Dense underflow into a lake or reservoir - supercritical flow solutions

Steady two-dimensional flow from an angled structure into a lake or a reservoir where the interface between the intrusion and the ambient fluid separates from a solid wall is considered. The fluid is assumed to be of finite depth and the incoming channel makes a downward angle α with the horizontal axis. This simple configuration provides a model for the plunging inflow and subsequent underflow of dense water in a reservoir or lake. Exact solutions are presented at infinite Froude number and compared with the solutions to the full nonlinear problem for supercritical flow. Limiting flows are found to separate from the upper boundary at a stagnation point, and regions of non-uniqueness in the solution domain are found.