On the response of a reservoir sidearm to diurnal heating and cooling

Abstract

During the day, the shallower regions of a reservoir sidearm absorb more heat per unit volume than the deeper parts, leading to a horizontal pressure gradient that drives a circulation in the sidearm. At night, the shallow regions cool more rapidly, leading to a circulation in the opposite direction. Since the spin-up time of a typical sidearm is at least of the same order as a day, the flow within a diurnally forced sidearm is principally an inertia–buoyancy balance. In this paper, a diurnally forced sidearm is modelled by periodically forced natural convection in a triangular cavity. The periodic forcing enters the model via an internal heating/cooling term in the temperature equation. Reservoir sidearms typically have small bottom slopes and this fact can be exploited to obtain asymptotic solutions of the resulting equations. These solutions clearly demonstrate the transition from the viscous-dominated flow in the shallows to the inertia-dominated flow in the deeper parts. In the inertia-dominated region, the flow response significantly lags the forcing. Numerical solutions of the full nonlinear problem are consistent with the asymptotic solutions.