ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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The Craik-Criminale class of solutions to the incompressible Navier-Stokes and similar equations

Bruce Fabijonas
Department of Mathematics, Southern Methodist University, Dallas, TX.

Tuesday, June 25, 2002 15:00-16:00,
Room 145, NIST North (820)
Tuesday, June 25, 2002 13:00-14:00,
Room 4511

Abstract: Navier-Stokes equations expressed as a sum of a `base' flow which is linear in the spatial coordinates in an unbounded domain and a `disturbane' in the form of a standing wave. A classic example of such a solution is Bayly's elliptic instability. Bayly (1986) perturbed a rotating column of inviscid, incompressible fluid with elliptic streamlines by a modulated standing wave and found that for certain orientations of the wavevector, the amplitude grew exponentially in time in the linearized equations. The mechanism for this instability is parametric resonance. What Bayly failed to realize is that his solutions, including those which grow unbounded in time, are exact solutions to the nonlinear equations. The speaker's 1997 PhD thesis analyzed the stability of Bayly's solutions, and is the first known stability analysis of a Craik-Criminale solution. This talk will focus on the speaker's recent work in this field, including a stability analysis of a Craik-Criminale solution for the magnetohydrodynamic equations. This talk will also address Craik-Criminale solutions which appear in the Lagrangian averaged Navier-Stokes-alpha model of turbulence, also known as the viscous Camassa-Holm equations, and discuss how the model alters Bayly's elliptic instability.
Contact: D. W. Lozier

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.

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