Suppose the dispersion relation for a non-moving medium is: with k the wavenumber. Then for a medium with mean velocity vector V, the dispersion relationship with Doppler shift becomes: where k is the wavenumber vector, related to k as: k = |k|. The dot product k•V is equal to: k•V = kV cos α, with V the length of the mean velocity vector V: V = |V|. And α the angle between the wave propagation direction and the mean flow direction. For waves and current in the same direction, k•V=kV. See also Other articles on dispersion Dispersive partial differential equation Capillary wave Dispersive water-wave models Airy wave theory Benjamin–Bona–Mahony equation Boussinesq approximation (water waves) Cnoidal wave Camassa–Holm equation Davey–Stewartson equation Kadomtsev–Petviashvili equation (also known as KP equation) Korteweg–de Vries equation (also known as KdV equation) Luke's variational principle Nonlinear Schrödinger equation Shallow water equations Stokes' wave theory Trochoidal wave Wave turbulence Whitham equation Notes References , 2 Parts, 967 pages. Originally published in 1879, the 6th extended edition appeared first in 1932. External links Mathematical aspects of dispersive waves are discussed on the Dispersive Wiki. Water waves Wave mechanics Fluid dynamics Physical oceanography