Solitary axisymmetric Rossby waves of finite amplitude

Abstract

Low-frequency Rossby waves, similar to drift waves in plasma, can propagate in a thin layer of fluid on a rotating sphere. The theory of Rossby waves was developed primarily for quasigeostrophic motions of low amplitude (the relative vortlcity is much less than the angular velocity of rotation of the sphere Ω and the layer thickness H differs little from the unperturbed thickness H0) [1]. Of particular interest are nearly axisymmetric solitary waves describing isolated vortex formations moving uniformly opposite to the direction of rotation of the sphere (to the west). Quasigeostrophic waves of low amplitude, inside which the fluid rotates in the opposite direction to the rotation of the sphere (anticyclonically), were considered in [2, 3]. Anticyclones of finite amplitude were investigated in [4], where it was shown that the structure of a solitary wave depends on the previous history of its formation. In this paper, equations are derived for the description of the slow evolution of flows of finite amplitude in a thin spherical layer of homogeneous rotating fluid and the structure of a smooth axisymmetric solitary Rossby wave is analyzed.