic behaviors of particles in turbulent Rayleigh–Bénard convection particulate flows. Direct numerical simulations combined with a Lagrangian point-particle strategy were carried out in the range of Stokes numbers 2 × 10 − 4 ≤ S t L ≤ 7.3 × 10 − 2 for Rayleigh numbers from 2 × 10 6 to 10 8 at the Prandtl number P r = 0.678. A two-way coupling model is employed in which the momentum exchange between the dispersed particles and the carrier fluid is taken fully into account. Based on various patterns of particle motion, we find three transport modes of inertial particles which are labeled as the circling transport (CCT) mode, the channel transport (CNT) mode, and the downpour transport (DPT) mode, respectively. These modes can switch to each other when Stokes numbers and Rayleigh numbers vary and exhibit different effects of particle motions on the flow field and heat transfer. For the CCT and DPT modes, compared with the CNT, a weakening alteration of flow structures and thermal plumes leads to no significant effect on the transport of momentum and heat. For the CNT mode, a pronounced effect of particles on enhancements of the turbulent momentum transport and heat transfer relates to the strong interaction between the particle clusters and the chaotic structures of eddies. What is more, the particles tend to homogeneously distribute for the CCT and DPT modes, although the particles exhibit different transport states. As for the CNT mode, under both preferential sweeping and centrifugal effects, particles accumulate into clusters that hover toward the region of high strain rate and the edges of eddies. We found that the averaged particle settling speeds are almost proportional to the Stokes number. The particle settling speeds are larger than the terminal velocity of Stokesian particles for the CCT and CNT modes as particles tend to settle in the downward fluid. In contrast, it becomes smaller than the terminal velocity for the DPT mode due to the drag of the upward fluid. [ABSTRACT FROM AUTHOR]

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We investigate the dynamic couplings between particles and fluid in turbulent Rayleigh–Bénard (RB) convection laden with isothermal inertial particles. Direct numerical simulations combined with the Lagrangian point-particle mode were carried out in the range of Rayleigh number $1\times 10^6 \le {Ra}\le 1 \times 10^8$ at Prandtl number ${Pr}=0.678$ for three Stokes numbers ${St_f}=1 \times 10^{-3}$ , $8 \times 10^{-3}$ and $2.5 \times 10^{-2}$. It is found that the global heat transfer and the strength of turbulent momentum transfer are altered a small amount for the small Stokes number and large Stokes number as the coupling between the two phases is weak, whereas they are enhanced a large amount for the medium Stokes number due to strong coupling of the two phases. We then derived the exact relation of kinetic energy dissipation in the particle-laden RB convection to study the budget balance of induced and dissipated kinetic energy. The strength of the dynamic coupling can be clearly revealed from the percentage of particle-induced kinetic energy over the total induced kinetic energy. We further derived the power law relation of the averaged particles settling rate versus the Rayleigh number, i.e. $S_p/(d_p/H)^2{\sim} Ra^{1/2}$ , which is in remarkable agreement with our simulation. We found that the settling and preferential concentration of particles are strongly correlated with the coupling mechanisms. [ABSTRACT FROM AUTHOR]

The heat transfer enhancement achieved by the additional electric field in Rayleigh–Bénard convection (RBC) of a dielectric fluid is numerically studied beyond the Rayleigh number Ra = 105. We carried out direct numerical simulations of RBC in a rectangular enclosure under the strong injection condition with a fixed non-dimensional injection parameter C = 10, a fixed mobility number M = 10, two Rayleigh numbers Ra = 105 and Ra = 106, and two Prandtl numbers Pr = 1 and Pr = 10 to investigate the characteristics of flow structure and heat transfer and evaluate the dependence on these parameters. It is observed that the flow structure exhibits multiple states with various steady or unsteady flow patterns such as four cells, three cells, and two cells (up/down). It is found that the introduction of an electric field is an effective way to achieve heat transfer enhancement. The heat flux is augmented more efficiently for a large Prandtl number and a low Rayleigh number, where the electric field has a strong effect relative to buoyancy. It is also found that heat transfer is most efficient when the flow pattern is in a three cells flow state. [ABSTRACT FROM AUTHOR]

