Whitaker, J. S. and C. Snyder,1993:
The effects of spherical geometry on the evolution of baroclinic waves, J. Atmos. Sci.,
50, 597-612.
ABSTRACT
The effects of spherical geometry on the evolution of baroclinic waves
Jeffrey S. Whitaker and Chris Snyder
National Center for Atmospheric Research, Boulder, CO
Abstract
The effects of spherical geometry on the nonlinear evolution of baroclinic waves
are investigated by comparing integrations of a two-layer primitive equation
(PE) modelin spherical and cartesian geometry. To isolate the geometrical
effects, the integrations use basic states with nearly identical potential
vorticity (PV) structure.
Although the linear normal modes are very similar, significant differences
develop at finite amplitude. Anticyclones (cyclones) in spherical geometry are
relatively stronger (weaker) than those in Cartesian geometry. For this basic
state, the strong anticyclones on the sphere are associated with anticyclonic
wrapping of high PV in the upper layer (i.e. high PV air is advected southward
and westward relative to the wave). In Cartesian geometry, large
quasi-barotropic cyclonic vortices develop, and no anticyclonic wrapping of PV
occurs. Because of their influence on the synoptic-scale flow, spherical
geometric effects also lead to significant differences in the structure of
mesoscale frontal features.
A standard midlatitude scale analysis indicates that the effects of spherical
geometry enter in the next-order correction to b-plane quasi-geostrophic (QG)
dynamics. At leading order these spherical terms only affect the PV inversion
operator (through the horizontal Laplacian) and the advection of PV by the
non-divergent wind. Scaling arguments suggest, and numerical integrations of
the barotropic vorticity equation confirm, that the dominant geometric effects
are in the PV inversion operator. The dominant metric in the PV inversion
operator is associated with the equatorward spreading of meridians on the
sphere, and causes the anticyclonic (cyclonic) circulations in the spherical
integrations to become relatively stronger (weaker) than those in the Cartesian
integration.
This study demonstrates that the effects of spherical geometry can be as
important as the leading-order ageostrophic effects in determining the structure
and evolution of dry baroclinic waves and their embedded mesoscale structures.