Hydraulic Jump in One-dimensional Flow

In the presence of viscosity the hydraulic jump in one dimension is seen to be a first-order transition. A scaling relation for the position of the jump has been determined by applying an averaging technique on the stationary hydrodynamic equations. This gives a linear height profile before the jump, as well as a clear dependence of the magnitude of the jump on the outer boundary condition. The importance of viscosity in the jump formation has been convincingly established, and its physical basis has been understood by a time-dependent analysis of the flow equations. In doing so, a very close correspondence has been revealed between a perturbation equation for the flow rate and the metric of an acoustic white hole. We finally provide experimental support for our heuristically developed theory.Comment: 17 Pages, 8 Figures, 1 Table. To appear in European Physical Journal

Numerical Simulation of Shedding Pattern of Near Wake Vortices Behind a Circular Cylinder Near a Plane Boundary

In this paper, flow past a circular cylinder is numerically simulated under the influence of a plane boundary. The vorticity-stream function formulation is used for a wide range of Reynolds numbers consistent of two-dimensional flow. The conventional finite difference implicit scheme is used by implementing the appropriate boundary conditions at all boundaries. The transition from twin vortex regime to vortex shedding regime is studied. The transition is delayed as the gap between the cylinder and wall decreases. The same is because of the interaction between the wake of the cylinder and the boundary wall vorticity. The results are compared with the previous observations of the inhibition of the vortex shedding for body placed inside a channel as well as near a plane wall. The unsteady vortex shedding regime from a pattern similar to the von-karman street when the cylinder is far from the plane wall to a single row of same sign vortices as the body approaches the wall. The separated vortex dynamics leading to this tropological modification is presented