Balanced and Wave Interactions in Rotating Shallow Water
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David J. Muraki, Simon Fraser University
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The rotating shallow water equations have long been used as
a simple model which exhibits both balanced and wave
dynamics.  An exact decomposition is presented which extends
quasigeostrophy (QG) to include finite Rossby number effects.=20
Key features of this new formulation include an exact
potential vorticity (PV) streamfunction, a perturbation theory
for balanced corrections beyond QG, and a nonlinear wave dynamics
in the absence of PV.  As this theory preserves the coexistence
of balanced and wave dynamics, it provides a quantitative
basis for analyzing the phenomena of gravity wave adjustment
and emission, and instability.
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In particular, we focus on the wave part of the decomposition to
investigate the recent observation of unstable waves associated
with balanced dipole propagation in three-dimensional simulations
of Plougonven and Snyder.  Although only a two-dimensional analog,
a direct computation of the linearized eigenvalues addresses
the possible stability of modon dipoles within the rotating shallow
water system.  This work is in collaboration with Chris Snyder
(NCAR) and Riwal Plougonven (LMD).