The difference between Doppler and real radial velocity in the single volume scattering

The scattering of electromagnetic waves by turbulence is considered. It is shown that the Doppler velocity (the ratio of Doppler shift and Bragg wave number) includes two terms. The first term is the mean radial velocity in the scattering volume. The second term, which the authors call the correlation velocity, is caused by a correlation between the fluctuations of velocity and of refractive index. The correlation velocity is proportional to the imaginary part of the Bragg wave vector component of the three-dimensional spatial cross spectrum of refractive index and radial wind velocity. In the electromagnetic case in the atmosphere, the correlation velocity provides information about the combination of humidity and heat fluxes. In the acoustic case, it provides information about the flux of sensible heat (in the atmosphere) or about some combination of salinity and heat fluxes (in water). In situ measurements of the temperature, humidity, and wind fluctuations in the atmosphere are analyzed to estimate the magnitude of the correlation velocity.