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We study energy scale transfer in Rayleigh–Taylor (RT) flows by coarse graining in physical space without Fourier transforms, allowing scale analysis along the vertical direction. Two processes are responsible for kinetic energy flux across scales: baropycnal work $\\varLambda$, due to large-scale pressure gradients acting on small scales of density and velocity; and deformation work $\\varPi$, due to multiscale velocity. Our coarse-graining analysis shows how these fluxes exhibit self-similar evolution that is quadratic-in-time, similar to the RT mixing layer. We find that $\\varLambda$ is a conduit for potential energy, transferring energy non-locally from the largest scales to smaller scales in the inertial range where $\\varPi$ takes over. In three dimensions, $\\varPi$ continues a persistent cascade to smaller scales, whereas in two dimensions $\\varPi$ rechannels the energy back to larger scales despite the lack of vorticity conservation in two-dimensional (2-D) variable density flows. This gives rise to a positive feedback loop in 2-D RT (absent in three dimensions) in which mixing layer growth and the associated potential energy release are enhanced relative to 3-D RT, explaining the oft-observed larger $\\alpha$ values in 2-D simulations. Despite higher bulk kinetic energy levels in two dimensions, small inertial scales are weaker than in three dimensions. Moreover, the net upscale cascade in two dimensions tends to isotropize the large-scale flow, in stark contrast to three dimensions. Our findings indicate the absence of net upscale energy transfer in three-dimensional RT as is often claimed; growth of large-scale bubbles and spikes is not due to ‘mergers’ but solely due to baropycnal work $\\varLambda$.

An initially perturbed interface between two fluids of different densities is usually unstable when driven by an acceleration or a shock wave; it is known as a Rayleigh–Taylor instability or a Richtmyer–Meshkov instability. One of the most significant issues in these instabilities is the spatiotemporal development of fingers generated at the interface, which plays an important role in both scientific research (e.g. supernova explosion) and engineering applications (e.g. inertial confinement fusion). Accurate theoretical solution of these interfacial fingers remains as an unsolved and challenging problem since Taylor's seminal work more than seven decades ago. This paper reports a unified theory established for such phenomena by combining the classical potential-flow theory and a dual-source model to address the long-standing difficulty highlighted by the initial-value sensitivity and strong nonlinearity. It is the first time for a theory to accurately predict the long-time developments in both growth rate and shape curvature of interfacial fingers at all density ratios in two and three dimensions. Moreover, the new theory clearly reveals the nonlinear coupling mechanism for interfacial evolution, and especially explains the origin of overshot in the growth rate curve.

The highly nonlinear evolution of the single-mode stratified compressible Rayleigh–Taylor instability (RTI) is investigated via direct numerical simulation over a range of Atwood numbers ($A_T=0.1$–$0.9$) and Mach numbers ($Ma=0.1$–$0.7$) for characterising the isothermal background stratification. After the potential stage, it is found that the bubble is accelerated to a velocity which is well above the saturation value predicted in the potential flow model. Unlike the bubble re-acceleration behaviour in quasi-incompressible RTI with uniform background density, the characteristics in the stratified compressible RTI are driven by not only vorticity accumulation inside the bubble but also flow compressibility resulting from the stratification. Specifically, in the case of strong stratification and high$A_T$, the flow compressibility dominates the bubble re-acceleration characters. To model the effect of flow compressibility, we propose a novel model to reliably describe the bubble re-acceleration behaviours in the stratified compressible RTI, via introducing the dilatation into the classical model that takes into account only vorticity accumulation.

For a small sessile or pendant droplet it is generally assumed that gravity does not play any role once the Bond number is small. This is even assumed for evaporating binary sessile or pendant droplets, in which convective flows can be driven due to selective evaporation of one component and the resulting concentration and thus surface tension differences at the air–liquid interface. However, recent studies have shown that in such droplets gravity indeed can play a role and that natural convection can be the dominant driving mechanism for the flow inside evaporating binary droplets (Edwards et al., Phys. Rev. Lett., vol. 121, 2018, 184501; Li et al., Phys. Rev. Lett., vol. 122, 2019, 114501). In this study, we derive and validate a quasi-stationary model for the flow inside evaporating binary sessile and pendant droplets, which successfully allows one to predict the prevalence and the intriguing interaction of Rayleigh and/or Marangoni convection on the basis of a phase diagram for the flow field expressed in terms of the Rayleigh and Marangoni numbers.

