A scaling analysis of transient natural convection in a reservoir model induced by iso-flux heating

摘要

This study presents a detailed scaling analysis quantifying the transient behaviour of natural convection in a reservoir model induced by iso-flux surface heating. It is found that horizontal conduction, which has often been neglected in previous analyses, plays an important role in the development of the flow. Depending on the Rayleigh number, three possible pathways through which the flow develops towards the final steady state are identified. A thermal boundary layer initially grows downwards from the surface. When the thermal boundary layer reaches the sloping bottom and becomes indistinct, a horizontal temperature gradient establishes due to the increasing water depth in the offshore direction. A flow is then driven towards the offshore direction by a buoyancy-induced horizontal pressure gradient, which convects away the heat input from the water surface. On the other hand, the horizontal temperature gradient also conducts heat away. The flow behaviour is determined by the interaction between the horizontal conduction and convection. An interesting flow feature revealed by the present scaling analysis is that the region across which the thermal boundary layer encompasses the full water depth shrinks over time at a certain stage of the flow development. The shrinking process eventually stops when this region coincides with a conduction-dominated subregion. The present scaling results are verified by corresponding numerical simulations.