Thermal convection in a tilted three-dimensional rectangular box has been systematically investigated by direct numerical simulation. The Rayleigh number Ra varies from 107 to 109, the Prandtl number Pr is set to 0.7, and the tilted angle β ranges from 0° to 90°. The effects of tilting on large-scale circulation (LSC), Nusselt number (Nu), Reynolds number (Re), and boundary layers (BLs) and the Ra-dependency are investigated. For large β exceeding certain values, say 45°, the stable temperature stratification forms in the bulk, resulting in low Re and Nu. It is found that the tilting leads to a distinct trend for Nu and Re: Nu first increases to some extent for small β, then nearly stays unchanged for moderate β, and finally decreases for large β, while Re initially increases for small β and then directly declines with increasing β. Based on the analysis of flow structures, with increasing β, it is found that the volume of the high-velocity tube (HVT) initially increases for 107 ≤ Ra ≤ 108 but decreases for Ra = 109, which is responsible for the variation in Nu at small β. The probability density functions of instantaneous convective heat transport within the HVT show higher probabilities for large values when β increases, implying that LSC tends to be more coherent and causing different tilting behaviors between Nu and Re. Finally, we find that, except for β = 90°, the normalized profiles of viscous and thermal BLs tend to have universal profiles, deviating from the BL of the Prandtl–Blasius–Pohlhausen (PBP) type to some extent regardless of β. Only the thermal BL for β = 90° is found to be in good agreement with the classic PBP laminar BL profile. [ABSTRACT FROM AUTHOR]

We carry out numerical simulations of oscillatory Rayleigh–Bénard convection under lateral periodic conditions over the Rayleigh number range of 10 6 ≤ Ra ≤ 10 8 and the vibration frequency range of 0 ≤ ω ≤ 1000. It is demonstrated that high-frequency vibration achieves a significant enhancement of the intensity of convective flows and the heat-transport efficiency. The phase decomposition method is adopted to distinguish between the vibration-generated oscillatory flows and the fluctuating fields. It is shown that although the contribution of oscillatory flows on heat transport vanishes, the oscillating properties in near-wall regions introduce a strong shear effect to increase the intensity of fluctuating velocities both in the bulk regime and within boundary layers, destabilize thermal boundary layers, and trigger massive eruptions of thermal plumes, which achieves an enhancement of heat transfer. Our results further reveal a universal scaling law between the vibrational Reynolds and Rayleigh numbers, i.e., Re vib ∼ Ra vib 1 / 2 , which can be well described by our proposed analytical model. Moreover, it is shown that vibrational influences are different for the fluctuating velocity and temperature fields. [ABSTRACT FROM AUTHOR]

We carry out direct numerical simulations of turbulent Rayleigh–Bénard convection in a square box with rough conducting plates over the Rayleigh number range $10^7\leqslant Ra\leqslant 10^9$ and the Prandtl number range $0.01\leqslant Pr\leqslant 100$. In Zhang et al. (J. Fluid Mech., vol. 836, 2018, R2), it was reported that while the measured Nusselt number $Nu$ is enhanced at large roughness height $h$ , the global heat transport is reduced at small $h$. The division between the two regimes yields a critical roughness height $h_c$ , and we now focus on the effects of the Prandtl number ($Pr$) on $h_c$. Based on the variations of $h_c$ , we identify three regimes for $h_c(Pr)$. For low $Pr$ , thermal boundary layers become thinner with increasing $Pr$. This makes the boundary layers easier to be disrupted by rough elements, leading to the decrease of $h_c$ with increasing $Pr$. For moderate $Pr$ , the corner-flow rolls become much more pronounced and suppress the global heat transport via the competition between the corner-flow rolls and the large-scale circulation (LSC). As a consequence, $h_c$ increases with increasing $Pr$ due to the intensification of the corner–LSC competition. For high $Pr$ , the convective flow transitions to the plume-controlled regime. As the rough elements trigger much stronger and more frequent plume emissions, $h_c$ again decreases with increasing $Pr$. [ABSTRACT FROM AUTHOR]

Turbulent Rayleigh-Bénard convection in a square cavity with rough horizontal walls is investigated at a fixed Prandtl number Pr = 0.7 over the Rayleigh number range of 106 ≤ Ra ≤ 109. We have proposed five models with rough elements of the same height but different spatial distributions to evaluate their influences on the heat transport and flow structures of the system. It is found that the flow reversal can be promoted at a Rayleigh number around 107. In all the rough models, the heat transfer is impeded at a low Ra and enhanced at a Rayleigh number beyond a critical value. Interestingly, the heat transfer and flow structure can be clustered by the sparsity of the rough element distribution. Different scaling exponents for heat transfer are identified for sparsely distributed rough models and compactly distributed models. On the other hand, the spatial distribution of rough elements has little effect on the scaling of the Reynolds number. [ABSTRACT FROM AUTHOR]

We report an experimental study of turbulent Rayleigh-Bénard convection in a cylindrical cell of aspect ratio unity, focusing on the effects of the Prandtl number (Pr). Purified water was used as the convecting fluid. Five different Pr between 3.58 and 9.40 were achieved by changing the mean temperature of water, and the measurements were carried out over the Rayleigh number range 2.63 × 108 ≤ Ra ≤ 3.89 × 1010. Over the present parameter range, the measured Nusselt number Nu is found to scale as Nu ∼ Raβ with β = 0.30 and to be independent of Pr. Based on the oscillation period of the measured temperature, the Reynolds number Re scales as Re ∼ Ra0.47Pr−0.72. The local temperature fluctuations at the cell center and near the cell's sidewall were measured, and their relations with Ra and Pr were studied. Our results further reveal that the non-Oberbeck-Boussinesq effects of water have a relatively small influence on the measured scaling relation Nu ∼ Raβ. [ABSTRACT FROM AUTHOR]

