Group velocities
From Glossary of Meteorology
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group velocity
- The velocity of the envelope of a group of waves of nearly equal frequencies.
From the dispersion relation k(ω) the group velocity is defined as dω/dk, as distinguished from the phase velocity (or phase speed) ω/k. The origin of this term is made clearer by considering the superposition of two equal-amplitude plane harmonic waves with wavenumbers k ± Δk and frequencies ω ± Δω:Because
, this composite wave may be looked upon as a high-frequency wave, with phase velocity ω/k, modulated by a wave of much lower frequency Δω. The envelope of the high- frequency wave is a low-frequency wave propagating with the group velocity Δω/Δk. Note the similarity with beating. Indeed, a group of waves may be looked upon as a moving beat.
In deep water, on the basis of linear water wave theory, it can be shown to be equal to one half the phase velocity.
