Energetics of internal solitary waves in a background sheared current

• Published in: Nonlinear processes in geophysics Vol. 17; no. 5; pp. 553 - 568
• Main Author: Lamb, K G
• Format: Journal Article
• Language: English
• Published: Gottingen Copernicus GmbH 08.10.2010; Copernicus Publications
• Subjects: Comparative studies; Mathematical models; Nonlinear systems; Oceanography; Simulation
• ISSN: 1607-7946; 1023-5809; 1607-7946
• DOI: 10.5194/npg-17-553-2010

The energetics of internal waves in the presence of a background sheared current is explored via numerical simulations for four different situations based on oceanographic conditions: the nonlinear interaction of two internal solitary waves; an internal solitary wave shoaling through a turning point; internal solitary wave reflection from a sloping boundary and a deep-water internal seiche trapped in a deep basin. In the simulations with variable water depth using the Boussinesq approximation the combination of a background sheared current, bathymetry and a rigid lid results in a change in the total energy of the system due to the work done by a pressure change that is established across the domain. A final simulation of the deep-water internal seiche in which the Boussinesq approximation is not invoked and a diffuse air-water interface is added to the system results in the energy remaining constant because the generation of surface waves prevents the establishment of a net pressure increase across the domain. The difference in the perturbation energy in the Boussinesq and non-Boussinesq simulations is accounted for by the surface waves.