= Equatorial wave velocity polarization
{title2=$u=\frac{i(\omega yv-kv')}{\omega^2-k^2},\quad\eta=\frac{i(kyv-\omega v')}{\omega^2-k^2}$}
In dimensionless <equatorial wave> units with <gravity wave> speed and <beta plane> coefficient one, a Fourier mode $e^{i(kx-\omega t)}$ obeys $\omega u-k\eta=iyv$ and $\omega\eta-ku=-iv'$. Inverting this two-by-two <linear system> gives the displayed <wave polarization>, provided $\omega^2\ne k^2$. Inserting it in the meridional momentum equation gives the <Hermite differential equation> after a Gaussian factor is removed. At singular values the original equations, rather than these quotient formulae, determine whether a trapped mode exists.
Back to article page
