Long wave dynamics for a liquid CO_2 lake in the deep ocean

摘要

A long-wave model for the evolution of long waves at the interface of a deep and a shallow fluid is put forward. The model allows for a uniform stream in one of the layers, and the existence of interfacial capillarity. The model can be used to study the dynamics of the interface between liquid CO2 and seawater in the deep ocean, including the evolution of the hydrate layer.If restricted to unidirectional waves the model has the form of a Benjamin-type equation found by Benjamin [2]. Steady periodic solutions of the Benjamin equation are found using a numerical bifurcation code based on a pseudo-spectral projection. The bifurcation patterns are complex, with some branches featuring turning points and secondary bifurcations. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.