Direct numerical simulations of homogeneous turbulence subject to periodic shear

We perform direct numerical simulations (DNS) of homogeneous turbulence subject to periodic shear - S = S-max sin(omega t), where omega is the forcing frequency and S-max is the maximum shear. The lattice Boltzmann method (LBM) is employed in our simulations and a periodic body force is introduced to produce the required shear. We find that the turbulence behaviour is a strong function of the forcing frequency. There exists a critical frequcncy - omega(cr)/S-max approximate to 0.5 - at which the observed behaviour bifurcates. At lower forcing frequencies (omega < omega(cr)), turbulence is sustained and the kinetic energy grows. At highcr frequencies, the kinetic energy decays. It is shown that the phase difference betwet-n the applied strain and the Reynolds stress decreases monotonically from pi in the constant shear case to pi/2 in very high frequency shear cases. As a result, the net turbulerce production per cycle decreases with increasing frequency. In fact, at omega/S-max >= 10, decaying isotropic turbulence results are recovered. The frequencydependence of e.nisotropy and Reynolds stress budget are also investigated in detail. It is shown that inviscid rapid distortion theory (RDT) does not capture the observed features: it precticts purely oscillatory behaviour at all forcing frequencies. Second moment closurc models do predict growth at low frequencies and decay at high frequencies, but the critical frequency value is underestimated. The challenges posed by this flow to turbulence closure modelling are identified.