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Yang, Hongwei; Zhao, Qingfeng; Yin, Baoshu; Dong, Huanhe

A new integro-differential equation for Rossby solitary waves with topography effect in deep rotational fluids. (English) Zbl 1432.76067

Abstr. Appl. Anal. 2013, Article ID 597807, 8 p. (2013).
Summary: From rotational potential vorticity-conserved equation with topography effect and dissipation effect, with the help of the multiple-scale method, a new integro-differential equation is constructed to describe the Rossby solitary waves in deep rotational fluids. By analyzing the equation, some conservation laws associated with Rossby solitary waves are derived. Finally, by seeking the numerical solutions of the equation with the pseudospectral method, by virtue of waterfall plots, the effect of detuning parameter and dissipation on Rossby solitary waves generated by topography are discussed, and the equation is compared with KdV equation and BO equation. The results show that the detuning parameter \(\alpha\) plays an important role for the evolution features of solitary waves generated by topography, especially in the resonant case; a large amplitude nonstationary disturbance is generated in the forcing region. This condition may explain the blocking phenomenon which exists in the atmosphere and ocean and generated by topographic forcing.

Cited in 17 Documents

MSC:

76B25 Solitary waves for incompressible inviscid fluids
45K05 Integro-partial differential equations
35C08 Soliton solutions
35Q53 KdV equations (Korteweg-de Vries equations)
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
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References:

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