Related papers: "Ultimate state" of two-dimensional Rayleigh-Benar…
We prove the first rigorous bound on the heat transfer for three-dimensional Rayleigh-B\'enard convection of finite-Prandtl-number fluids between free-slip boundaries with an imposed heat flux. Using the auxiliary functional method with a…
We are concerned with infinite Prandtl number Rayleigh--B\'enard convection with Navier-slip boundary conditions. The goal of this work is to estimate the average upward heat flux measured by the nondimensional Nusselt number $Nu$ in terms…
The non-hydrostatic, quasigeostrophic approximation for rapidly rotating Rayleigh-B\'enard convection admits a class of exact `single mode' solutions. These solutions correspond to steady laminar convection with a separable structure…
The central open question about Rayleigh--B\'enard convection -- buoyancy-driven flow in a fluid layer heated from below and cooled from above -- is how vertical heat flux depends on the imposed temperature gradient in the strongly…
Steady flows that optimize heat transport are obtained for two-dimensional Rayleigh-B\'enard convection with no-slip horizontal walls for a variety of Prandtl numbers $Pr$ and Rayleigh number up to $Ra\sim 10^9$. Power law scalings of…
We study Rayleigh B\'enard convection based on the Boussinesq approximation. We are interested in upper bounds on the Nusselt number $\mathrm{Nu}$, the upwards heat transport, in terms of the Rayleigh number $\mathrm{Ra}$, that…
We study the effects of Prandtl number $Pr$ and Rayleigh number $Ra$ in two-dimensional Rayleigh-B\'enard convection without boundaries, i.e. with periodic boundary conditions. In the limits of $Pr \to 0$ and $\infty$, we find that the…
The Rayleigh-Benard theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] is extended towards very large Prandtl numbers Pr. The Nusselt number Nu is found here to be independent of Pr. However, for fixed Rayleigh numbers Ra>…
We revisit the optimal heat transport problem for Rayleigh-B\'enard convection in which a rigorous upper bound on the Nusselt number, $Nu$, is sought as a function of the Rayleigh number $Ra$. Concentrating on the 2-dimensional problem with…
Bounds on heat transfer have been the subject of previous studies concerning convection in the Boussinesq approximation: in the Rayleigh-B\'enard configuration, the first result obtained by \cite{howard63} states that $Nu < (3/64 \…
We present experimental heat transport measurements of turbulent Rayleigh-B\'{e}nard convection with rotation about a vertical axis. The fluid, water with Prandtl number ($\sigma$) about 6, was confined in a cell which had a square cross…
New bounds are proven on the mean vertical convective heat transport, $\overline{\langle wT \rangle}$, for uniform internally heated (IH) convection in the limit of infinite Prandtl number. For fluid in a horizontally-periodic layer between…
Results from direct numerical simulation for three-dimensional Rayleigh-B\'enard convection in samples of aspect ratio $\Gamma=0.23$ and $\Gamma=0.5$ up to Rayleigh number $Ra=2\times10^{12}$ are presented. The broad range of Prandtl…
The heat transport in rotating Rayleigh-B\'enard convection is considered in the limit of rapid rotation (small Ekman number $E$) and strong thermal forcing (large Rayleigh number $Ra$). The analysis proceeds from a set of asymptotically…
We report experimental results for heat-transport measurements, in the form of the Nusselt number \Nu, by turbulent Rayleigh-B\'enard convection in a cylindrical sample of aspect ratio $\Gamma \equiv D/L = 0.50$ ($D = 1.12$ m is the…
Steady but generally unstable solutions of the 2D Boussinesq equations are obtained for no-slip boundary conditions and Prandtl number 7. The primary solution that bifurcates from the conduction state at Rayleigh number $Ra \approx 1708$…
We investigate the influence of the thermal properties of the boundaries in turbulent Rayleigh-B\'enard convection on analytical upper bounds on convective heat transport. We model imperfectly conducting bounding plates in two ways: using…
We prove a new rigorous upper bound on the vertical heat transport for B\'enard-Marangoni convection of a two- or three-dimensional fluid layer with infinite Prandtl number. Precisely, for Marangoni number $Ma \gg 1$ the Nusselt number $Nu$…
The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number…
We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is $Ra = \left[10^6, 10^8…