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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.
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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.
Rayleigh--Taylor fluid turbulence through a bed of rigid, finite-size, spheres is investigated by means of high-resolution Direct Numerical Simulations (DNS), fully coupling the fluid and the solid phase via a state-of-the art Immersed Boundary Method (IBM). The porous character of the medium reveals a totally different physics for the mixing process when compared to the well-known phenomenology of classical RT mixing. For sufficiently small porosity, the growth-rate of the mixing layer is linear in time (instead of quadratical) and the velocity fluctuations tend to saturate to a constant value (instead of linearly growing). We propose an effective continuum model to fully explain these results where porosity originated by the finite-size spheres is parameterized by a friction coefficient.
Using direct numerical simulations, we study the statistical properties of reversals in two-dimensional Rayleigh-Benard convection for infinite Prandtl number. We find that the large-scale circulation reverses irregularly, with the waiting time between two consecutive genuine reversals exhibiting a Poisson distribution on long time scales, while the interval between successive crossings on short time scales shows a power law distribution. We observe that the vertical velocities near the sidewall and at the center show different statistical properties. The velocity near the sidewall shows a longer autocorrelation and $1/f^2$ power spectrum for a wide range of frequencies, compared to shorter autocorrelation and a narrower scaling range for the velocity at the center. The probability distribution of the velocity near the sidewall is bimodal, indicating a reversing velocity field. We also find that the dominant Fourier modes capture the dynamics at the sidewall and at the center very well. Moreover, we show a signature of weak intermittency in the fluctuations of velocity near the sidewall by computing temporal structure functions.
We present mesoscale numerical simulations of Rayleigh-Benard (RB) convection in a two-dimensional model emulsion. The systems under study are constituted of finite-size droplets, whose concentration Phi_0 is systematically varied from small (Newtonian emulsions) to large values (non-Newtonian emulsions). We focus on the characterisation of the heat transfer properties close to the transition from conductive to convective states, where it is known that a homogeneous Newtonian system exhibits a steady flow and a time-independent heat flux. In marked contrast, emulsions exhibit a non-steady dynamics with fluctuations in the heat flux. In this paper, we aim at the characterisation of such non-steady dynamics via detailed studies on the time-averaged heat flux and its fluctuations. To understand the time-averaged heat flux, we propose a side-by-side comparison between the emulsion system and a single-phase (SP) system, whose viscosity is constructed from the shear rheology of the emulsion. We show that such local closure works well only when a suitable degree of coarse-graining (at the droplet scale) is introduced in the local viscosity. To delve deeper into the fluctuations in the heat flux, we propose a side-by-side comparison between a Newtonian emulsion and a non-Newtonian emulsion, at fixed time-averaged heat flux. This comparison elucidates that finite-size droplets and the non-Newtonian rheology cooperate to trigger enhanced heat-flux fluctuations at the droplet scales. These enhanced fluctuations are rooted in the emergence of space correlations among distant droplets, which we highlight via direct measurements of the droplets displacement and the characterisation of the associated correlation function. The observed findings offer insights on heat transfer properties for confined systems possessing finite-size constituents.
Steady flows that optimize heat transport are obtained for two-dimensional Rayleigh-Benard convection with no-slip horizontal walls for a variety of Prandtl numbers $Pr$ and Rayleigh number up to $Rasim 10^9$. Power law scalings of $Nusim Ra^{gamma}$ are observed with $gammaapprox 0.31$, where the Nusselt number $Nu$ is a non-dimensional measure of the vertical heat transport. Any dependence of the scaling exponent on $Pr$ is found to be extremely weak. On the other hand, the presence of two local maxima of $Nu$ with different horizontal wavenumbers at the same $Ra$ leads to the emergence of two different flow structures as candidates for optimizing the heat transport. For $Pr lesssim 7$, optimal transport is achieved at the smaller maximal wavenumber. In these fluids, the optimal structure is a plume of warm rising fluid which spawns left/right horizontal arms near the top of the channel, leading to downdrafts adjacent to the central updraft. For $Pr > 7$ at high-enough Ra, the optimal structure is a single updraft absent significant horizontal structure, and characterized by the larger maximal wavenumber.
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