Turbulent unsteady flow profiles over an adverse slope

Abstract

When an unsteady free surface flow encounters an adverse slope, it results in a decelerating flow up the adverse slope. The time dependent turbulent flow is treated here by appropriately reducing the two-dimensional Reynolds averaged Navier-Stokes equation along with the equation of continuity considering turbulence closure. With suitable choice of parameters, the resulting differential equations are numerically solved to compute free surface and streamwise velocity profiles with time. It is found that initially the advancing free surface is convex upwards for a short time, followed by a jump of the free surface with a negative streamwise velocity that is a backwater rolling breaker due to deceleration of flow. At later time, however, the velocity becomes positive, that is, the breakers roll forward. This dual feature of motion, that is a surge followed by rolling breakers, is repeated for sometime before the jumps stop. The theoretical analysis presented here is motivated by tidal bores propagating upstream in an estuarine river.