by Volker John, William J. Layton, Niyazi Sahin.

**Series:** 2002-14, Preprints

- MSC:
- 76D10 Boundary-layer theory, separation and reattachment, higher-order effects

**Abstract:**

The problem of predicting features of turbulent flows occurs in many

applications such as geophysical flows, turbulent mixing, pollution

dispersal and even in the design of artificial hearts. One

promising approach is large eddy simulation (LES), which seeks to predict

local spacial averages $\ov{\bu}$ of the fluid's velocity $\bu$.

There are several core difficulties in LES. Closure models are very

important in applications in which the equations must be integrated over a

long time interval. In engineering applications, however, often the

equations are solved over moderate time intervals and the core difficulty

is associated with modeling near wall turbulence in complex geometries.

Thus, one important problem in LES is to find appropriate boundary conditions for the

flow averages which depend on the behavior of the unknown flow near the

wall. Inspired by early works of Navier and Maxwell, we develop such

boundary conditions of the form

$$

\ov{\bu} \cdot \bn = 0 \mbox{ and } \beta(\delta,Re,|\ov{\bu} \cdot

\btau|) \ov{\bu}\cdot \btau +2Re^{-1}\bn \cdot \D(\ov\bu) \cdot \btau = 0

$$

on the wall. We derive effective friction coefficients $\beta$ appropriate

for both channel flows and recirculating flows and study their

asymptotic behavior as the averaging radius $\delta\to 0$ and as

the Reynolds number $Re \to \infty$. In the first limit, no--slip conditions

are recovered. In the second, free--slip conditions are recovered.

**Keywords:**

large eddy simulation, near wall models, turbulence, boundary layer