Issue
Europhys. Lett.
Volume 73, Number 6, March 2006
Page(s) 851 - 857
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
DOI http://dx.doi.org/10.1209/epl/i2005-10486-2
Published online 15 February 2006
Europhys. Lett., 73 (6), pp. 851-857 (2006)
DOI: 10.1209/epl/i2005-10486-2

Response maxima in time-modulated turbulence: Direct numerical simulations

A. 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

a.k.kuczaj@utwente.nl
d.lohse@utwente.nl

received 24 September 2005; accepted in final form 30 January 2006
published online 15 February 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 $\omega$. 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 $1/\omega$. 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 $\omega$ the phase shift approaches roughly $90^{\circ}$ for the total energy and $180^{\circ}$ for the energy dissipation rate.

PACS
47.27.Rc - Turbulence control.
47.27.E- - Turbulence simulation and modeling.
47.27.Gs - Isotropic turbulence; homogeneous turbulence.

© EDP Sciences 2006