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:
“During our twenties...we act toward the new adulthood the way sociologists tell us new waves of immigrants acted on becoming Americans: we adopt the host culture’s values in an exaggerated and rigid fashion until we can rethink them and make them our own. Our idea of what adults are and what we’re supposed to be is composed of outdated childhood concepts brought forward.”
—Roger Gould (20th century)
“Someone had literally run to earth
In an old cellar hole in a byroad
The origin of all the family there.
Thence they were sprung, so numerous a tribe
That now not all the houses left in town
Made shift to shelter them without the help
Of here and there a tent in grove and orchard.”
—Robert Frost (1874–1963)