We investigate the coupling effect of buoyancy and shear based on an annular centrifugal Rayleigh–Bénard convection (ACRBC) system in which two cylinders rotate with an angular velocity difference. Direct numerical simulations are performed in a Rayleigh number range $10^6\\leq Ra\\leq 10^8$, at fixed Prandtl number $Pr=4.3$, inverse Rossby number $Ro^{-1}=20$, and radius ratio $\\eta =0.5$. The shear, represented by the non-dimensional rotational speed difference $\\varOmega$, varies from $0$ to $10$, corresponding to an ACRBC without shear and a radially heated Taylor–Couette flow with only the inner cylinder rotating, respectively. A stable regime is found in the middle part of the interval for $\\varOmega$, and divides the whole parameter space into three regimes: buoyancy-dominated, stable and shear-dominated. Clear boundaries between the regimes are given by linear stability analysis, meaning the marginal state of the flow. In the buoyancy-dominated regime, the flow is a quasi-two-dimensional flow on the $r\\varphi$ plane; as shear increases, both the growth rate of instability and the heat transfer are depressed. In the shear-dominated regime, the flow is mainly on the $rz$ plane. The shear is so strong that the temperature acts as a passive scalar, and the heat transfer is greatly enhanced. The study shows that shear can stabilize buoyancy-driven convection, makes a detailed analysis of the flow characteristics in different regimes, and reveals the complex coupling mechanism of shear and buoyancy, which may have implications for fundamental studies and industrial designs.

The evolution of buoyancy-driven homogeneous variable-density turbulence (HVDT) at Atwood numbers up to 0.75 and large Reynolds numbers is studied by using high-resolution direct numerical simulations. To help understand the highly non-equilibrium nature of buoyancy-driven HVDT, the flow evolution is divided into four different regimes based on the behaviour of turbulent kinetic energy derivatives. The results show that each regime has a unique type of dependence on both Atwood and Reynolds numbers. It is found that the local statistics of the flow based on the flow composition are more sensitive to Atwood and Reynolds numbers compared to those based on the entire flow. It is also observed that, at higher Atwood numbers, different flow features reach their asymptotic Reynolds-number behaviour at different times. The energy spectrum defined based on the Favre fluctuations momentum has less large-scale contamination from viscous effects for variable-density flows with constant properties, compared to other forms used previously. The evolution of the energy spectrum highlights distinct dynamical features of the four flow regimes. Thus, the slope of the energy spectrum at intermediate to large scales evolves from -7/3 to -1 , as a function of the production-to-dissipation ratio. The classical Kolmogorov spectrum emerges at intermediate to high scales at the highest Reynolds numbers examined, after the turbulence starts to decay. Finally, the similarities and differences between buoyancy-driven HVDT and the more conventional stationary turbulence are discussed and new strategies and tools for analysis are proposed.

The linear stability of thermal buoyant flow in a fluid-saturated vertical porous slab is studied under the assumption of weak and strong horizontal heterogeneities of the permeability. The two end vertical isothermal boundaries are impermeable and some paradigmatic cases of linear, quadratic and exponential heterogeneity models are deliberated. The stability/instability of the basic flow is examined by carrying out a numerical solution of the governing equations for the disturbances as Gill's proof (A.E. Gill, J. Fluid Mech, vol. 35, 1969, pp. 545–547) of linear stability is found to be ineffective. The possibilities of base flow becoming unstable due to heterogeneity in permeability are recognized, in contrast to Gill's stability problem. The neutral stability curves are presented and the critical Darcy–Rayleigh number for the onset of convective instability is computed for different values of the variable permeability constant. The similarities and differences between different heterogeneity models on the stability of fluid flow are clearly discerned.

