On stability of Rossby-Haurwitz waves and Verkeley's modons in the barotropic atmosphere

Resumen

Stability of Verkeley's modons and Rossby-Haurwitz (R-H) waves of subspace H1 Hn is analyzed within the vorticity equation of an ideal incompressible fluid on a rotating sphere. Here Hn is the eigen subspace of the spherical Laplace operator corresponding to the eigenvalue n(n+1). Conservation laws and independent sets of any perturba- tions of R-H waves and small perturbations of Verkley's modon are found.

It is proved that any super-rotation flow is Lyapunov stable but any dipole modon or non-zonal R-H wave of H1 Hn where n ≥ 2 are Lyapunov unstable because of the algebraic growth of perturbations caused by asynchro- nous oscillations of waves.