Wave action (continuum mechanics)

is the intrinsic frequency of the slowly modulated waves – intrinsic here implying: as observed in a frame of reference moving with the mean velocity of the motion.

Whitham (1965) derived the conservation of wave action – identified as an adiabatic invariant – from an averaged Lagrangian description of slowly varying nonlinear wave trains in inhomogeneous media: where

However, wave action is a quantity which is conserved for the wave-part of the motion.

The equation for the conservation of wave action is for instance used extensively in wind wave models to forecast sea states as needed by mariners, the offshore industry and for coastal defense.

Also in plasma physics and acoustics the concept of wave action is used.

The derivation of an exact wave-action equation for more general wave motion – not limited to slowly modulated waves, small-amplitude waves or (non-dissipative) conservative systems – was provided and analysed by Andrews & McIntyre (1978) using the framework of the generalised Lagrangian mean for the separation of wave and mean motion.

Five-day forecast of the significant wave height for the North Atlantic on November 22, 2008, by NOAA 's Wavewatch III model. This wind wave model generates forecasts of wave conditions through the use of wave-action conservation and the wind-field forecasts (from weather forecasting models ). [ 1 ]