The effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh-B\'enard convection

TL;DR

This study investigates how different velocity boundary conditions affect heat transfer and flow patterns in two-dimensional Rayleigh-Bénard convection, revealing significant impacts on flow types and heat transport across various parameters.

Contribution

It systematically analyzes the influence of no-slip, stress-free, and periodic boundary conditions on flow topology and heat transfer, highlighting their substantial effects in 2D Rayleigh-Bénard convection.

Findings

Heat transport varies with boundary conditions and aspect ratio.

Two flow types, roll-like and zonal, are identified with distinct dynamics.

Flow type depends heavily on boundary conditions and affects heat transfer.

Abstract

The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-B\'enard convection. Combinations of no-slip, stress-free and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers Ra between $10^8$ and $10^{11}$ the heat transport is lower for $\Gamma = 0.33$ than for $\Gamma = 1$ in case of no-slip sidewalls. This is surprisingly opposite for stress-free sidewalls, where the heat transport increases for lower aspect-ratio. In wider cells the aspect-ratio dependence is observed to disappear for $\text{Ra} \ge 10^{10}$. Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and horizontal zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll-like. In two-dimensional Rayleigh-B\'enard convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.