Abstract
In a series of papers on the resistance experienced by a fluid in turbulent motion and on the application of statistical mechanics to the theory of turbulent fluid motion, it was attempted to obtain a picture of the relative probabilities of the various possible patterns of the secondary motion, in order to arrive at a calculation of the magnitude of the turbulent shearing stress and of the resistance experienced by the primary motion in consequence of this stress1). Serious difficulties, however, were encountered, which did not permit to bring the calculations to a satisfactory result, and which gave rise to doubts concerning the suitability of the method applied. In the last paper of the series it was suggested that it might be worth while to investigate the properties of certain systems of mathematical equations, which, although much simpler in structure than the equations of hydrodynamics, nevertheless show features which can be considered as the analogues of typical properties of the hydrodynamic equations.
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