Energy and momentum integrals for progressive capillary-gravity waves

Definitions of energy density, energy flux and momentum flux for capillary—gravity waves are derived by integration of the equations of motion and also by Whitham's averaged Lagrangian method. We then confirm recent results due to Hogan (1979) both in the general case and in the case of pure capillary waves. Comparison with the Lagrangian results also allows us to give general definitions of ‘wave action density’ and ‘wave action flux’.