  In the hybrid RANS-LES simulations, proper turbulent fluctuations should be
added at the RANS-to-LES interface to drive the numerical solution restoring to
a physically resolved turbulence as rapidly as possible. Such turbulence
generation methods mostly need to know the distribution of the characteristic
length scale of the background RANS model, which is important for the recovery
process. The approximation of the length scale for the Spalart-Allmaras (S-A)
model is not a trivial issue since the model's one-equation nature. As a direct
analogy, the approximations could be obtained from the definition of the
Prandtl's mixing length. Moreover, this paper proposes a new algebraic
expression to approximate the intrinsic length scale of the S-A model. The
underlying transportation mechanism of S-A model are largely exploited in the
derivation of this new expression. The new proposed expression is employed in
the generation of synthetic turbulence to perform the hybrid RANS-LES
simulation of canonical wall-bounded turbulent flows. The comparisons
demonstrated the feasibility and improved performance of the new length scale
on generating synthetic turbulence at the LES inlet.
