Capillary-gravity waves and the Navier-Stokes equation (Q2766090)

The paper gives a brief and elementary introduction to water waves and their relation to Navier-Stokes equations. After the authors have shown that the velocity potential satisfies Laplace's equation, they derive equations for velocity and displacement of a water element under the action of a harmonic wave. Finally, from the requirement that the harmonic wave satisfies Navier-Stokes equations, the authors obtain the dispersion relation for gravity and capillarity-gravity waves.