TY - JOUR
T1 - Extended time-dependent mild-slope and wave-action equations for wave-bottom and wave-current interactions
AU - Toledo, Yaron
AU - Hsu, Tai Wen
AU - Roland, Aron
PY - 2012/1/8
Y1 - 2012/1/8
N2 - 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.
AB - 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.
KW - Mild-slope equations
KW - Water waves
KW - Wave-action equations
KW - Wave-current interactions
UR - http://www.scopus.com/inward/record.url?scp=84856001065&partnerID=8YFLogxK
U2 - 10.1098/rspa.2011.0377
DO - 10.1098/rspa.2011.0377
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AN - SCOPUS:84856001065
SN - 1364-5021
VL - 468
SP - 184
EP - 205
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2137
ER -