G. K. Batchelor 



I think Dr. Kraichnan is the only one to have given thought to that. 



R. Kraichnan 



I did this formally, but as to what exactly the time dependence is, we don't 

 know too much about that. Guesses about that are probably less secure than about 

 the space-correlation. 



From the Floor 



You have the formula with the space-time correlation? 



R. Kraichnan 



Yes, a four dimensional treatment. 



From the Floor 



I am not going to attempt to discuss Dr. Batchelor's valuable contribution to the 

 study of wave scattering due to turbulence, but there is a practical observation I should 

 like to make, and I don't think it is entirely irrelevant. 



It concerns the interpretation of the twinkling of sound transmitted in the 

 ocean. In the sea, of course, we have a moving boundary, the surface of the sea, 

 and a fixed surface, the bottom, and it may well be that these have a greater effect 

 on the twinkling under certain conditions than does the volume scattering. 



D. Mintzer 



It is true that at long ranges, where you may have reflections from the sur- 

 face, this will play an important role; however, there are many cases, including several 

 reported in the literature, in which the sound wave goes completely through the volume 

 without touching the surface; in this case the simple formulation is correct. 



I will make another comment, concerning time correlation problems, which 

 someone previously mentioned. The scattering of sound in a time-varying randomly- 

 inhomogeneous medium has been done for the case of scalar inhomogeneities. 



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