On the normal mode instability of harmonic waves on a sphere |
| |
| Authors: | Yu. N. Skiba |
| |
| Affiliation: | Centro de Ciencias de la Atmósfera, Universidad National Autónoma de México , Circuito Exterior, CU, México, D.F., 04510, Mexico |
| |
| Abstract: | Abstract The normal mode instability of harmonic waves in an ideal incompressible fluid on a rotating sphere is analytically studied. By the harmonic wave is meant a Legendrepolynomial flow αPn(μ) (n ≥ 1) and steady Rossby-Haurwitz wave of set F 1 ⊕ Hn where Hn is the subspace of homogeneous spherical polynomials of the degree n(n ≥ 2), and F 1 is the one-dimensional subspace generated by the Legendre-polynomial P1(μ). A necessary condition for the normal mode instability of the harmonic wave is obtained. By this condition, Fjörtoft's (1953) average spectral number of the amplitude of each unstable mode must be equal to  | |
| Keywords: | Normal mode instability Legendre-polynomial flow Rossby-Haurwits wave |
|
|
