Tendency to occupy a statistically dominant spatial state of the flow as a driving force for turbulent transition

Abstract

A simple analytical model for a turbulent flow is proposed, which considers the flow as a collection of localized spatial structures that are composed of elementary "cells" in which the state of the particles (atoms or molecules) is uncertain. The Reynolds number is associated with the ratio between the total phase volume for the system and that for the elementary cell. Calculating the statistical weights of the collections of the localized structures, it is shown that as the Reynolds number increases, the elementary cells group into the localized structures, which successfully explains the onset of turbulence and some other characteristic properties of turbulent flows. It is also shown that the basic assumptions underlying the model are involved in the derivation of the Navier-Stokes equation, which suggests that the driving force for the turbulent transition described with the hydrodynamic equations is essentially the same as in the present model, i.e. the tendency of the system to occupy a statistically dominant state plays a key role. The instability of the flow can then be a mechanism to initiate the structural rearrangement of the flow to find this state.Comment: 7 pages, 4 figures, and Supplementary Material (2 pages, 3 figures), to be submitted to "Foundations of Physics". arXiv admin note: substantial text overlap with arXiv:1102.515