Time evolution of the eddy viscosity in two-dimensional
Navier-Stokes flow
Abstract
The time evolution of the eddy viscosity associated with an
unforced two-dimensional incompressible Navier-Stokes flow is
analyzed by direct numerical simulation. The initial condition
is such that the eddy viscosity is isotropic and negative. It
is shown by concrete examples that the Navier-Stokes dynamics
stabilizes negative eddy viscosity effects. In other words,
this dynamics moves monotonically the initial negative eddy
viscosity to positive values before relaxation due to viscous
term occurs.