Computation of advancing gravity currents in ambient flows

The interaction of gravity currents with head and tail ambient flows is investigated by computation using the adaptive grids moving with the head of the current. The incompressible Navier-Stokes equation for a heterogeneous fluid, the continuity equation and the transport equation of the relative variation of density are discretized by the finite volume method. The use of the moving grid system raises the computational efficiency as well as the resolution of the moving head. The ambient flow is incorporated with the implementation of the inflow and outflow boundary conditions. The results indicate that the front speed relative to the ambient flow varies in a nonlinear fashion when the boundary layer develops along the wall. The tail wind makes the head round and thicker, and hence it reduces the speed of the head. On the other hand, the head wind makes the head sharp, thinner, and longer, and then the stable interface suppresses the mixing across the density interface. It is found that the boundary layer along the wall affects the inner structure of the current head according to the ambient flows.