Hydrodynamics — On the application of statistical mechanics to the theory of turbulent fluid motion. IV

Abstract

The present ager is a continuation of some investigations which have been published in 1929¹); in particular it intends to give a further development to the formulation of the problem, indicated in §11 of Paer III. In connection with the latter point it is necessary to recollect that the point of view taken in constructing an equation which should govern the various possible “states” of the turbulent motion, had been shifted during the course of this former work, so that it consisted of three sections, the first one formed by Parts I and II (§§ 1–7). the second one by §§ 8–10 of Part III, and the third one by § 11²). On account of this circumstance it may be useful to summarize the leading assumptions upon which the statistical considerations were founded, the more so, as it might be asked what is the purpose of introducing a rather abstract and complicated system of statistical formulae, while in the last three years such remarkable successes have been obtained by the theories put forth by Prandtl and by von Karman ³). A few words may be said about these latter theories first.