Gravity currents propagating into ambients with arbitrary shear and density stratification: vorticity‐based modelling. (29th February 2016) - Nasr‐Azadani, M. M.; Meiburg, E.
Abstract : We develop a vorticity‐based approach for modelling quasi‐steady, supercritical gravity currents propagating into a finite‐height channel with arbitrary density and velocity stratification. The model enforces the conservation of mass, horizontal and vertical momentum. In contrast to previous approaches, it does not rely on empirical, energy‐based closure assumptions. Instead, the effective energy loss of the flow can be calculated a posteriori . The present model results in the formulation of a second‐order, nonlinear ordinary differential equation (ODE) that can be solved in a straightforward fashion to determine the gravity‐current velocity, along with the downstream ambient velocity and density profiles. Comparisons between model predictions and direct numerical simulations (DNS) show excellent agreement. Furthermore, they indicate that, for high Reynolds numbers, the gravity‐current height adjusts itself so as to maximize the loss of energy.