Convectively driven shear and decreased heat flux

We report on direct numerical simulations of two-dimensional, horizontally periodic Rayleigh–Bénard convection between free-slip boundaries. We focus on the ability of the convection to drive large-scale horizontal flow that is vertically sheared. For the Prandtl numbers ($\mathit{Pr}$) between 1 and 10 simulated here, this large-scale shear can be induced by raising the Rayleigh number ($\mathit{Ra}$) sufficiently, and we explore the resulting convection for $\mathit{Ra}$ 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 $\mathit{Ra}\rightarrow \infty$. 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 $\mathit{Ra}$. When the large-scale shear is present with $\mathit{Pr}\lesssim 2$, 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 $\mathit{Ra}$ for $\mathit{Pr}=1$. When the shear is present with $\mathit{Pr}\gtrsim 3$, the flow does not burst, and convective heat transport is sustained at all times. Nusselt numbers then grow roughly as powers of $\mathit{Ra}$, but the growth rates are slower than any previously reported for Rayleigh–Bénard convection without large-scale shear. We find that the Nusselt numbers grow proportionally to $\mathit{Ra}^{0.077}$ when $\mathit{Pr}=3$ and to $\mathit{Ra}^{0.19}$ when $\mathit{Pr}=10$. Analogies with tokamak plasmas are described.