E. J. Skudrzyk 209 
. Fig. 12.11. Fluctuations in which 
the left half are in antiphase to the 
right half. 
fortunately, no satisfactory explanation has yet been found, but a plausible 
explanation can be derived with the aid of a statistical method [6] that was 
introduced by Lande in 1913. This method, which represents an expansion of the 
procedures used in thermodynamics today, analyzes the physical system by 
counting the number of its degrees of freedom and by attributing a certain energy 
to each of them. The degrees of freedom are identified with the number of pa- 
rameters that are required to describe the system, such as the number of the 
Fourier coefficients that are finite. This method has been very successful in 
recent years [7], although it does not seem to be fully understood at present. 
The temperature fluctuation within the finite layer of water between the surface 
and the point of measurement can be represented by a Fourier series. If isotropy 
is assumed in this layer, no consideration need be given to what happens at 
greater depth, and the layer canbe assumed to be repeated periodically. Because 
of the continuity of the temperature distribution, the lower boundary has to be 
a plane of symmetry in this periodic pattern of layers, and the longest wave- 
length required to represent the temperature pattern is therefore equal to four 
times the depth. Since the lower boundary of the layer is not plane but distorted 
and fuzzy, the phenomenon is not strictly represented by a Fourier series but 
by a Fourier integral. However, the envelope of the spectrum may still be con- 
sidered as approximately that of the series, with the low frequencies also filled 
in (because of the nonperiodicity of the actual temperature pattern). 
12.2. THE CHARACTERISTICS OF THE TEMPERATURE STRUCTURE OF THE SEA 
The static thermal conductivity of water is extremely small. Temperature 
patches would have a lifetime of many months if they were not split up and de- 
formed by turbulent motion. There is, therefore, little doubt that these patches 
are originally generated by turbulent motion and represent "frozen turbulence." 
The energy that is fed into the water by the radiation of the sun and by the 
wind acting on the sea surface seems to be predominantly used for the generation 
of very large turbulence patches and temperature patches (see Fig. 12.6). The 
large patches eventually split up into very small patches; thus, the turbulent 
and the thermal energies are passed down by a kind of cascade process to the 
range of the small and very small patches (or space wave numbers). The in- 
tensity of the large-diameter patches depends on the weather and on the depth 
