Heat transfer and stability of horizontal convection with a moving forcing boundary

Horizontal convection describes a buoyancy-driven flow driven by a non-uniform supply of buoyancy across a horizontal forcing boundary achieved by a combination of heating and cooling. Horizontal convection establishes a horizontal flow in a thin boundary layer adjacent to the forcing boundary, and an overturning circulation is completed by way of a diffuse slow-moving return flow outside of the forcing boundary layer. Horizontal convection bears some similarity to global ocean currents, and so this fundamental study considers a second driving mechanism in conjunction with buoyancy, horizontal movement of the forcing boundary, as a model for wind-driven forcing on the flow. We characterize the combinations of Rayleigh number for buoyancy forcing and Reynolds number for mechanical forcing that produce three distinct regimes of behaviour: a forced-convection regime at high Reynolds numbers and low Rayleigh numbers, a mixed regime, and a free-convection regime dominated by Rayleigh number.