Space‐time analysis of wave propagation through a turbulent medium

The Kolmogorov hypothesis of an inertial range within the spectrum of steady state turbulence is used to show that the space‐time structure function for the velocity fluctuations in a fluid has the form of ( r 4/3 + ∈ 2/3 t 2 ) ½ where r and t are the space and time lags and ∈ the energy, for a reference frame in which the mean velocity is zero. The associated space‐time spectra are also derived. Equations for the propagation of the N event space‐time correlation functions of the complex electric field are derived assuming that the width of the angular spectrum of plane waves is much less than a radian.