An Equation of the β-gyre Growth of a Cyclone in a Non-uniformly Straining Environmental Flow

[摘要] An equation of the β-gyre growth of a cyclone is derived in a barotropic nondivergent system. The environmental flow is assumed to be an arbitrary quadratic function of coordinates, and therefore non-uniformly straining. The cyclone flow is assumed to consist of a symmetric cyclonic circulation and a flow of β-gyres. Other components of higher wave-number are assumed small and are neglected.The derived equation says the following: The contribution of the β-effect to the β-gyre growth is proportional to βcosα. Here, α is the azimuthal angle of the anticyclonic β-gyre centre around the cyclone centre, measured counterclockwise from the east. The first spatial derivative of the environmental flow affects the β-gyre growth only through the deformation. This contribution is proportional to λcos(2λ-2α). Here, λ and γ are, respectively, the strain rate and azimuthal angle of the dilatation axis of the environmental deformation matrix at the cyclone centre. These results are consistent with the already known results in the case of an environmental flow with a constant shear.The second spatial derivative of the environmental flow affects the β-gyre growth only through the relative vorticity gradient. This contribution is proportional to |∂iΩ|sin(Θ-α). Here ∂iΩ and Θ are respectively the relative vorticity gradient and its azimuthal angle at the cyclone centre.While the β-effect induces the energy transfer between the β-gyres and symmetric cyclonic circulation, the relative vorticity gradient in addition to this induces energy transfer between the β-gyres and environment.

[学科分类] 大气科学