High resolution simulation revealing Ra1/4 scaling regime for Nusselt number in horizontal convection

A non-uniform thermal forcing imposed along a horizontal boundary gives rise to horizontal convective flow, which finds application as a simple model to study ocean circulation, the Earth’s mantle convection and industrial processes. The strength of thermal forcing is characterised by the Rayleigh number. At high Rayleigh numbers, horizontal convection is convectively dominant, featuring thin thermal and velocity boundary layers adjacent to the forcing boundary. At sufficiently high Rayleigh numbers, horizontal convection flow has been observed to become unsteady. The scaling of Nusselt number, quantifying heat transport, and the Rayleigh number quantifying thermal forcing, yields a 1/5-power scaling which is well understood at low Rayleigh number. In this study, a high-order spectral element solver is used to study horizontal convection at high Rayleigh number within a rectangular enclosure with buoyancy forcing imposed along a horizontal forcing boundary. These high-resolution simulations provide insight into the dynamics of horizontal convection at high Rayleigh number to reveal the existence of a 1/4-power scaling. This 1/4- regime is generated by the horizontal convection of cooler fluid over the hot end of the forcing boundary, spontaneous plume eruptions upstream of the enclosure end-wall carry heat directly into the interior overturning flow. This violates Rossby’s balance between vertical thermal diffusion from the boundary into the adjacent boundary layer and the horizontal transport of heat within the boundary layer.