TY - JOUR
T1 - A parabolic equation for the combined refraction diffraction of Stokes waves by mildly varying topography
AU - Kirby, James T.
AU - Dalrymple, Robert A.
PY - 1983/11
Y1 - 1983/11
N2 - A parabolic equation governing the leading order amplitude for a forward scattered Stokes wave is derived using a multiple scale perturbation method, and the connection between the linearized version and a previously derived approximation of the linear mild slope equation is investigated. Two examples are studied numerically for the situation where linear refraction theory leads to caustics, and the nonlinear model is shown to predict the development of wave jump conditions and significant reductions in amplitude in the vicinity of caustics.
AB - A parabolic equation governing the leading order amplitude for a forward scattered Stokes wave is derived using a multiple scale perturbation method, and the connection between the linearized version and a previously derived approximation of the linear mild slope equation is investigated. Two examples are studied numerically for the situation where linear refraction theory leads to caustics, and the nonlinear model is shown to predict the development of wave jump conditions and significant reductions in amplitude in the vicinity of caustics.
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U2 - 10.1017/S0022112083002232
DO - 10.1017/S0022112083002232
M3 - Article
AN - SCOPUS:0020849684
SN - 0022-1120
VL - 136
SP - 453
EP - 466
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -