= Anelastic reduced-pressure Kelvin wave
{title2=$\omega^2=N^2k^2/[k^2+m^2+1/(4H^2)]$}
For an isothermal <anelastic approximation> with vertical momentum $w_t-b+\Phi_z=0$, buoyancy $b_t+N^2w=0$, and zero meridional velocity, eliminating pressure yields $\partial_t^2(w_{xx}+w_{zz}-w_z/H)+N^2w_{xx}=0$. A factor $e^{z/(2H)+imz}$ gives the displayed <dispersion relation>. Meridional balance produces $e^{-y^2/(2L_D^2)}$, with $L_D^2=(\omega/k)/\beta$ and an eastward intrinsic speed. The limit $L_D^2=2NH/\beta$ requires both $|m|H\ll1$ and $|k|H\ll1$.
Back to article page
