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In this paper the wave action balance equation in terms of frequency-direction spectrum is derived.A theoretical formulation is presented to generate an invariant frequency space to replace the varying wavenumber space through a Jacobian transformation in the wave action balance equation.The physical properties of the Jacobian incorporating the effects of water depths are discussed.The results provide a theoretical basis of wave action balance equations and ensure that the wave balance equations used in the SWAN or other numerical models are correct.It should be noted that the Jacobian is omitted in the wave action balance equations which are identical to a conventional action balance equation.
In this paper the wave action balance equation in terms of frequency-direction spectrum is derived. A theoretical formulation is presented to generate an invariant frequency space to replace the varying wavenumber space through a Jacobian transformation in the wave action balance equation. The physical properties of the Jacobian incorporating the effects of water depths are discussed. The results provide a theoretical basis of wave action balance equations and ensure that the wave balance equations used in the SWAN or other numerical models are correct. Should be noted that the Jacobian is omitted in the wave action balance equations which are identical to a conventional action balance equation.