On the physical effects of variable filtering lengths and times in LES
The Large Eddy Simulation of turbulent flows is based on the application of a filtering operator that separates the resolved eddies from the unresolved ones. If the flow is inhomogeneous this resolution is different from region to region, and different filtering lengths or times are required. Variable filtering operators do not commute with differentiation, and this problem is presently the subject of many studies. In the present paper this problem is addressed by considering a particular class of filters, the differential ones, that are provided with simple properties and can be easily applied to the Navier-Stokes equations. The results are read physically, by considering the effect that a variable filtering length or time has on simple evolutionary equations. It is shown in particular that a differential elliptic filter with a variable filtering length produces a diffusive effect, while a differential low pass filter provided with a variable filtering time is responsible for a modification of the convective velocity. © 2002 Kluwer Academic Publishers.
