Response maxima in time-modulated turbulence: Direct numerical simulations

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

Corresponding authors: a.k.kuczaj@utwente.nl d.lohse@utwente.nl

Received: 24 September 2005
Accepted: 30 January 2006

Abstract

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 ω. 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 ω the phase shift approaches roughly for the total energy and for the energy dissipation rate.