The unifying theory of scaling in thermal convection (Grossmann & Lohse, J. Fluid. Mech., vol. 407, 2000, pp. 27–56; henceforth the GL theory) suggests that there are no pure power laws for the Nusselt and Reynolds numbers as function of the Rayleigh and Prandtl numbers in the experimentally accessible parameter regime. In Grossmann & Lohse (Phys. Rev. Lett., vol. 86, 2001, pp. 3316–3319) the dimensionless parameters of the theory were fitted to 155 experimental data points by Ahlers & Xu (Phys. Rev. Lett., vol. 86, 2001, pp. 3320–3323) in the regime $3\\times 1{0}^{7} \\leq \\mathit{Ra}\\leq 3\\times 1{0}^{9} $ and $4\\leq \\mathit{Pr}\\leq 34$ and Grossmann & Lohse (Phys. Rev. E, vol. 66, 2002, p. 016305) used the experimental data point from Qiu & Tong (Phys. Rev. E, vol. 64, 2001, p. 036304) and the fact that $\\mathit{Nu}(\\mathit{Ra}, \\mathit{Pr})$ is independent of the parameter $a$ , which relates the dimensionless kinetic boundary thickness with the square root of the wind Reynolds number, to fix the Reynolds number dependence. Meanwhile the theory is, on the one hand, well-confirmed through various new experiments and numerical simulations; on the other hand, these new data points provide the basis for an updated fit in a much larger parameter space. Here we pick four well-established (and sufficiently distant) $\\mathit{Nu}(\\mathit{Ra}, \\mathit{Pr})$ data points and show that the resulting $\\mathit{Nu}(\\mathit{Ra}, \\mathit{Pr})$ function is in agreement with almost all established experimental and numerical data up to the ultimate regime of thermal convection, whose onset also follows from the theory. One extra $\\mathit{Re}(\\mathit{Ra}, \\mathit{Pr})$ data point is used to fix $\\mathit{Re}(\\mathit{Ra}, \\mathit{Pr})$ . As $\\mathit{Re}$ can depend on the definition and the aspect ratio, the transformation properties of the GL equations are discussed in order to show how the GL coefficients can easily be adapted to new Reynolds number data while keeping $\\mathit{Nu}(\\mathit{Ra}, \\mathit{Pr})$ unchanged.

This paper investigates the multilayer Rayleigh–Taylor instability (RTI) using statistically stationary experiments conducted in a gas tunnel. Employing diagnostics such as particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF), we make simultaneous velocity–density measurements to study how dynamics and mixing are linked in this variable density flow. Experiments are conducted in a newly built, blow-down three-layer gas tunnel facility. Mixing between three gas streams is studied, where the top and bottom streams are comprised of air, and the middle stream is an air–helium mixture. Shear is minimized between these streams by matching their inlet velocities. The four experimental conditions investigated here consist of two different density ratios (Atwood numbers 0.3 and 0.6), each investigated at two instability development times (or equivalently, two streamwise locations), and all experiments are with the same middle stream thickness of 3 cm. The growth of the middle layer is measured using laser-based planar Mie scattering visualization. The mixing width is found to grow linearly with time at late times. Various quantitative measures of molecular mixing indicate a very high degree of molecular mixing at late times in the multilayer RTI flow. The vertical turbulent mass flux $a_y$ is calculated. In addition to mostly negative values of $a_y$, typical of buoyancy-dominated flows due to negative correlation between velocity and density fluctuations, positive regions are also observed in profiles of $a_y$ due to entrainment and erosion at the lower edge of the mixing region. Global energy budgets are calculated for the multilayer RTI flow at late times and it is found that the majority of potential energy released has been dissipated due to viscous effects, and a large value of mixing efficiency ($\\sim$60 %) is observed.

We examine experimentally the influence of non-Darcy effects on convective dissolution in Hele-Shaw cells. We focus on buoyancy-driven convection, where the flow is controlled by the Rayleigh–Darcy number, $Ra$ , which measures the strength of convection compared to diffusion. The Hele-Shaw cell is suitable to mimic Darcy flows only under certain geometrical constraints, and a recent theoretical work (Letelier et al., J. Fluid Mech., vol. 864, 2019, pp. 746–767) demonstrated that a precise limit exists for the parameter $\\unicode[STIX]{x1D716}^{2}Ra$ – $\\unicode[STIX]{x1D716}\\sim$ thickness-to-height ratio – beyond which the flow exhibits non-Darcy effects. In this work, we run experiments for solute convection in Rayleigh–Bénard-like configuration. We examine a wide range of the parameters space $(Ra,\\unicode[STIX]{x1D716})$ and we clearly identify the application limits of Darcy flow assumptions. Besides confirming previous theoretical predictions, current results are of relevance in the context of porous media flows – which are often studied experimentally with Hele-Shaw set-ups. Using our original datasets, we have been able to explain and reconcile the discrepancies observed between scaling laws previously proposed for Rayleigh–Bénard-like experiments and simulations in similar contexts. Specifically, we attribute an important role to the parameter $\\unicode[STIX]{x1D716}^{2}Ra$ , which clearly establishes thresholds beyond which Hele-Shaw experiment results are influenced by three-dimensional effects.