Small scale response and modeling of periodically forced turbulence

Wouter Bos, LMFA, Ecole Centrale de Lyon, UCBL, INSA, CNRS, France Timothy T. Clark, Tau Technologies, Albuquerque, NM USA Robert Rubinstein, NASA Langley Research Center, Hampton, VA USA Abstract The response of the small scales of isotropic turbulence to periodic large scale forcing is studied using two-point closures. The frequency response of the turbulent kinetic energy and dissipation rate, and the phase shifts between production, energy and dissipation are determined as functions of Reynolds number. It is observed that the amplitude and phase of the dissipation exhibit nontrivial frequency and Reynolds number dependence that reveals a filtering effect of the energy cascade. Perturbation analysis is applied to understand this behavior which is shown to depend on distant interactions between widely separated scales of motion. Finally, the extent to which finite dimensional models (standard two-equation models and various generalizations) can reproduce the observed behavior is discussed.