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

Monday, September 24, 2012 - 2:00pm - 2:50pm
Keller 3-180
Margaret Beck (Heriot-Watt University)
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.
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