Plenary Lecture

A Modified Scale Invariant Statistical Theory of Turbulence

Professor Siavash H. Sohrab
Robert McCormick School of Engineering and Applied Science
Department of Mechanical Engineering
Northwestern University, Evanston, Illinois 60208
USA
 

Abstract: A scale-invariant model of statistical mechanics is applied to derive the invariant forms of the conservation equations for mass, energy, and linear and angular momentum. The connection between the modified and the classical Navier-Stokes equation of motion will be described and the historical evolution of important features of the latter will be critically examined. The modified form of the equation of motion will be shown to lead to a modified statistical theory of turbulence. General aspects of the modified invariant statistical theory of turbulence will be described and its predictions will be compared with the existing experimental data. In addition, the phenomena of super-fluidity, super-conductivity, and super-luminosity (laser-action) will be discussed in terms of transitions from turbulent (highly dissipative) to laminar (weakly dissipative) flows for the statistical fields respectively corresponding to molecular-dynamic, electro-dynamic, and chromo-dynamic scales. It will be shown that the notion of Reynolds stresses and their role in the closure problem of turbulence is harmonious with the modified theory. The implications of the modified theory to the phenomenon of turbulent energy spectra, energy dissipation, Kolmogorov length scale, and the inertial subrange will also be discussed.