Plenary Lecture
Euler, Navier-Stokes, and Modified Equations of Motion and Their Connections to Schrödinger and Dirac Wave Equations of Quantum Mechanics
Professor Siavash H. Sohrab
Robert McCormick School of Engineering and Applied Science
Department of Mechanical Engineering
Northwestern University
Evanston, Illinois
USA
E-mail: s-sohrab@northwestern.edu
Abstract: After the introduction of a scale invariant model of statistical mechanics, the exact relations between Euler, Navier-Stokes, and a modified form of equations of motions are described and their connections to Schrödinger and Dirac wave equations of quantum mechanics are discussed. The quantum mechanical foundation of the problem of turbulence is described and the phenomenon of turbulent dissipation in general and the role of Heisenberg spectral kinematic viscosity in such dissipation processes are examined. Also, the central role of vorticity in turbulent dissipation based on a modified form of Helmholtz vorticity equation is discussed. Finally, the scale invariant nature of Reynolds stresses are described and their role in the closure problem of turbulence are addressed.
Brief Biography of the Speaker: Siavash H. Sohrab received his PhD in Engineering Physics in 1981 from University of California, San Diego, his MS degree in Mechanical Engineering from San Jose State University in 1975, and his BS degree in Mechanical Engineering from the University of California, Davis in 1973. He joined Northwestern University in 1982 and since 1990 he is Associate Professor of Mechanical Engineering at the Northwestern University.