Some specific mathematical constraints on 2D turbulence

Citations of this article
Mendeley users who have this article in their library.
Get full text


We derive upper and lower bounds for ensemble averages of energy, enstrophy, and palinstrophy for the 2D periodic Navier-Stokes equations. This is carried out both in the general case, and in the case where the energy power law for fully developed turbulence holds. In the turbulent case, the bounds are sharp, up to a logarithm, and provide a new lower bound on the Landau-Lifschitz degrees of freedom. We also prove two properties of the inertial term under the turbulence assumption. One is that as the Grashof number is increased, the ensemble average of this term approaches the force. The other is that an estimate of it via the Ladyzhenskaya inequality is sharp on a considerable portion of the global attractor. © 2008.




Dascaliuc, R., Foias, C., & Jolly, M. S. (2008). Some specific mathematical constraints on 2D turbulence. Physica D: Nonlinear Phenomena, 237(23), 3020–3029.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free