THE LEVICH INSTITUTE ANNOUNCES THE FOLLOWING SEMINAR

Tuesday, 11/10/98
4:00 PM
Steinman Hall, Room #1M-22
Professor Demetrios Papageorgiou
New Jersey Institute of Technology
Department of Mathematics
"The Onset of Chaos in a Class of Exact Navier-Stokes Solutions"


ABSTRACT

The flow between parallel walls driven by the time-periodic oscillation of one of the walls is investigated. The flow is characterized by a non-dimensional amplitude Delta and a Reynolds number R. At small values of the Reynolds number the flow is synchronous with the wall motion and is stable. If the amplitude of oscillation is held fixed and the Reynolds number is increased there is a symmetry breaking bifurcation at a finite value of R. When R is further increased, additional bifurcations take place, but the structure which develops, essentially chaotic flow resulting from a Feigenbaum cascade or a quasiperiodic flow, depends on the amplitude of oscillation. The flow in the different regimes is investigated by a combination of asymptotic and numerical methods. In the small amplitude high Reynolds number limit we show that the flow structure develops on two time scales with chaos occurring on the longer time scale. The chaos in that case is shown to be associated with the unsteady breakdown of a steady streaming flow.The chaotic flows which we describe are of particular interest because they correspond to exact Navier Stokes solutions of stagnation point form. These flows are relevant to a wide variety of flows of practical importance.

BRIEF ACADEMIC/EMPLOYMENT HISTORY:

• 1986       Ph.D. Mathematics - Imperial College, London
• 1985-87  Courant Institute of Mathematical Sciences, NYU
• 1987-90   Levich Institute/Chemical Engineering Department, CCNY
• 1990-      Professor, Mathematics Department, NJIT

RESEARCH INTERESTS:

My interests include many aspects of applied mathematics and in particular the modelling, analysis and computation of different physical or dynamical problems. I am currently engaged in research involving fluid flows with free interfaces, breakup of jets, and complex flow patterns in fluids (chaotic dynamics). These efforts combine a careful analysis and computation of nonlinear partial differential equations of the evolution type. Formation of finite-time singularities and their analysis and computation is also of interest in the description of many severe physical phenomena, and this is a subject of current research for models of high-speed aerodynamic flows as well as interfacial problems.


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