Rotating planar gravity currents at moderate Rossby numbers: fully resolved simulations and shallow-water modelling

摘要

The flow of a gravity current of finite volume and density released from rest from a rectangular lock (of height) into an ambient fluid of density $unicode[STIX] in a system rotating with about the vertical is investigated by means of fully resolved direct numerical simulations (DNS) and a theoretical model (based on shallow-water and Ekman layer spin-up theories, including mixing). The motion of the dense fluid includes several stages: propagation in the direction accompanied by Coriolis acceleration/deflection in the direction, which produces a quasi-steady wedge-shaped structure with significant anticyclonic velocity, followed by a spin-up reduction of accompanied by a slow drift, and oscillation. The theoretical model aims to provide useful insights and approximations concerning the formation time and shape of wedge, and the subsequent spin-up effect. The main parameter is the Coriolis number, is the reduced gravity. The DNS results are focused on a range of relatively small Coriolis numbers, (i.e. Rossby number) in the range, and a large range of Schmidt numbers; the Reynolds number is large in all cases. The current spreads out in the direction until it is arrested by the Coriolis effect (in revolution of the system). A complex motion develops about this state. First, we record oscillations on the inertial time scale (which are a part of the geostrophic adjustment), accompanied by vortices at the interface. Second, we note the spread of the wedge on a significantly longer time scale; this is an indirect spin-up effect - mixing and entrainment reduce the lateral (angular) velocity, which in turn decreases the Coriolis support to the slope of the wedge shape. Contrary to non-rotating gravity currents, the front does not remain sharp as it is subject to (i) local stretching along the streamwise direction and (ii) convective mixing due to Kelvin-Helmholtz vortices generated by shear along the spanwise direction and stemming from Coriolis effects. The theoretical