An Equation of the β-Gyre Rotation of a Cyclone in a Non-uniformly Straining Environmental Flow

Abstract

An equation of the β-gyre rotation of a cyclone in a non-uniformly straining environmental flow is derived in a barotropic non-divergent system. The environmental flow, which is generally both zonally and meridionally varying, is assumed to be a quadratic function of coordinates. The total flow is assumed to consist of the environmental flow, a symmetric cyclonic circulation and a flow of β-gyres. The resulting equation says the followings. The β effect forces the β-gyre centres to lie perpendicular to the direction of β, i. e., of the gradient of the Coriolis parameter. The symmetric cyclonic circulation advects the β-gyres counter-clockwise. The deformational component of the environmental flow forces the β-gyres centres to lie along the dilatation axis of the defomation matrix. The rotational component of the environmental flow rotates the β-gyres with an angular velocity equal to half the environmental relative vorticity. The second derivative of the environmental flow affects the β-gyre rotation only through the relative vorticity gradient, and the other components of the second derivative have no influence on the rotation.