Incompressible Fluids, Turbulence and Mixing
In honor of Peter Constantin’s 60th birthday

Claude Bardos
Afilliation: Laboratoire Jacques Louis Lions University Pierre and Marie Curie

Title: Boundary Effect and Turbulence

Abstract: A series of recent results seem to indicate that it is the presence of boundary with the Reynolds number going to infinity that the relation between weak convergence and statistical theory of turbulence is the most obvious. In this situation one can show that the absence of turbulence is characterized by the following equivalent facts:

1. Non conservation of energy.
2. Anomalous energy dissipation.
3. Anomalous energy dissipation in a boundary layer of size $o(\nu)$.
4. Non $0$ Reynolds stress tensor.

As a justification of this point of view I can also consider the similarity between the Navier-Stokes$\rightarrow$ Euler limit and the Boltzmann $\rightarrow$ Euler limit.

Slides: BardosClaude2.pdf
Paper: BardosClaude.pdf

Center for Nonlinear Analysis   |   Department of Mathematical Sciences   |   Carnegie Mellon University