Shallow-water dispersion relation (${\omega }^2=gh{\kappa }^2$)

For linear surface gravity waves with wavelength much larger than the depth, ${\omega }^2=gh{\kappa }^2$. It follows from ${\omega }^2=g\kappa \tanh (\kappa h)$ when $\kappa h\ll 1$, and the wave speed is $\sqrt{gh}$.