Kármán--Howarth Theorem for the Lagrangian averaged Navier-Stokes alpha model

Abstract

The Kármán--Howarth theorem is derived for the Lagrangian averaged Navier-Stokes alpha (LANS$-α$) model of turbulence. Thus, the LANS$-α$ model's preservation of the fundamental transport structure of the Navier-Stokes equations also includes preservation of the transport relations for the velocity autocorrelation functions. This result implies that the alpha-filtering in the LANS$-α$ model of turbulence does not suppress the intermittency of its solutions at separation distances large compared to alpha.

11 pages, no figures. Includes an important remark by G. L. Eyink in the conclusions