Trapped waves on interfacial hydraulic falls over bottom obstacles

Hydraulic falls on the interface of a two-layer density stratified fluid flow in the presence of bottom topography are considered. We extend the previous work [Philos. Trans. R. Soc. London A 360, 2137 (2002)] to two successive bottom obstructions of arbitrary shape. The forced Korteweg-de Vries and modified Korteweg-de Vries equations are derived in different asymptotic limits to understand the existence and classification of fall solutions. The full Euler equations are numerically solved by a boundary integral equation method. New solutions characterized by a train of trapped waves are found for interfacial flows past two obstacles. The wavelength of the trapped waves agrees well with the prediction of the linear dispersion relation. In addition, the effects of the relative location, aspect ratio, and convexity-concavity property of the obstacles on interface profiles are investigated.