|
| << previous | next >> |
Journal description
All volumes of the corresponding journal
All issues of the corresponding volume
All articles of the corresponding issues
Details for article 114 of 204 found articles
| Title: |
On the normal mode instability of harmonic waves on a sphere |
| Author: |
Skiba, Yu. N. |
| Appeared in: |
Geophysical & astrophysical fluid dynamics |
| Paging: | Volume 92 (2000) nr. 1-2 pages 115-127 |
| Year: |
2000-07-01 |
| Contents: |
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 F1⊕ Hn where Hn is the subspace of homogeneous spherical polynomials of the degree n(n ≥ 2), and F1 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, Fjortoft's (1953) average spectral number of the amplitude of each unstable mode must be equal to [image omitted]. It is noted that flow αPn(μ) is Liapunov (and hence, exponentially and algebraically) stable to all the disturbances whose zonal wavenumber m satisfies condition |m| ≥ n. The bounds of the growth rate of unstable normal modes are estimated as well. It is also shown that the amplitude of each unstable, decaying or non-stationary mode is orthogonal to the harmonic wave. The new instability condition can be useful in the search of unstable perturbations to a harmonic wave and on trials of numerical stability study algorithms. For a Legendre-polynomial flow, it complements Kuo's (1949) condition in the sense that while the latter is related to the basic flow structure; the former characterizes the structure of a growing perturbation. |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 114 of 204 found articles
| << previous | next >> |