The Equivalence of the Lagrangian-Averaged Navier-Stokes-{\alpha} Model and the Rational LES model in Two Dimensions

TL;DR

This paper demonstrates that in two dimensions, the Rational LES model and the Lagrangian-Averaged Navier-Stokes-α model are mathematically equivalent, linking two different turbulence modeling approaches.

Contribution

It establishes the equivalence between the Rational LES and Lagrangian-Averaged Navier-Stokes-α models in two-dimensional turbulence.

Findings

The two models are mathematically identical in two dimensions.

The equivalence provides insights into turbulence modeling approaches.

Supports the use of either model for improved turbulence simulation.

Abstract

In the Large Eddy Simulation (LES) framework for modeling a turbulent flow, when the large scale velocity field is defined by low-pass filtering the full velocity field, a Taylor series expansion of the full velocity field in terms of the large scale velocity field leads (at the leading order) to the nonlinear gradient model for the subfilter stresses. Motivated by the fact that while the nonlinear gradient model shows excellent a priori agreement in resolved simulations, the use of this model by itself is problematic, we consider two models that are related, but better behaved: The Rational LES model that uses a sub-diagonal Pade approximation instead of a Taylor series expansion and the Lagrangian Averaged Navier-Stokes-{\alpha} model that uses a regulariza- tion approach to modeling turbulence. In this article, we show that these two latter models are identical in two dimensions.