Finite-depth vortex-sheet dispersion relation
= Finite-depth vortex-sheet dispersion relation
For an equal-density vortex sheet a distance $h$ above a rigid wall, with lower and upper base velocities $U$ and zero, a mode $e^{i(kx-\omega t)}$ satisfies
$$
(\omega-kU)^2\coth(|k|h)+\omega^2=0.
$$
The wall changes the inertia of the lower perturbation through the factor $\coth(|k|h)$.