Gravity currents with internal stratification in channels of non-rectangular cross-section

We investigate by theoretical means the motion of a gravity current (GC) released from a lock into an ambient fluid in a horizontal channel of non-rectangular cross-section area (CSA) like triangle, trapezoid or semicircle. The lock contains an internal stratification, in particular a layer of density ρ L overlain by a layer of density ρ U , where ρ o ρ U ρ L and ρ o is the density of the ambient fluid. Assuming a Boussinesq and large Reynolds flow, we develop a new self-contained model for the prediction of the motion of the GC, in particular the position and speed of the nose x N ( t ) and u N ( t ) , where t is the time from release. Upon an appropriate scaling the system of equations and boundary conditions is reduced to a form amenable to analysis and solution by the methods employed for the non-stratified flow. The solution reveals an initial slumping with constant u N , and eventually the transition at x V to the viscous regime. A self similar phase of the form x N ∼ t β can develop only for CSA of power-law shape, in which case the constant β depends on the shape but not on the stratification. The stability is also considered, and we show that the flow is stable with few exception. Unfortunately, experimental data for comparisons are not available, and we hope that the sharp present results will motivate the performance of needed experimental tests.