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The counter‐propagating Rossby‐wave perspective on baroclinic instability. Part IV: Nonlinear life cycles
Author(s) -
Methven J.,
Hoskins B. J.,
Heifetz E.,
Bishop C. H.
Publication year - 2005
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 - 10.1256/qj.04.23
Subject(s) - baroclinity , rossby wave , physics , zonal and meridional , instability , phase velocity , potential vorticity , frontogenesis , mechanics , momentum (technical analysis) , geology , classical mechanics , vorticity , atmospheric sciences , meteorology , vortex , optics , mesoscale meteorology , finance , economics
Pairs of counter‐propagating Rossby waves (CRWs) can be used to describe baroclinic instability in linearized primitive‐equation dynamics, employing simple propagation and interaction mechanisms at only two locations in the meridional plane—the CRW ‘home‐bases’. Here, it is shown how some CRW properties are remarkably robust as a growing baroclinic wave develops nonlinearly. For example, the phase difference between upper‐level and lower‐level waves in potential‐vorticity contours, defined initially at the home‐bases of the CRWs, remains almost constant throughout baroclinic wave life cycles, despite the occurrence of frontogenesis and Rossby‐wave breaking. As the lower wave saturates nonlinearly the whole baroclinic wave changes phase speed from that of the normal mode to that of the self‐induced phase speed of the upper CRW. On zonal jets without surface meridional shear, this must always act to slow the baroclinic wave. The direction of wave breaking when a basic state has surface meridional shear can be anticipated because the displacement structures of CRWs tend to be coherent along surfaces of constant basic‐state angular velocity, U . This results in up‐gradient horizontal momentum fluxes for baroclinically growing disturbances. The momentum flux acts to shift the jet meridionally in the direction of the increasing surface U , so that the upper CRW breaks in the same direction as occurred at low levels. Copyright © 2005 Royal Meteorological Society