Coherence and radiative energy transfer for linear surface gravity waves in water of constant depth

The radiative energy transfer for partially coherent water waves is analysed. For linear gravity waves in water of constant depth, the coherence properties are described within the framework of optical coherence theory. Exact energy transfer relations are derived and compared to similar relations for acoustical compression waves. On the basis of previous results for non-dispersive waves, an exact, geometrical description of the radiative energy transfer for dispersive water waves is derived. The theory reduces to the classical theory of radiative energy transfer within a quasihomogeneous wave model. The results are discussed in relation to the applications of the classical description for local wave energy prediction.