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On the assumption that the vortex and the vertical velocity component of the current aresmall,a mild-slope equation for wave propagation on non-uniform flows is deduced from the basichydrodynamic equations,with the terms of (V_hh)~2 and (V_h~2)h included in the equation.The terms of bot-tom friction,wind energy input and wave nonlinearity are also introduced into the equation.The wind en-ergy input functions for wind waves and swells are separately considered by adopting Wen′s(1989)empiri-cal formula for wind waves and Snyder′s observation results for swells.Thus,an extended mild-slope equa-tion is obtained,in which the effects of refraction,diffraction,reflection,current,bottom friction,wind en-ergy input and wave nonlinearity are considered synthetically.
On the assumption that the vortex and the vertical velocity component of the current aresmall, a mild-slope equation for wave propagation on non-uniform flows is deduced from the basichydrodynamic equations, with the terms of (V_hh) ~ 2 and (V_h ~ 2 h included in the equation. These terms of bot-tom friction, wind energy input and wave nonlinearity are also introduced into the equation. The wind en-ergy input functions for wind waves and swells are separately considered by Wen’s (1989 ) empiri-cal formula for wind waves and Snyder’s observation results for swells.Thus, an extended mild-slope equa-tion is obtained, in which the effects of refraction, diffraction, reflection, current, bottom friction, wind en-ergy input and wave nonlinearity are considered synthetically