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A note on the derivation of wave action balance equation in frequency space

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Abstract

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.

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Authors and Affiliations

  1. Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, 701, China

    Tai-Wen Hsu

  2. Taiwan Ocean Research Institute, National Applied Research Laboratories, Kaohsiung, 852, China

    Jian-Ming Liau

  3. Department of Marine Environmental Informatics, National Taiwan Ocean University, Keelung, 202, China

    Shin-Jye Liang

  4. Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, 202, China

    Shan-Hwei Ou

  5. Institute of Ocean Technology and Marine Affairs, National Cheng Kung University, Tainan, 701, China

    Yi-Ting Li

Authors
  1. Tai-Wen Hsu
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  2. Jian-Ming Liau
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  3. Shin-Jye Liang
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  4. Shan-Hwei Ou
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  5. Yi-Ting Li
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Corresponding author

Correspondence to Tai-Wen Hsu.

Additional information

This research is financially supported by the Science Council, with contract number NSC95-2221-E-006-462 and Research Center of Ocean Environment and Technology, under the contract NCKU-NSYSU.

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Hsu, TW., Liau, JM., Liang, SJ. et al. A note on the derivation of wave action balance equation in frequency space. China Ocean Eng 25, 133–138 (2011). https://doi.org/10.1007/s13344-011-0011-z

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  • DOI: https://doi.org/10.1007/s13344-011-0011-z

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