ABSTRACT
C;, Ko and a}., a;, I can be different for different statistical moments. In Chapter 7, the von Karman and Gaussian spectra are used to calculate the statistical moments of a sound field in the Rytov and parabolic equation methods. These statistical moments depend on the correlation function of temperature fluctuations Br (R) and on the longitudinal correlation function of medium velocity fluctuations BRR(R) (see the last paragraph in section 7.2). Therefore, the relationship between q., C;, Ko and ai, a;, I can be obtained by comparing the correlation functions of temperature fluctuations BfK(R) and B?(R) and by comparing the longitudinal correlation functions of medium velocity fluctuations
B~~(R) and B~R(R), for the von Karman and Gaussian spectra. We shall assume that the correlation functions BfK(R) and B?(R) are equal
at R = 0, and that the same is true for B~~(R) and B~R(R): B;K(O) = B?(O) , B~~(O) = B~R(O) . (6.48)
(6.49)
To obtain the relationship between I and Ko, we shall assume that, for the von Karman and Gaussian spectra, the integral lengths of the normalized correlation functions of temperature fluctations are the same, and that the same is true for the integral lengths of the normalized longitudinal correlation functions of medium velocity fluctuations:
o (6.50)
Substituting BfK(R) from equation (6.46) and B¥(R) from equation (6.39) into equation (6.50) and calculating the integrals over R yields the relationship between I and Ko:
The same relationship is obtained when substituting B~~(R) given by equation (6.47) and B~R(R) given by equation (6.41) into equation (6.50) and calculating the integrals over R.
