On the computation of nonlinear planetary waves

Details On the computation of nonlinear planetary waves On the computation of nonlinear planetary waves

Feb 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987stam...76...37e&link_type=abstract

Studies in Applied Mathematics (ISSN 0022-2526), vol. 76, Feb. 1987, p. 37-67.

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Computational Fluid Dynamics, Iterative Solution, Nonlinear Systems, Planetary Waves, Solitary Waves, Variational Principles, Convergence, Parallel Flow, Vorticity Equations

Scientific paper

A numerical method is developed to solve a class of nonlinear, nonlocal eigenvalue problems defined in an infinite strip, and is applied to compute solitary plenetary waves in a sheared zonal current on the beta-plane. This method, an iterative procedure derived from the natural variational structure of these problems, is implemented in the physical case when the ambient parallel flow has a linear or a quadratic velocity profile. The results of the numerical experiments establish rigorous limits on the range of validity of the formal asymptotic theory of weakly nonlinear long waves, and also reveal some new phenomena involving strongly nonlinear waves. The iterative procedure is analyzed in a general setting, and is shown to be globally convergent without restriction on the wave amplitude.

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