ON THE APPLICATION OF TIME-DEPENDENT SCALING TO THE MODELING OF TURBULENCE UNDERGOING COMPRESSION

In this paper we study the implications of a time dependent scaling which makes the Navier-Stokes equations invariant under an external isotropic compression. In addition to the use of Rapid Distortion Theory (RDT), a rescaling of the elapsed time allows the non-linear turbulence mechanisms to be accounted for in a straightforward way. The approach provides analytical laws for the evolution of the kinetic energy (k), its dissipation rate (epsilon) and the typical length scales, under isotropic compression. Several (k-epsilon) models are compared for different compression laws, including applications to reciprocating engines. Finally, an extension towards axisymmetrical compression is proposed using both specific RDT calculations and the "isotropic" time-rescaling. Promising comparisons are made with "best" (in accordance with the above comparisons) k-epsilon models and with direct numerical simulations.