  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.
