Bolgiano-Obukhov scaling in two-dimensional Rayleigh-Bénard convection at extreme Rayleigh numbers

Through high-resolution direct numerical simulations, we demonstrate that energy transfers in two-dimensional (2D) thermal convection exhibit Bolgiano-Obukhov scaling. This is in contrast with convection in three dimensions which follows the Kolmogorov-Obukhov phenomenology. This difference arises from the presence of inverse cascade in 2D which leads to a negative kinetic energy flux at small wavenumbers. The magnitude of this flux decreases with wavenumber due to the effect of buoyancy. We also demonstrate that entropy dissipation in the thermal boundary layers displays a scaling law that is observable from the entropy flux curves.