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Ito, T., and H. Kanehisa, 2013: Analytical solutions of vortex Rossby waves in a discrete barotropic model. J. Meteor. Soc. Japan, 91, 775-788.
https://doi.org/10.2151/jmsj.2013-604
Graphical Abstract

Highlights:

• The initial value problem of vortex Rossby waves (VRWs) is analytically solved in a linearized barotropic system on an ƒ plane. The basic axisymmetric vorticity q is assumed to be piecewise uniform in the radial direction (see Fig.1).
• For a basic vorticity q with an annular vorticity ring ( r₁ < r < r₂ in Figs.1,2), and if the radial distribution of q satisfies a certain additional condition (the Fjørtoft condition), the solution with azimuthal wave number |m|≠1 exponentially or linearly grows in time as a result of the interaction of counterpropagating VRWs at the edges of the ring (see Fig.2).
• Although the solution with |m|=1 cannot exponentially grow for any q, it can grow as a linear function of time. This linear growth may be regarded as a result of the resonance between two internal modes of the system.