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Generation of solitary Rossby waves by unstable topography. (English) Zbl 1247.76022

Summary: The effect of topography on generation of the solitary Rossby waves is researched. Here, the topography, as a forcing for waves generation, is taken as a function of longitude variable \(x\) and time variable \(t\), which is called unstable topography. With the help of a perturbation expansion method, a forced mKdv equation governing the evolution of amplitude of the solitary Rossby waves is derived from quasi-geostrophic vorticity equation and is solved by the pseudo-spectral method. Basing on the waterfall plots, the generational features of the solitary Rossby waves under the influence of unstable topography and stable topography are compared and some conclusions are obtained.

MSC:

76B25 Solitary waves for incompressible inviscid fluids
76B65 Rossby waves (MSC2010)
76E20 Stability and instability of geophysical and astrophysical flows
76M22 Spectral methods applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
35Q53 KdV equations (Korteweg-de Vries equations)
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