= Rotational coupling of shear and pseudo-Alfvén waves
{title2=$\omega_I/\omega_A\sim2\Omega/(k_\perp v_A)$}
With aligned uniform <magnetic field> and rotation, pressure projection couples the two incompressible transverse <wave polarization> states at rate $\omega_I\sim2\Omega|k_\parallel|/k_\perp$. Each nonrotating <Alfvén wave> has rate $\omega_A=|k_\parallel|v_A$. Their ratio is independent of the anisotropy. Leading finite-timescale decoupling therefore needs $k_\perp v_A\gg2\Omega$, with rotational coupling also slow relative to any retained nonlinear evolution. At finite amplitude the usual anisotropic reduction still permits passive <advection> of pseudo-Alfvénic fluctuations by the Alfvénic subsystem; removing rotational mixing does not eliminate that one-way interaction. Because the two Alfvén polarizations are degenerate, weak coupling can still mix them over the longer time $\omega_I^{-1}$.
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