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Metastability and rapid convergence to quasi-stationary bar states for the 2D Navier-Stokes Equations

Presenter
September 24, 2012
Keywords:
  • Dynamical systems in fluid mechanics
MSC:
  • 37N10
Abstract
Quasi-stationary, or metastable, states play an important role in two-dimensional turbulent fluid flows where they often emerge on time-scales much shorter than the viscous time scale, and then dominate the dynamics for very long time intervals. We propose a dynamical systems explanation of the metastability of an explicit family of physically relevant quasi-stationary solutions, referred to as bar states, of the two-dimensional incompressible Navier-Stokes equation with small viscosity on the torus. Linearization about these states leads to a time-dependent operator. We show that if we approximate this operator by dropping a higher-order, non-local term, it produces a decay rate much faster than the viscous decay rate. This is joint work with C. Eugene Wayne.