E. J. Skudrzyk 231 
diffuse scatterer within the small grazing angles existing at the longer ranges. 
At long ranges, where the signal is specularly reflected, the fluctuations in both 
the direct and the reflected signal have the same causes; at short ranges, the 
diffuse reflection from the surface is an additional and more important source 
of variability. 
Figure 12.18 shows two plots of the direct-signal fluctuations for one day. 
The solid lines represent the solution that would be computed if a Gaussian cor- 
relation function were assumed. By assuming a suitable value of the correlation 
distance R and of the rms fluctuation of the temperature, lines can be drawn 
that pass through the measured points with reasonable accuracy. To obtain a 
better fit for the low values of range, the correlation function would have to be 
assumed to consist of two exponential terms. Figure 12.19 shows the results 
of measurements made in July, when measurements of the temperature micro- 
structure were made simultaneously. The results of the measurements make 
it possible to test the prediction of Gaussian correlation functions and the 
Kolmogorov theory. 
The natural way to deal with scattering is to assume a continuous distribu- 
tion of patch sizes from the beginning, such as is given by the Kolmogorov law. 
This theory leads to considerably better agreement with the experimental 
results than the procedures based on the experimental or Gaussian correlation 
function. The values predicted on the basis of this theory are of the right mag- 
nitude, and the frequency and range variations are reproduced in a better manner 
than with the Gaussian correlation-function theory. Future measurements will, 
therefore, have tobe based exclusively on a Kolmogorov-type power spectrum of 
the sound velocity fluctuations. 
REFERENCES 
1. R. J. Urick and C.W. Searfoss, "The Microthermal Structure of the Ocean Near Key West, Florida,” 
Part I—Description, Naval Research Laboratory Report No. S-3392 (December 7, 1948); Part II—Analy- 
sis, Naval Research Laboratory Report No. S-3444 (April 12, 1949). 
2, D.C. Whitmarsh, E. J. Skudrzyk, and R. J. Urick, "Forward Scattering of Sound in the Sea and Its Cor- 
relation with the Temperature Microstructure,” J. Acoust. Soc. Am., Vol. 29, 1124-1143 (1957). 
3, A.N. Kolmogorov, "Local Turbulence Structure in an Incompressible Liquid for Very Large Reynolds 
Numbers,” Doklady Akad. Nauk SSSR, Vol. 30, 299-303 (1941). 
4, W. Heisenberg, "Zur Statistischen Theorie der Turbulenz," Z.Tech. Phys., Vol. 124, 628 (1948). 
5. D.I. Blokhinstev, Acoustics of an Inhomogeneous Moving Medium (Gostekhizdat, Moscow, 1946). 
6. Lande, Geiger Scheel, Handbuch der Physik, Bd. XX, 453. 
7. L.C. Kober, "Stérung und Stérbefreiung von Riickstrahlung in Wellenfeldern,” 217-225; "Riickstrahlung 
von Reflexions Kérpern in Wellenfeldern," 217, Osterr. Ing.-Arch. (1951). 
8. C.K. Bachelor, Theory of Homogeneous Turbulence (Cambridge University Press, 1956) p. 123; the 
formula in the text is obtained by correcting for the scalar nature of the temperature fluctuations. 
9. Lord Rayleigh, The Theory of Sound (Dover Publications, Inc., New York, 1945). 
10. Wolfgang Grébner and Nikolaus Hofreiter, Integraltafel (Springer-Verlag, Vienna, 1949), 
11. Bierens De Haan, Nouvelles Tables D'Integrales Definies (G.E. Stechert and Co., New York, 1939). 
12. E. J. Skudrzyk, "The Scattering of Sound in an Inhomogeneous Medium,” Pennsylvania State Univ. (May 
10, 1960). 
13. V.I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Co., Inc., New York, 1961). 
14, A.M. Obukhov, "On the Scattering of Sound in a Turbulent Flow," Doklady Akad. Nauk SSSR, 30, 611 
(1941). 
15. V. A. Krasilnikov, "On the Propagation of Sound in a Turbulent Atmosphere," Doklady Akad. Nauk SSSR, 
Vol, 47, 486 (1945). 
16. P.G. Bergmann, "Propagation of Radiation in a Medium with Random Inhomogeneities," Abstract, Phys. 
Rey., Vol. 69 (1946). 
17. V. A. Krasilnikov, "On Amplitude Fluctuations of Sound Propagating in a Turbulent Atmosphere,” Dok- 
lady Akad. Nauk SSSR, Vol. 58, 1353 (1947). 