We present a study of absolute and convective instabilities in electrohydrodynamic flow subjected to a Poiseuille flow (EHD-Poiseuille). The electric field is imposed on two infinite flat plates filled with a non-conducting dielectric fluid with unipolar ion injection. Mathematically, the dispersion relation of the linearised problem is studied based on the asymptotic response of an impulse disturbance imposed on the base EHD-Poiseuille flow. Transverse, longitudinal and oblique rolls are investigated to identify the saddle point satisfying the pinching condition in the corresponding complex wavenumber space. It is found that when the ratio of Coulomb force to viscous force increases, the transverse rolls can transit from convective instability to absolute instability. The ratio of hydrodynamic mobility to electric mobility, which exerts negligible effect on the linear stability criterion when the cross-flow is small, has significant influence on the convective–absolute instability transition, especially when the ratio is small. As we change the value of the mobility ratio, a saddle point shift phenomenon occurs in the case of transverse rolls. The unstable longitudinal rolls are convectively unstable as long as there is a cross-flow, a result which is deduced from a one-mode Galerkin approximation. Longitudinal rolls have a larger growth rate than transverse rolls except for a small cross-flow. Finally, regarding the oblique rolls, a numerical search for the saddle point simultaneously in the complex streamwise and transverse wavenumber spaces always yields an absolute transverse wavenumber of zero, implying that oblique rolls give way to transverse rolls when the flow is unstable. [ABSTRACT FROM AUTHOR]

The instabilities and transitions of flow in a vertical cylindrical cavity with heated bottom, cooled top and insulated sidewall are investigated by linear stability analysis. The stability boundaries for the axisymmetric flow are derived for Prandtl numbers from 0.02 to 1, for aspect ratio $A$ ($A= H/ R= \mathrm{height} / \mathrm{radius} $) equal to 1, 0.9, 0.8, 0.7, respectively. We found that there still exists stable non-trivial axisymmetric flow beyond the second bifurcation in certain ranges of Prandtl number for $A= 1$, $0. 9$ and 0.8, excluding the $A= 0. 7$ case. The finding for $A= 0. 7$ is that very frequent changes of critical mode (azimuthal Fourier mode) of the second bifurcation occur when the Prandtl number is changed, where five kinds of steady modes $m= 1, 2, 8, 9, 10$ and three kinds of oscillatory modes $m= 3, 4, 6$ are presented. These multiple modes indicate different flow structures triggered at the transitions. The instability mechanism of the flow is explained by kinetic energy transfer analysis, which shows that the radial or axial shear of base flow combined with buoyancy mechanism leads to the instability results. [ABSTRACT FROM PUBLISHER]

Transient growth of perturbations due to non-normality for the curved channel Poiseuille flow (CCPF) is presented. The study covers a wide range of the radii ratios η as well as axial and azimuthal modes, with the purpose of complementing the results of linear stability for this flow with a study of the optimal linear growth possible in the linearly stable parameter regions. For the wide-gap case, the transient growth of streamwise-azimuthal modes that grow most is of low level and suppressed by curvature. It is also found that as curved channel flow approaches the flow in a straight channel enough, both the normal and non-normal stability characteristics are almost identical to that of plane Poiseuille flow. The modulation of the basic circular Poiseuille flow by the presence of azimuthal streaks resulting from the significant growth of initial perturbations can be clearly visualized. For the transition region between the wide-gap case and the narrow-gap case, the sensitivity of eigenvalues is shown to be closely related to the magnitude of transient growth, which is tuned by curvature in a smooth way. [ABSTRACT FROM AUTHOR]

The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high-resolution piecewise parabolic method (PPM), in which the viscous and turbulence effects are both considered. The bubble is of the same size and is accelerated by a planar shock of different Mach numbers (Ma). The results of low Ma cases agree quantitatively with those of experiments [G. Layes, O. Le Métayer, Phys. Fluids 19 (2007) 042105]. With the increase of Ma, the final geometry of the bubble becomes quite different, the compression ratio is highly raised, and the time-dependent mean bubble velocity is also influenced. The compression ratios measured can be well normalized when Ma is low, while less agreement has been achieved for high Ma cases. In addition, the mixedness between two fluids is enhanced greatly as Ma increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high Ma cases. [ABSTRACT FROM AUTHOR]