Extended time-dependent mild-slope and wave-action equations for wave-bottom and wave-current interactions

Yaron Toledo, Tai Wen Hsu, Aron Roland

Research output: Contribution to journalArticlepeer-review

Abstract

Extended mild-slope (MS) and wave-action equations (WAEs) are derived by taking into account high-order derivatives of the bottom profile and the depth-averaged current that were previously neglected. As a first step for this derivation, a time-dependent MS-type equation in the presence of ambient currents that consists of these high-order components is constructed. This mild-slope equation is used as a basis to form a waveaction balance equation that retains high-order refraction and diffraction terms of varying depths and currents. The derivation accurately accounts for the effects of the currents on the Doppler shift. This results in an 'effective' intrinsic frequency and wavenumber that differ from the ones of wave ray theory. Finally, the new WAE is derived for the phase-averaged frequency-direction spectrum in order to allow its use in stochastic waveforecasting models.

Original languageEnglish
Pages (from-to)184-205
Number of pages22
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume468
Issue number2137
DOIs
StatePublished - 8 Jan 2012
Externally publishedYes

Keywords

  • Mild-slope equations
  • Water waves
  • Wave-action equations
  • Wave-current interactions

All Science Journal Classification (ASJC) codes

  • General Engineering
  • General Physics and Astronomy
  • General Mathematics

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