A Novel Approach to the Kinetic Theory of Fluids—Onset of Turbulent Motion
It is well known that the macroscopic properties of a fluid in a state of motion are described by the classical equations of hydrodynamics due to Euler, Lagrange, and Stokes. The equations that have been “derived” by an ingenious application of Newton’s laws of motion to an infinitesimally small volume of fluid have found a variety of applications to specific physical or engineering situations. For instance, in the case of the flow pattern around some body or the flow around a high-speed projectile and in many other problems of a highly intricate nature have been studied by many workers in this field. While problems of this type based on the original equation of Euler and others are reaching a comparatively saturated state, the elucidation of the physical basis of the equations of hydrodynamics has not received much attention until quite recently. Only in the past few years some attempts have been made toward a deduction of the laws of fluid motion from the results of the kinetic theory of fluids.1 Encouraged by such attempts, the author2 has attempted to derive macroscopic properties with the help of certain correlation functions called product densities which are familiar in the theory of stochastic point processes.3 The hydrodynamical equations that follow from the heirarchy of equations satisfied by the product densities have been shown to be valid only for configurations very near the equilibrium position determined by the Poisson approximation.
KeywordsKinetic Theory Local Energy Transport Coefficient Pair Correlation Function Turbulent Motion
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