Ito, T., and H. Kanehisa, 2013: Analytical solutions of vortex Rossby waves in a discrete barotropic model. J. Meteor. Soc. Japan, 91, 775-788.
- 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.