Stability of Rossby-Haurwitz waves

Exploiting a factorized form of the linear perturbation equation valid around Rossby-Haurwitz waves in the nonlinear barotropic vorticity equation system on the sphere, an elementary discrete numerical method for analysing the stability of these waves is proposed. In contrast with former approaches based on wave-interaction theory and its cumbersome triad-interaction coefficients, the discrete analysis proposed here is inspired by the spectral-transform technique, where nonlinearities are treated in physical space. This approach, based only on standard linear algebra techniques, is simpler than former ones and allows a large number of degrees of freedom to be retained in perturbation space. The merits and possible limitations of the method are discussed; some validations and results are presented.