An extended mild-slope equation

On the assumption that the vortex and the vertical velocity component of th e current are small, a mild-slope equation for wave propagation on non-unif orm flows is deduced from the basic hydrodynamic equations, with the terms of (V(h)h)(2) and V(h)(2)h included in the equation. The terms of bottom fr iction, wind energy input and wave nonlinearity are also introduced into th e equation. The wind energy input functions for wind waves and swells are s eparately considered by adopting Wen's (1989) empirical formula for wind wa ves and Snyder's observation results for swells. Thus, an extended mild-slo pe equation is obtained, in which the effects of refraction, diffraction, r eflection, current, bottom friction, wind energy input and wave nonlinearit y are considered synthetically.