= Critical balance in a rapidly rotating fluid
{title2=$k_\perp U\sim2\Omega |k_\parallel|/k_\perp$}
Balance the <inertial wave> rate against horizontal nonlinear advection. The anisotropy $\epsilon=|k_\parallel|/k_\perp$ is then of the same order as the <Rossby number> $k_\perp U/(2\Omega)$. Horizontal <geostrophic flow> gives kinematic <pressure> amplitude $\delta p\sim2\Omega U/k_\perp\sim U^2/\epsilon$. The first <ageostrophic flow> is $O(\epsilon U)$ and supplies the small horizontal divergence balancing $-\partial_z u_\parallel$. Rapid inertial oscillations are excluded by this slow-time ordering.
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