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Related papers: Wall-to-wall optimal transport in two dimensions

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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 $Nu$…

Fluid Dynamics · Physics 2020-01-01 Giovanni Fantuzzi , Camilla Nobili , Andrew Wynn

A systematic theory for the scaling of the Nusselt number $Nu$ and of the Reynolds number $Re$ in strong Rayleigh-Benard convection is suggested and shown to be compatible with recent experiments. It assumes a coherent large scale…

chao-dyn · Physics 2017-05-17 Siegfried Grossmann , Detlef Lohse

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…

Fluid Dynamics · Physics 2015-05-13 Yuanming Liu , Robert E. Ecke

In this paper we estimate the relative strengths of various terms of the Rayleigh-B\'enard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity, $U$, or the P\'eclet number that…

Fluid Dynamics · Physics 2016-11-29 Ambrish Pandey , Abhishek Kumar , Anando G. Chatterjee , Mahendra K. Verma

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 $Ra \approx 1708$…

Fluid Dynamics · Physics 2015-06-11 Fabian Waleffe , Anakewit Boonkasame , Leslie M. Smith

Penetrative turbulent Rayleigh-B\'enard convection which depends on the density maximum of water near $4^\circ\rm{C}$ is studied using two-dimensional (2D) and three-dimensional (3D) direct numerical simulations (DNS). The working fluid is…

Fluid Dynamics · Physics 2019-06-26 Qi Wang , Quan Zhou , Zhen-Hua Wan , De-Jun Sun

We report the statistical properties of temperature and thermal energy dissipation rate in low-Prandtl number turbulent Rayleigh-B\'enard convection. High resolution two-dimensional direct numerical simulations were carried out for the…

Fluid Dynamics · Physics 2019-12-12 Ao Xu , Le Shi , Heng-Dong Xi

Heat transport in highly turbulent convection is not well understood. In this paper, we simulate compressible convection in a box of aspect ratio 4 using computationally-efficient MacCormack-TVD finite difference method on single and…

Fluid Dynamics · Physics 2024-11-18 Harshit Tiwari , Lekha Sharma , Mahendra K. Verma

We report on direct numerical simulations of two-dimensional, horizontally periodic Rayleigh-B\'enard convection, focusing on its ability to drive large-scale horizontal flow that is vertically sheared. For the Prandtl numbers ($Pr$)…

Fluid Dynamics · Physics 2015-11-20 David Goluskin , Hans Johnston , Glenn R. Flierl , Edward A. Spiegel

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…

Fluid Dynamics · Physics 2010-08-17 Ralf W. Wittenberg

It is shown using three series of Rayleigh number simulations of varying aspect ratio AR and Prandtl number Pr that the normalized dissipation at the wall, while significantly greater than 1, approaches a constant dependent upon AR and Pr.…

Chaotic Dynamics · Physics 2009-10-31 Robert M. Kerr

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 \…

Fluid Dynamics · Physics 2024-03-08 T. Alboussière , Y. Ricard , S. Labrosse

This study investigates the effect of compliant walls on the turbulent heat transfer in channel flows over viscous-hyperelastic walls. We perform Direct Numerical Simulations, fully resolving the mutual fluid-structure interactions between…

Fluid Dynamics · Physics 2026-04-02 Morie Koseki , Marco Edoardo Rosti

Two-dimensional direct numerical simulations are conducted for convection sustained by uniform internal heating in a horizontal fluid layer. Top and bottom boundary temperatures are fixed and equal. Prandtl numbers range from 0.01 to 100,…

Fluid Dynamics · Physics 2015-03-13 David Goluskin , Edward A. Spiegel

In this paper, we have used the QUICK scheme of the finite volume method to investigate the problem of steady 2-D free convective incompressible flow with heat and mass transfer in an inclined rectangular domain at different Rayleigh…

Fluid Dynamics · Physics 2017-08-28 V. Ambethkar , D. Kushawaha

We investigate states of rapidly rotating Rayleigh-B\'enard convection in a cylindrical cell over a range of Rayleigh number $3\times10^5\leq Ra \leq 5\times10^{9}$ and Ekman number $10^{-6} \leq Ek \leq 10^{-4}$ for Prandtl number $Pr =…

Fluid Dynamics · Physics 2024-04-16 Xuan Zhang , Philipp Reiter , Olga Shishkina , Robert E. Ecke

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…

Analysis of PDEs · Mathematics 2026-03-24 Christian Seis

An equation for the evolution of mean kinetic energy, $ E $, in a 2-D or 3-D Rayleigh-B\'enard system with domain height $ L $ is derived. Assuming classical Nusselt number scaling, $ Nu \sim Ra^{1/3} $, and that mean enstrophy, in the…

Fluid Dynamics · Physics 2025-11-05 Erik Lindborg

The Rayleigh (Ra) and Prandtl (Pr) number scaling of the Nusselt number Nu, the Reynolds number Re, the temperature fluctuations, and the kinetic and thermal dissipation rates is studied for (numerical) homogeneous Rayleigh-Benard…

Chaotic Dynamics · Physics 2007-05-23 Enrico Calzavarini , Detlef Lohse , Federico Toschi , Raffaele Tripiccione

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…

Analysis of PDEs · Mathematics 2014-12-17 Antoine Choffrut , Camilla Nobili , Felix Otto