Abstract
The statistical theory of turbulence, initiated by Taylor (1935) and v. Kármán & Howarth (1938), has recently been developed so far that a satisfactory explanation of the spectral distribution of energy among the turbulent eddies can be given. In fact Kolmogoroff (1941
a, b
) and independently Onsager (1945) and v. Weizsaecker (1948) have introduced a similarity hypothesis, which allows a determination of the spectrum for eddies with large Reynolds numbers, and the author (Heisenberg 1948) has extended these calculations to include those frequency components which have small Reynolds numbers. Since the distribution of energy among the largest eddies must be a geometrical and not a statistical problem, one may say that the statistical part of the spectrum is now well understood. Recently Batchelor & Townsend (1947, 1948
a, b
) have studied the decay of turbulent motion caused by a mesh grating in a wind tunnel, and the following discussions will apply the statistical theory to this problem. For the calculations the notation of Heisenberg (1948) will be used. If
pF(k)dk
denotes the energy contained between the wave numbers
k
and
k
+
dk
, the following equation for the dissipation of energy was given (Heisenberg 1948, equation (13)):
S
k
= {
μ + pk
∫(
F
(
k
'') /
k
''
3
)
dk
" } ∫
k
0
2
F
(
k
')
k
'
2
dk
'.
Reference12 articles.
1. Batchelor G. K. 1948 Proc. Roy. Soc. A 195 (in the Press).
2. Batchelor G. K. & TownsendA. A. 1947 Proc. Roy. A 190 534.
3. Proc. Roy;Batchelor G. K.;Soc. A,1948
4. 6 Proc. Roy;Batchelor G. K.;Soc. A,1948
5. Heisenberg W. 1948 Z.Phys. 124 628.
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