The lack of a simple paradigm in fully developed turbulence: characteristics of local concentrations of vorticity and Reynolds stress in turbulent shear flows

Abstract

Fully developed turbulence is characterized by regions of concentrated temporally coherent activity in which dynamically relevant turbulence variables are concentrated. Concentrations can be identified in all turbulence variables at all turbulence scales, and are often perceived to play a major, even dominant, role in the kinematic and dynamic description of turbulent flows². The highest intensity values of enstrophy, for example, are observed to lie within structures that resemble classical models of vortex tubes and sheets (many studies). Implicitly, and sometimes explicitly, we assume that these vortical structures dominate the dynamics of turbulence evolution, at least at the small scales. Similarly, the dynamical role of short-lived quadrant two (Q2) Reynolds shear stress events in the near-wall region of turbulent boundary layers, as associated with the instability and breakdown of horseshoe-shaped vortices and internal shear layers, is often implicitly transferred to the description of fully turbulent shear flows in general. Underlying this discussion is the question “to what extent do paradigms such as vortex sheets, vortex tubes and Q2 Reynolds shear stress events characterize the dynamical evolution of fully developed turbulent flows?”

The analysis underlying this discussion is mostly contained in the Ph.D. thesis of Dr. Wenquei Lin (1993), currently of Delphi Harrison Thermal Systems, 200 Upper Mountain Road, Lockport, NY 14094 USA.