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 ( 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 10¹⁰ . 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→ ∞ . 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 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 Ra for Pr=1 . When the shear is present with Pr 3 , 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–Bénard convection without large-scale shear. We find that the Nusselt numbers grow proportionally to Ra0.077 when Pr=3 and to Ra0.19 when Pr=10 . Analogies with tokamak plasmas are described.