In this study, energy spectrum of the large-scale atmospheric
motions is examined in the framework of the 3D normal mode decomposition.
The horizontal scale of disturbance is measured by the phase
speed of a Rossby mode $c$.
According to the analysis result
for the barotropic component of the atmosphere,
we obtain a characteristic energy spectrum with distinct slopes
for the turbulence and wave regimes separated by the
spherical Rhines speed.
In order to explain the observational finding that the energy spectrum
is proportional to $c^2$, we put forward a hypothesis based on the
criterion of Rossby wave breaking
such that the local meridional gradient of potential vorticity becomes
negative, $\partial q/\partial y <0$, somewhere in the domain.
With a constant $m$ describing a total mass of the atmosphere for unit area,
we have shown that the barotropic energy spectrum of the general
circulation $E$ can be represented as $E=mc^2$.

Full Article: http://air.geo.tsukuba.ac.jp/~tanaka/papers/paper141.pdf

Last Updated: 2007-02-27