The difference between Doppler velocity and real wind velocity in single scattering from refractive index fluctuations

Scattering of electromagnetic waves by turbulence is considered. It is shown that Doppler velocity (the ratio of Doppler shift and Bragg wave number) includes two terms: The first is the mean radial velocity in the scattering volume, and the second is what we call the “correlation velocity,” caused by a correlation between the fluctuations of velocity and those 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. It appears that the correlation velocity, which cannot be directly measured with existing radar wind profilers, could be separated from the total Doppler shift by means of bistatic radars. A potential application is the profiling of fluxes using bistatic systems.