Two-layer hydraulics with comparable internal wave speeds

Abstract

Two-layer hydraulics is developed for problems in which the moving layers can have stagnant layers above and below, the two internal wave modes can have comparable speeds and the total depth of the moving layers may vary. The general development allows both Boussinesq and non-Boussinesq problems to be studied. Solutions are presented in the Froude-number plane and the effect of different layer densities on the form of the solution space is shown. The theory is applied to two-layer plunging flows and a variety of controlled solutions are found. Solutions for the 2½-layer theory and the plunging flow theory are demonstrated experimentally. Shear instability is often observed in the divergent section of the channel.