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Register a new userUniversal fluctuations in the bulk of Rayleigh-Benard turbulence
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We present an investigation of the root-mean-square (rms) temperature $sigma_T$ and the rms velocity $sigma_w$ in the bulk of Rayleigh-Benard turbulence, using new experimental data from the current study and experimental and numerical data from previous studies. We find that, once scaled by the convective temperature $theta_*$, the value of $sigma_T$ at the cell centre is a constant, i.e. $sigma_{T,c}/theta_* approx 0.85$, over a wide range of the Rayleigh number ($10^{8}leq Raleq 10^{15}$) and the Prandtl number ($0.7leq Pr leq 23.34$), and is independent of the surface topographies of the top and bottom plates of the convection cell. A constant close to unity suggests that $theta_*$ is a proper measure of the temperature fluctuation in the core region. On the other hand, $sigma_{w,c}/w_*$, the vertical rms velocity at the cell centre scaled by the convective velocity $w_*$, shows a weak $Ra$-dependence ($sim Ra^{0.07pm0.02}$) over $10^8leq Raleq 10^{10}$ at $Prsim4.3$ and is independent of plate topography. Similar to a previous finding by He & Xia ({it Phys. Rev. Lett.,} vol. 122, 2019, 014503), we find that the rms temperature profile $sigma_T(z)/theta_*$ in the region of the mixing zone with a mean horizontal shear exhibits a power-law dependence on the distance $z$ from the plate, but now the universal profile applies to both smooth and rough surface topographies and over a wider range of $Ra$. The vertical rms velocity profile $sigma_w(z)/w_*$ obey a logarithmic dependence on $z$. The study thus demonstrates that the typical scales for the temperature and the velocity are the convective temperature $theta_*$ and the the convective velocity $w_*$, respectively. Finally, we note that $theta_*$ may be utilised to study the flow regime transitions in the ultra-high-$Ra$-number turbulent convection.
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We study numerically the melting of a horizontal layer of a pure solid above a convecting layer of its fluid rotating about the vertical axis. In the rotating regime studied here, with Rayleigh numbers of order $10^7$, convection takes the form of columnar vortices, the number and size of which depend upon the Ekman and Prandtl numbers, as well as the geometry -- periodic or confined. As the Ekman and Rayleigh numbers vary, the number and average area of vortices vary in inverse proportion, becoming thinner and more numerous with decreasing Ekman number. The vortices transport heat to the phase boundary thereby controlling its morphology, characterized by the number and size of the voids formed in the solid, and the overall melt rate, which increases when the lower boundary is governed by a no-slip rather than a stress-free velocity boundary condition. Moreover, the number and size of voids formed are relatively insensitive to the Stefan number, here inversely proportional to the latent heat of fusion. For small values of the Stefan number, the convection in the fluid reaches a slowly evolving geostrophic state wherein columnar vortices transport nearly all the heat from the lower boundary to melt the solid at an approximately constant rate. In this quasi-steady state, we find that the Nusselt number, characterizing the heat flux, co-varies with the interfacial roughness, for all the flow parameters and Stefan numbers considered here. This confluence of processes should influence the treatment of moving boundary problems, particularly those in astrophysical and geophysical problems where rotational effects are important.
Inertialess anisotropic particles in a Rayleigh-Benard turbulent flow show maximal tumbling rates for weakly oblate shapes, in contrast with the universal behaviour observed in developed turbulence where the mean tumbling rate monotonically decreases with the particle aspect ratio. This is due to the concurrent effect of turbulent fluctuations and of a mean shear flow whose intensity, we show, is determined by the kinetic boundary layers. In Rayleigh-Benard turbulence prolate particles align preferentially with the fluid velocity, while oblate ones orient with the temperature gradient. This analysis elucidates the link between particle angular dynamics and small-scale properties of convective turbulence and has implications for the wider class of sheared turbulent flows.
Direct numerical simulations are employed to reveal three distinctly different flow regions in rotating spherical Rayleigh-Benard convection. In the low-latitude region $mathrm{I}$ vertical (parallel to the axis of rotation) convective columns are generated between the hot inner and the cold outer sphere. The mid-latitude region $mathrm{II}$ is dominated by vertically aligned convective columns formed between the Northern and Southern hemispheres of the outer sphere. The diffusion-free scaling, which indicates bulk-dominated convection, originates from this mid-latitude region. In the equator region $mathrm{III}$ the vortices are affected by the outer spherical boundary and are much shorter than in region $mathrm{II}$. Thermally driven turbulence with background rotation in spherical Rayleigh-Benard convection is found to be characterized by three distinctly different flow regions. The diffusion-free scaling, which indicates the heat transfer is bulk-dominated, originates from the mid-latitude region in which vertically aligned vortices are stretched between the Northern and Southern hemispheres of the outer sphere. These results show that the flow physics in rotating convection are qualitatively different in planar and spherical geometries. This finding underlines that it is crucial to study convection in spherical geometries to better understand geophysical and astrophysical flow phenomena.
We analyse the nonlinear dynamics of the large scale flow in Rayleigh-Benard convection in a two-dimensional, rectangular geometry of aspect ratio $Gamma$. We impose periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. As Rayleigh number Ra increases, a large scale zonal flow dominates the dynamics of a moderate Prandtl number fluid. At high Ra, in the turbulent regime, transitions are seen in the probability density function (PDF) of the largest scale mode. For $Gamma = 2$, the PDF first transitions from a Gaussian to a trimodal behaviour, signifying the emergence of reversals of the zonal flow where the flow fluctuates between three distinct turbulent states: two states in which the zonal flow travels in opposite directions and one state with no zonal mean flow. Further increase in Ra leads to a transition from a trimodal to a unimodal PDF which demonstrates the disappearance of the zonal flow reversals. On the other hand, for $Gamma = 1$ the zonal flow reversals are characterised by a bimodal PDF of the largest scale mode, where the flow fluctuates only between two distinct turbulent states with zonal flow travelling in opposite directions.
Penetrative turbulence, which occurs in a convectively unstable fluid layer and penetrates into an adjacent, originally stably stratified layer, is numerically and theoretically analyzed. We chose the most relevant example, namely thermally driven flow of water with a temperature around $T_mapprox 4^circrm{C}$, where it has its density maximum. We pick the Rayleigh-Benard geometry with the bottom plate temperature $T_b > 4^circrm{C}$ and the top plate temperature $T_t le 4^circrm{C}$. Next to the overall thermal driving strength set by the temperature difference $Delta = T_b - T_t$ (the Rayleigh number $Ra$ in dimensionless form), the crucial new control parameter as compared to standard Rayleigh-Benard convection is the density inversion parameter $theta_m equiv (T_m - T_t ) / Delta$. The crucial response parameters are the relative mean mid-height temperature $theta_c$ and the overall heat transfer (i.e., the Nusselt number $Nu$). We theoretically derive the universal (i.e., $Ra$-independent) dependence $theta_c (theta_m) =(1+theta_m^2)/2$, which holds for $theta_m$ below a $Ra$-dependent critical value, beyond which $theta_c (theta_m)$ sharply decreases and drops down to $theta_c=1/2$ at $theta_m=theta_{m,c}$. Our direct numerical simulations with $Ra$ up to $10^{10}$ are consistent with these results. The critical density inversion parameter $theta_{m,c}$ can be precisely predicted by a linear stability analysis. The heat flux $Nu(theta_m)$ monotonically decreases with increasing $theta_m$ and we can theoretically derive a universal relation for the relative heat flux $Nu(theta_m)/Nu(0)$. Finally, we numerically identify and discuss rare transitions between different turbulent flow states for large $theta_m$.
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