Upstream Internal Hydraulic Jumps

Abstract

In stratified tidal flow over a sill, the character of the upstream response is determined by a Froude number Fs based on the stratification near the surface. This is distinguished from the Froude number governing the response in the neighborhood of the sill crest, which is based on the weak density step associated with a flow bifurcation. For moderate values of Fs, the upstream response consists of nonlinear waves or a weak undular bore. For larger values of Fs, a strong, quasi-stationary, internal hydraulic jump dominates the upstream response. At sufficiently large values of Fs, the upstream bore is swept downstream and lost. Acoustic backscatter and velocity data are presented for the case of a strong internal bore or gravity current in a tidally modulated sill flow. Numerical simulations with varying near-surface stratification are presented to illustrate the upstream responses at different values of Fs. The theory of two-layer hydraulic flows is invoked to account for the development of the upstream jump.