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 language | English |
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Pages (from-to) | 184-205 |
Number of pages | 22 |
Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 468 |
Issue number | 2137 |
DOIs | |
State | Published - 8 Jan 2012 |
Externally published | Yes |
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