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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, 443–453, 2010
https://doi.org/10.5194/npg-17-443-2010
© 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, 443–453, 2010
https://doi.org/10.5194/npg-17-443-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 10 Sep 2010

Research article | 10 Sep 2010

The lifecycle of axisymmetric internal solitary waves

J. M. McMillan1 and B. R. Sutherland2 J. M. McMillan and B. R. Sutherland
  • 1Department of Physics, University of Alberta, Edmonton, AB, T6G 2G7, Canada
  • 2Departments of Physics and of Earth and Atmospheric Sciences, University of Alberta, Edmonton, AB, T6G 2G7, Canada

Abstract. The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as r-p with p=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as r-1.

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