On enstrophy dissipation in 2D turbulence
Seminar Room 1, Newton Institute
We consider dissipation of enstrophy, one half the integral of squared vorticity, in 2D incompressible, turbulent flows at very high Reynolds number. We prove rigorously that, if fully developed turbulence is to be modeled mathematically by irregular (weak) solutions of the 2D Euler equations in the limit of vanishing viscosity, then there is no dissipation as long as the initial enstrophy is finite. We also provide examples of dissipative flows when the initial enstrophy is infinite. Our analysis is inspired by work of G. Eyink. This is joint work with Helena and Milton Lopes.