Statistical theory of turbulence III-Distribution of dissipation of energy in a pipe over its cross-section

The success of the theory of turbulence given in Part I, in predicting the connection between the rate of dissipation of energy in turbulent motion and the shape of the Ky correlation curve, suggests that it may be possible to use measurements of correlation in order to find out how the dissipation of energy is distributed over a field of turbulent flow. This is a fundamental question in any theory of turbulent motion which attempts to penetrate beyond the stage of empirical assumptions. By a fortunate coincidence the necessary observations already exist for the analysis of one case of flow from this point of view. The rate o f dissipation of energy of turbulent flow is W = 7·5 μ¯¯(∂u/∂y)2 = 15 μ ¯u2/λ2.