Suppression of Rayleigh–Bénard convection and restratification by horizontal convection

We investigate the competition between horizontal convection (HC) and Rayleigh–Bénard convection (RBC) in a fluid layer subject to a uniform destabilising buoyancy flux at the bottom and a horizontally varying buoyancy distribution at the top. The RBC forcing imposes negative horizontal mean vertical buoyancy gradients at the top and bottom of the fluid layer. But if the HC forcing is sufficiently strong then the volume-averaged vertical buoyancy gradient, left angle bracket b Subscript z Baseline right angle bracket ⟨ b z ⟩ bz , is positive i.e. opposite in sign to destabilising RBC buoyancy gradients at the boundaries. If left angle bracket b Subscript z Baseline right angle bracket greater than 0 ⟨ b z ⟩ > 0 bz > 0 we say that the layer has been ‘restratified’. Using scaling analysis based on power integrals together with two-dimensional direct numerical simulations at Rayleigh numbers up to 10 Superscript 10 10 10 10¹⁰ , we identify two cases: a neutral stratification state, in which HC first offsets RBC so that left angle bracket b Subscript z Baseline right angle bracket equals 0 ⟨ b z ⟩ = 0 bz = 0 , and a strong stratification regime, in which HC dominates and left angle bracket b Subscript z Baseline right angle bracket ⟨ b z ⟩ bz is opposite in sign, and greater in magnitude, than the prescribed destabilising vertical buoyancy gradient at the layer boundaries. For the range of parameters explored in this study, we derive scaling laws for the onset of these regimes in terms of the horizontal and vertical flux Rayleigh numbers, upper R a Subscript upper H R a H RaH and upper R a Subscript upper V <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core