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Bounds on the growth rate and phase velocity of instabilities in non‐divergent barotropic flow on a sphere: A semicircle theorem
Author(s) -
Thuburn John,
Haynes Peter H.
Publication year - 1996
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49712253111
Subject(s) - barotropic fluid , plane (geometry) , angular velocity , flow (mathematics) , geostrophic wind , shear flow , phase (matter) , phase plane , mathematics , growth rate , shear (geology) , physics , mechanics , mathematical analysis , classical mechanics , geometry , geology , petrology , quantum mechanics , nonlinear system
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.