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On the Doppler effect in a transient gravity‐wave spectrum
Author(s) -
Pulido Manuel
Publication year - 2005
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1256/qj.03.220
Subject(s) - physics , gravity wave , doppler effect , gravitational wave , spectral density , power law , classical mechanics , mathematics , astrophysics , quantum mechanics , statistics
The power‐spectrum evolution of a transient gravity‐wave disturbance propagating conservatively upwards in a shear flow is examined. It is proven that the wave action for a disturbance suffering Doppler shifting is invariant in the wave‐number space. On the other hand, vertical wave‐momentum flux, even when it is invariant for waves of fixed frequency, is not invariant in the wave‐number space for a transient disturbance. The principle is used to derive a transformation law between a source spectrum and the resultant Doppler‐shifted spectrum. The Doppler‐shifted spectrum has a −3 power law in the spectral tail, the asymptotic behaviour of the tail is shown to be independent of the gravity‐wave source. The result is obtained in two ways: from the gravity‐wave energy equation and also by Fourier transforming the solution to the gravity‐wave equations. The derived spectral transformation law should be a key point in spectral gravity‐wave parametrizations. Copyright © 2005 Royal Meteorological Society