Convectively driven shear and decreased heat flux

TL;DR

This study uses direct numerical simulations to show how large-scale shear driven by Rayleigh-Bénard convection influences heat flux and flow dynamics, revealing new scaling laws and oscillatory behaviors at high Rayleigh numbers.

Contribution

It demonstrates the emergence of large-scale shear in 2D convection at high Rayleigh numbers and quantifies its impact on heat transport and flow oscillations, providing new scaling laws.

Findings

Shear accounts for most kinetic energy at high Ra.

Shear reduces vertical heat flux and causes bursty transport at low Pr.

Nusselt number scales as Ra^{0.077} for Pr=3 and Ra^{0.19} for Pr=10.

Abstract

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 ($Pr$) between 1 and 10 simulated here, this large-scale shear can be induced by raising the Rayleigh number ($Ra$) sufficiently, and we explore the resulting convection for $Ra$ up to $10^{10}$. When present in our simulations, the sheared mean flow accounts for a large fraction of the total kinetic energy, and this fraction tends towards unity as $Ra\to\infty$. The shear helps disperse convective structures, and it reduces vertical heat flux; in parameter regimes where one state with large-scale shear and one without are both stable, the Nusselt number of the state with shear is smaller and grows more slowly with $Ra$. When the large-scale shear is present with $Pr\lesssim2$, the convection undergoes strong global oscillations on long timescales, and heat transport occurs in bursts. Nusselt numbers, time-averaged over these bursts, vary non-monotonically with $Ra$ for $Pr=1$. When the shear is present with $Pr\gtrsim3$, the flow does not burst, and convective heat transport is sustained at all times. Nusselt numbers then grow roughly as powers of $Ra$, but the growth rates are slower than any previously reported for Rayleigh-B\'enard convection without large-scale shear. We find the Nusselt numbers grow proportionally to $Ra^{0.077}$ when $Pr=3$ and to $Ra^{0.19}$ when $Pr=10$. Analogies with tokamak plasmas are described.