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

The flow of a gravity current of finite volume and density ro1 released from rest from a rectangular lock (of height h0) into an ambient fluid of density ro0 (Ekman layer spin-up theories, including mixing). The motion of the dense fluid includes several stages: propagation in the x-direction accompanied by Coriolis acceleration/deflection in the y-direction, which produces a quasi-steady wedge-shaped structure with significant anticyclonic velocity v, followed by a spin-up reduction of v accompanied by a slow x 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. The DNS results are focused on a range of relatively small Coriolis numbers, 0.1 <= C <= 0:25 (i.e. Rossby number Ro in the range 2-5), and a large range of Schmidt numbers; the Reynolds number is large in all cases. The current spreads out in the x direction until it is arrested by the Coriolis effect (in 1/4 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 dh/dx 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 model predicts that the length of the wedge scales as C^2/3 (in contrast to the Rossby radius 1/C which is relevant for large C; and in contrast to C^1/2 for the axisymmetric lens).