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Critical layer instability in baroclinic flows
Author(s) -
Bretherton F. P.
Publication year - 1966
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.49709239302
Subject(s) - inviscid flow , potential vorticity , baroclinity , vorticity , instability , boundary layer , adiabatic process , geostrophic wind , mechanics , physics , classical mechanics , vortex , thermodynamics
It is shown that for all inviscid, adiabatic, quasi‐geostrophic motions in a Boussinesq liquid or in a compressible atmosphere, subject to the usual boundary conditions, the integral over the fluid of the northward eddy flux of potential vorticity vanishes, provided a generalized interpretation of potential vorticity is adopted near rigid horizontal boundaries. For an infinitesimal disturbance in a normal mode to a general zonal flow, the presence of a critical layer within the fluid excludes the existence of stable modes, except in exceptional circumstances. A stable, or slowly growing mode, is associated with a down‐gradient flux of potential vorticity near the critical layer, which does not vanish as the growth rate tends to zero, and can only be balanced by the general growth in the disturbance.