Large amplitude capillary-gravity solitary waves in a stratified fluid sandwiched between two deep homogeneous layers

The study addresses the propagation of plane capillary gravity solitary waves of permanent form in a three layer formulation. The intermediate fluid is assumed to be stratified, while the upper and lower ones are homogeneous and infinitely deep. One or both interfaces separating these layers are subject to capillarity. The research can be applied to the case of two deep fluids when one of these fluids is stratified near the interface. The latter formulation is relevant to studies of capillary gravity waves in the transitional area between sea water and liquid carbon dioxide in the deep ocean. This has become an issue of importance for the secure storage of carbon dioxide, which is an environmental/technological problem in modern days. Therefore, we address a capillary-gravity wave motion beyond the well-examined cases of a free surface or two fluid flows. It is shown that in the considered formulation, capillary-gravity solitary waves of finite amplitude obey an integro-differential equation. This equation contains both Korteweg-de Vries (KdV) and Benjamin-Ono (BO) dispersion laws and a specific nonlinearity, which depends on the properties of the stratified layer. Capillary (KdV-type) dispersion dominates if the thickness of the stratified layer is d≪d_∗. When d≫d_∗, the gravitational (BO-type) dispersion determines the flow. The value d_∗ depends on the mode number, gravitational acceleration, and capillarity effects. Analytical solutions for the amplitude function and the streamline patterns are presented.