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

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

2001-05-17

arxiv.org/abs/nlin/0105042v2

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1017/S002211200200160X

The K\'arm\'an--Howarth theorem is derived for the Lagrangian averaged Navier-Stokes alpha (LANS$-\alpha$) model of turbulence. Thus, the LANS$-\alpha$ 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$-\alpha$ model of turbulence does not suppress the intermittency of its solutions at separation distances large compared to alpha.

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