Suppression of Rayleigh-Benard convection and restratification induced by horizontal convection

Despite the large flux Rayleigh number ($Ra_F \sim 10^{24}$) from geothermal heating, Rayleigh–Bénard convection (RBC) does not occur in the ocean, which remains stably stratified due to horizontal convection (HC) driven by the surface pole-to-equator temperature gradient ($\sim 30 K$), alongside winds and tides.

To understand how stratification is shaped from the interplay between RBC and HC, we study a fluid layer subject to bottom heating and a top sinusoidal buoyancy profile driving HC.

Using two-dimensional direct numerical simulations and theoretical analysis, we derive scaling laws for the mean vertical stratification ($\langle b_z \rangle$).

We find a sharp transition from RBC- to HC-dominated dynamics when both forcings are comparable, consistent with Couston et al. (2022).

Two asymptotic regimes are obtained: a neutral stratification regime ($\langle b_z \rangle = 0$), controlled by top flux transfer, and a strong stratification regime, where HC produces positive stratification sufficient to reverse the bottom flux.

These results show how HC suppresses RBC even under geothermal forcing, providing a framework for interpreting oceanic stratification in the presence of bottom heating.