Department Home Page About Us: • Contact Info. • Faculty • Staff • Teaching Assistants Academic Program: • Admission • Undergraduate • Graduate • Certificates Courses: • Course Description • Class Web Pages • Class Syllabi Research: • Colloquium • Interdisciplinary Seminar • Seminars • Steve Goldman Lectures in Mathematical Physics Links: • Completing Online GEP Courses • Best Jobs • Newsletter • Math Lab •Math Placement Test • Careers • American Mathematical Society • Mathematical Association of America

Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2004-2005 MATHEMATICS COLLOQUIUM SERIES 01/25/05 Colloquium Mr. Robert Rubenstein NASA Langley Research Center The dissipation rate transport equation in two-equation turbulence modeling Abstract:   The two equation turbulence model continues to be a mainstay of practical computations and currently has an important role in "hybrid" strategies for large-eddy simulation. Two equation modeling raises the theoretical problem of whether the scalar descriptors of an evolving Kolmogorov spectrum satisfy closed equations of motion. This problem can be compared to kinetic theory, where the scalar descriptors of a local Maxwellian, the hydrodynamic moments, do satisfy such equations, namely the Navier-Stokes equations. The theoretical possibility of a corresponding two-dimensional abridgement of turbulence dynamics will be considered with special attention to the dissipation rate equation, the theoretical basis of which remains uncertain. It will be argued that in self-similar flows, the balance of vortex stretching and enstrophy destruction required by this equation can be justified but that a universal dissipation rate equation valid for all self-similar flows does not exist. Some reasons why kinetic theory admits a finite dimensional abridgement but turbulence does not will be suggested.