Covariance functions and spectra for waves propagating in a turbulent medium to or from moving vehicles

In this paper theoretical expressions are derived for the time-lag covariance functions and frequency spectra of a wave propagating in a turbulent medium where either the source, receiver, or both are moving. The expressions are generalizations of the results of other workers. A Gaussian beam wave was considered but results are presented for plane and spherical waves also. It is also noted that a commonly used approximation may not be valid when focused beams are discussed.