IV-17 



C. THE WEAK INHOMOGENEITIES OF THE OCEAN 



The temperature distribution of the ocean exhibits a layered structure 

 in the vertical direction. This structure is largely the result of the energy input 

 due to weather conditions at the surface of the ocean (such as heat radiation of 

 the sun and evaporation) and the heat conduction of the water. The detail of the 

 layered structure changes with the time of day and witli the seasons. A typical 

 pattern of variation during the course of a day is shown in Figure IV-4. The 

 figure shows, for several times of day, the temperature distribution as a function 

 of depth, expressed in terms of a characteristic length scale which is the square 

 root of the product of the diffusivity of the heat conduction and the length of a day. 

 The resulting curves are seen to produce a surface layer of the order of 200 feet 

 in which the temperature fluctuates substantially with the time of day, and in 

 which the temperature gradients are negative during part of the day. These re- 

 verse gradients cause an unstable configuration which results in turbulent mixing. 

 As a consequence, the macroscopic structure of the uppermost layer of the ocean 

 has an isothermal character, although under examination in detail it will exhibit 

 innumerable patches of various sizes which result from the turbulent mixing 

 process. This top layer (of the order of magnitude of a few hundred feet) is called 

 the isothermal layer, although it is isothermal only in the large. Below the iso- 

 thermal layer, there is a region, called the thermocline, in which the temperature 

 gradient is practically constant. 



In addition to the instabilities occurring relatively near the surface of 

 the ocean, turbulence is caused by large scale internal waves and currents. In 

 all cases, the effect of the turbulence is to break up the systematic layered 

 structure of the ocean into a random, patchy structure. 



The resulting micro- structure of the temperature gives rise to a corre- 

 sponding micro- structure of the index of refraction, which is the principal type of 

 random inhomogeneity affecting wave propagation. 



The general range of sizes of the patches to be encountered may be 

 obtained from the following considerations. The largest patches to be encountered 

 at a depth h below the surface should be those resulting directly from the original 

 layered structure, and can therefore be expected to be patches extending between 

 the ocean surface and the depth of 2h. If these largest patches are more or less 

 spherical, we would expect their diameters to be of the order of 2h. The smallest 

 patches, on the otlier hand, would be determined by the heat conductivity of the 

 water. To quote Batchelor, who has investigated theoretically the statistical 

 properties of the microthermal structure: "The dominant feature of the action of 

 the turbulent motion on the temperature distribution is a continual reduction of the 

 length- scale of temperature variations . . . The continual increase in the magnitude 

 of temperature gradients due to random convection will ultimately be checked by the 



;arthur HMttU.linc. 



S-7001-0307 



