Mt. Montgomery et Lj. Shapiro, GENERALIZED CHARNEY-STERN AND FJORTOFT THEOREMS FOR RAPIDLY ROTATING VORTICES, Journal of the atmospheric sciences, 52(10), 1995, pp. 1829-1833
A generalized Charney-Stern theorem for rapidly rotating (large Rossby
number) baroclinic vortices, such as hurricanes, is derived based on
the asymmetric balance (AB) approximation. In the absence of dissipati
ve processes, a symmetrically stable baroclinic vortex is shown to be
exponentially stable to nonaxisymmetric perturbations if a generalized
potential vorticity gradient on theta surfaces remains single signed
throughout the vortex. The generalized potential vorticity gradient in
volves the sum of an interior potential vorticity gradient associated
with the symmetric vortex and surface contributions associated with th
e vertical shear of the tangential wind. The AB stability formulation
is then shown to yield Fjortoft's theorem as a corollary. In the moder
n view of shear instabilities the theorems admit simple interpretation
. The Charney-Stern theorem represents a necessary condition for the e
xistence of counterpropagating Rossby waves associated with the radial
potential vorticity gradient, while Fjortoft's theorem represents a n
ecessary condition for these waves to phase lock and grow in strength.
Potential application of these results as well as limitations of the
slow-manifold approach are briefly discussed.