Bounds on the growth rate and phase velocity of instabilities in non-divergent barotropic flow on a sphere: A semicircle theorem

✍ Scribed by John Thuburn; Peter H. Haynes

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 480 KB
• Volume: 122
• Category: Article
• ISSN: 0035-9009
• DOI: 10.1002/qj.49712253111

✦ Synopsis

Abstract

Bounds are presented for the growth rate and angular phase velocity of unstable modes in non‐divergent barotropic flow on a sphere. The bounds are given in terms of the minimum and maximum basic‐flow angular velocity. The result is analogous to the earlier results of Howard and of Pedlosky for plane parallel shear flow and for quasi‐geostrophic flow on a ß‐plane. An improvement to the earlier ß‐plane result, giving tighter bounds, is also presented.