Steady rotating flows over a ridge

Abstract

A model describing rotating single-layer flows over a parabolic ridge is investigated. A method of constructing steady solutions is introduced, and is used to extend previous results and determine exact regime diagrams describing the qualitative nature of the solution. Analytic expressions for the boundaries between transcritical flow and supercritical and subcritical flows are given as a function of obstacle height, Froude number of the upstream flow, and the flow inverse Burger number (a nondimensional number proportional to the square of the rotation rate). For fixed obstacle height, the nature of the supercritical transition is found to change as the rotation rate increases, with a hysteresis region like that in nonrotating flow being present only at lower rotation rates. At higher rotation rates, solutions with stationary jumps over the obstacle become stable, and abrupt transitions between supercritical and transcritical flow no longer occur. An exact analytic expression is also found for transcritical flow over the obstacle, which is closely related to the solutions for nonlinear inertia-gravity waves of limiting amplitude found by Shrira. For sufficiently high ridges in initially supercritical flow, a wave train of nonlinear inertia-gravity waves of limiting amplitude appears behind a downstream hydraulic jump.