Analysis of periodically-forced turbulence in the rapid distortion limit

Rapid Distortion Theory is used to perform calculations of unsteadily-forced initially isotropic turbulence so that the physics of such flows can be better understood. The results of these calculations show that there are three distinct regimes of physical behavior for the kind of turbulence that we are considering: (1) turbulence that is forced at a relatively low frequency in which the kinetic energy settles down to a constant value at later times, (2) turbulence that is forced at a slightly higher frequency in which the kinetic energy value oscillates for a time, but then increases dramatically, and (3) turbulence that is forced at a relatively high frequency in which the kinetic energy evolution exhibits a periodic behavior. To better understand the role of the rapid pressure-strain correlation, these results are also compared to Inertial Model results for the same set of forcing frequencies. The results of this comparison show that the rapid pressure plays a key role in determining the stability characteristics of unsteadily-forced turbulence. The evolution equation for kinetic energy is then used to propose a model that describes the behavior approximately in terms of a time lag between applied mean strain and the Reynolds stress. This model suggests that the different responses under the different frequencies of forcing correspond to different stress-strain time lags. Overall, then the results indicate that rapid pressure serves to create a time lag between applied stress and strain, and it is the extent of this time lag that causes turbulence to respond differently under various frequencies of forcing.