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The nonlinear ZK equation with a complete Coriolis force. (Chinese. English summary) Zbl 1399.35302

Summary: In barotropic fluids, the nonlinear \((2+1)\)-dimensional Zakharov-Kuznetsov equation in a potential vorticity equation which includes both the vertical and horizontal components of Coriolis force is derived to describe Rossby waves that propagate in a plane by using multiscale and perturbation method. It is shown that the horizontal component of the complete Coriolis force plays an important role in the structures of the Rossby waves. At the same time, beta effect, topographic effect and the external source are also important to inducing the \((2+1)\)-dimensional Rossby waves.

MSC:

35Q35 PDEs in connection with fluid mechanics
76B65 Rossby waves (MSC2010)
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