Transient Behaviour of Natural Convection in a Reservoir Model Induced by Surface Heating

We perform detailed numerical simulations of natural convection in a reservoir model induced by surface heating. The transient behaviour of the flow, including streamlines, isotherms, surface velocity profiles, volumetric flow rates, heat transfer rates, and temperature averaged over the local water depth are presented at different Rayleigh numbers. At an instantaneous time within the sloping bottom region, the surface velocity initially increases and then decreases with an increase of the offshore distance. Over a certain range of Rayleigh numbers, the location of the peak surface velocity may initially move in the offshore direction and then retract with the elapse of time. The point at which the rates of horizontal conduction and convection balance also retracts towards the tip region with the elapse of time. Some insight into understanding the mechanisms that drive the flow is provided according to the detailed transient behaviour of the flow.