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 among production, energy, and dissipation are determined as functions of the 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.
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