Response maxima in time-modulated turbulence: Direct numerical simulationsA. K. Kuczaj1, B. J. Geurts1, 2 and D. Lohse3
1 Department of Applied Mathematics and J. M. Burgers Center for Fluid Dynamics University of Twente - P.O. Box 217, 7500 AE Enschede, The Netherlands
2 Department of Applied Physics, Eindhoven University of Technology P.O. Box 513, 5300 MB Eindhoven, The Netherlands
3 Department of Applied Physics and J. M. Burgers Center for Fluid Dynamics University of Twente - P.O. Box 217, 7500 AE Enschede, The Netherlands
received 24 September 2005; accepted in final form 30 January 2006
published online 15 February 2006
The response of turbulent flow to time-modulated forcing is studied by direct numerical simulations of the Navier-Stokes equations. The large-scale forcing is modulated via periodic energy input variations at frequency . The response is maximal for frequencies in the range of the inverse of the large eddy turnover time, confirming the mean-field predictions of von der Heydt, Grossmann and Lohse (Phys. Rev. E, 67 (2003) 046308). In accordance with the theory the response maximum shows only a small dependence on the Reynolds number. At sufficiently high frequencies the amplitude of the kinetic energy response decreases as . For frequencies beyond the range of maximal response, a significant change in the phase-shift relative to the time-modulated forcing is observed. For large the phase shift approaches roughly for the total energy and for the energy dissipation rate.
47.27.Rc - Turbulence control.
47.27.E- - Turbulence simulation and modeling.
47.27.Gs - Isotropic turbulence; homogeneous turbulence.
© EDP Sciences 2006