Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Applied mathematics, Fluids and plasma physics
Abstract
We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion are then analysed to show that wave-current interaction is influenced only by the current profile in the ’strips’ adjacent to the surface and the interface. Small amplitude and long-wave approximations are also presented.
DOI
https://doi.org/10.1016/j.nonrwa.2016.09.010
Recommended Citation
Ivanov, R. (2017) Hamiltonian model for coupled surface and internal waves in the presence of currents. Nonlinear Analysis: Real World Applications Volume 34 (2017) Pages 316-334. doi:10.1016/j.nonrwa.2016.09.010
Funder
DIT
Included in
Mathematics Commons, Non-linear Dynamics Commons, Partial Differential Equations Commons
Publication Details
Nonlinear Analysis: Real World Applications, Volume 34 (2017) Pages 316-334, 2017.