Remarks on a strongly nonlinear model for two-layer flows with a top free surface

2018-07-10T12:21:34Z (GMT) by Ricardo Lopes-Barros
We revisit in this paper the strongly nonlinear long wave model for large amplitude internal waves in two-layer flows with a free surface proposed by Choi and Camassa [1] and Barros et al. [2]. Its solitary-wave solutions were the object of the work by Barros and Gavrilyuk [3], who proved that such solutions are governed by a Hamiltonian system with two degrees of freedom. A detailed analysis of the critical points of the system is presented here, leading to some new results. It is shown that conjugate states for the long wave model are the same as those predicted by the fully nonlinear Euler equations. Some emphasis will be given to the baroclinic mode, where interfacial waves are known to change polarity according to different values of density and depth ratios. A critical depth ratio separates these two regimes and its analytical expression is derived directly from the model. In addition, we prove that such waves cannot exist throughout the whole range of speeds.