Vorticity dynamics during the start-up phase of gravity currents

The flow during the start-up phase of two-dimensional gravity currents is investigated by numerical simulations. The focus of the study is on the dynamics of the initially vertical density interface which is deformed by the developing convective motion. Two different cases are considered, namely the lock-exchange flow and the release of a finite volume of dense fluid in deep surroundings. The viscous problem is addressed by direct numerical simulations based on the Boussinesq equations, which are integrated by high-order numerical schemes. The direct simulations are supplemented by vortex dynamics simulations using a vortex blob technique in order to study the underlying inviscid dynamics. Several distinct features of starting gravity currents are identified, among these the formation of start-up vortices very similar in nature to those observed for unstratified vortex sheets of finite extent. Moreover, the flow is shown to develop a pronounced Kelvin-Helmholtz-like instability at the interface, the details of which strongly depend on the ratio of buoyancy forces to viscous forces.