Waves On A Mean Current: Doppler Shift
Water waves on a mean flow (so a wave in a moving medium) experience a Doppler shift. 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 inner 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.
Read more about this topic: Dispersion (water Waves)
Famous quotes containing the words waves and/or shift:
“Like as the waves make towards the pebbled shore,
So do our minutes hasten to their end;
Each changing place with that which goes before,
In sequent toil all forwards do contend.”
—William Shakespeare (1564–1616)
““Circumstantial evidence is a very tricky thing,” answered Holmes thoughtfully. “It may seem to point very straight to one thing, but if you shift your own point of view a little, you may find it pointing in an equally uncompromising manner to something entirely different.””
—Sir Arthur Conan Doyle (1859–1930)