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Algebraic Rossby solitary waves excited by non-stationary external source. (English) Zbl 1264.76030

Summary: The paper deals with the effects of non-stationary external source forcing and dissipation on algebraic Rossby solitary waves. From quasi-geostrophic potential vorticity equation, basing on the multiple-scale method, an inhomogeneous Korteweg-de Vries-Benjamin-Ono-Burgers (KdV-B-O-Burgers) equation is obtained. This equation has not been previously derived for Rossby waves. By analysis and calculation, four conservation laws associated with the above equation are first obtained. With the help of pseudo-spectral method, the waterfall plots are obtained and the evolutional characters of algebraic Rossby solitary waves are studied. The results show that non-stationary external source and dissipation have great effect on the generation and evolution of algebraic solitary Rossby waves.

MSC:

76B65 Rossby waves (MSC2010)
76B47 Vortex flows for incompressible inviscid fluids
76E20 Stability and instability of geophysical and astrophysical flows
76M22 Spectral methods applied to problems in fluid mechanics
35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35L65 Hyperbolic conservation laws
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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