On axisymmetric rotating gravity currents: two-layer shallow-water and numerical solutions

Axisymmetric gravity currents released from behind a lock over a solid horizontal bottom in a system rotating about a vertical axis are investigated. The major parameters are , the ratio of Coriolis to inertia forces, and H , the ratio of the total height of the ambient fluid into which propagation occurs to the initial height of the dense fluid inside the lock. We focus attention on the small , almost inviscid case in which a significant radius of propagation is obtained. A two-layer shallow-water inviscid approximation is developed and it is shown that the angular velocities in the upper and lower layers are coupled by simple relationships which can be used to simplify both the time-dependent and the steady-state lens solutions. However, the major features predicted by the two-layer model differ only slightly from these obtained with a one-layer model. Finite-difference solutions of the full Navier–Stokes equations are also presented and compared with the shallow-water approximations.