TR No. 22 
INTRODUCTION 
The important problems in the theory of turbulence are; the 
determination of the energy spectrum function, E(K, t), and hence 
the total kinetic energy of the turbulence, E, and the rate, € , 
at which the energy is dissipated by viscosity; the change in E(K ,t), 
E and with decay. A limited number of theoretical predictions are 
available concerning the form of the energy spectrum function in the 
low wave number range of the spectrum, the reason being that the 
structure of turbulence in the low wave number range is, in general, 
inhomogeneous, anisotropic and strongly dependent on the mean flow from 
which the energy of the turbulence is derived. Such characterisitcs 
result in an intractable theoretical analysis. 
The structure of turbulence in the high wave number range of the 
spectrum, however, has been hypothesized (Kolmogoroff, 1941) to be 
homogeneous, isotropic and statistically independent of the mean flow. 
The Kolmogoroff hypothesis states that at sufficiently high wave numbers 
the statistical structure of turbulence has a universal form and is 
uniquely determined by the parameters€ and V, the kinematic viscosity. 
The range of wave numbers for which the preceding is applicable is known 
as the universal equilibrium range, Within this range it can be shown 
through dimensional analysis that the energy spectrum function can be 
written as 
HY iG 
E(Ge | ek ay), (1) 
where Fk/k,) is a universal function and 
as (2/25 (2) 
is the wave number (approximately) at which the maximum in the energy 
dissipation spectrum is located. 
