Deep-water capillary-wave dispersion relation
= Deep-water capillary-wave dispersion relation
{title2=$\omega^2=(T/\rho)|k|^3$}
For a capillary wave on deep water with surface tension $T$ and density $\rho$, the dispersion relation is
$$
\omega(k)=S|k|^{3/2},
\qquad
S=\sqrt{T/\rho}.
$$
Its group velocity is $(3S/2)|k|^{1/2}$ in the direction of the wavevector.