= Stratified magneto-Coriolis wave
{title2=$K^2(\omega^2-a^2)^2-4\Omega^2k_z^2\omega^2+Hh^2(\omega^2-a^2)=0$}
An incompressible <Boussinesq> fluid with uniform <magnetic field>, uniform vertical <rotation> and uniform temperature gradient supports waves combining <magnetic tension>, <Coriolis force> and <buoyancy>. Put $K=|\mathbf k|$, $h^2=K^2-k_z^2$, $a^2=(\mathbf B\cdot\mathbf k)^2/(\mu_0\rho)$ and $H=g\alpha\beta$, with $\partial_zT_0=-\beta$. Eliminating <pressure> and the temperature and magnetic perturbations gives the displayed <dispersion relation> for nonzero frequencies. Stable thermal stratification has $H<0$. Clearing frequency denominators requires checking any resulting zero roots in the original equations; a stationary magnetostatic-buoyancy balance can exist independently of the propagating branches.
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