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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 17, issue 5
Nonlin. Processes Geophys., 17, 553–568, 2010
https://doi.org/10.5194/npg-17-553-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Large amplitude internal waves in the coastal ocean

Nonlin. Processes Geophys., 17, 553–568, 2010
https://doi.org/10.5194/npg-17-553-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.

  08 Oct 2010

08 Oct 2010

Energetics of internal solitary waves in a background sheared current

K. G. Lamb K. G. Lamb
  • Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Abstract. 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.

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