This chapter discusses that the application of methods of statistical analysis and statistical mechanics to the problem of turbulent fluid motion has attracted much attention in recent years. It investigated a complicated system of nonlinear equations, in order to find out enough about the properties of the solutions of these equations that insight can be obtained into the various patterns exhibited by the field and that data can be derived concerning the relative frequencies of these patterns in the hope that in this way a basis may be found for the calculation of important values. The difficulties encounter are of a twofold nature: in part they are connected with the complicated geometrical character of the hydrodynamical equations; in part they are dependent upon the presence of nonlinear terms, containing derivatives of the first order of the velocity components, along with derivatives of the second order multiplied by the very small coefficient of viscosity. The latter feature is responsible for a number of important, characteristics of turbulence, among which are prominent those connected with the balance of energy and with the appearance of dissipation layers. These layer an important part in the energy exchange, as they represent the main regions where energy is dissipated.
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