We derive transport equations for the propagation of water wave action in the presence of a static, spatially random surface drift. Using the Wigner distribution W(x,k, t) to represent the envelope of the wave amplitude at position x contained in waves with wavevector k, we describe surface wave transport over static flows consisting of two length scales; one varying smoothly on the wavelength ...

We derive transport equations for the propagation of water wave action in the presence of subsurface random flows. Using the Wigner distribution W(x, k, t) to represent the envelope of the wave amplitude at position x, time t contained in high frequency waves with wave vector k/ε (where ε is a small parameter compared to a characteristic distance of propagation), we describe surface wave transp...