Colloquium
3:00 p.m., Friday
Math Annex 1100
Alexei Novikov
Caltech
Eddy viscosity of cellular lows
The goal of this work is to understand the phenomenon of
eddy viscosity in twodimensions. In the presence of
smallscale eddies the transport of largescale vector
quantities can be accompanied with depleted, and even
``negative" diffusion at large Reynolds number. For
stationary flows, the eddy viscosity is a tensor
in the equation that governs the transport of the
slow spatial modulations of highly oscillatory
cellular solutions (eddies) of the NavierStokes
equations.
Using multiscale techniques we derive eddy viscosity
of cellular flows  special periodic stationary solutions
of the Euler's equations. We justify this derivation using
bootstrapping and LittlewoodPaley type arguments. We design
a numerical upscaling method, that allows us to compute eddy
viscosity of cellular flows when ratio between the scales is
small, and compare it with the predictions of the multiscale
analysis. For cellular flows with closed streamlines we give
rigorous bounds on eddy viscosity at high Reynolds number
by means of saddle point variational principles for nonlocal,
nonselfadjoint operators.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
