Response maxima in time-modulated turbulence: Direct Numerical Simulations

– 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, 046308 (2003)). In accordance with the theory the response maximum shows only a small dependence on the Reynolds number and is also quite insensitive to the particular flow-quantity that is monitored, e.g., kinetic energy, dissipation-rate, or Taylor-Reynolds number. At sufficiently high frequencies the amplitude of the kinetic energy response decreases as 1/ω. For frequencies beyond the range of maximal response, a significant change in phase-shift relative to the time-modulated forcing is observed. Introduction. – Recently, response maxima in time modulated turbulence have been predicted within a mean field theory of turbulence [1]. Subsequently, such response maxima were found [2] in numerical simulations of simplified dynamical turbulence models such as the GOY model [3–5] or the reduced wave vector approximation (REWA) [6–9]. However, these response maxima computed in [2] were not pronounced at all, due to the approximate treatment of the small scales in either of these approaches. Indications of response maxima resulting from time-modulated forcing have subsequently also been seen in experiment [10]. The experimental observations were done by introducing a time-dependent swirl to fluid in a closed container and monitoring the energy-dissipation-rate. The selected set-up did not allow to identify possible flow-structuring under resonance conditions, nor to conclusively distinguish such resonance phenomena from flow-organization associated with the size of the container. (∗) e-mail: [email protected] (∗∗) e-mail: [email protected]