Experimental Study of the Bottleneck in Fully Developed Turbulence

Abstract

The energy spectrum of incompressible turbulence is known to reveal a pileup of energy at those high wavenumbers where viscous dissipation begins to act. It is called the bottleneck effect. Based on direct numerical simulations of the incompressible Navier-Stokes equations, results from Donzis & Sreenivasan (2010) pointed to a decrease of the strength of the bottleneck with increasing intensity of the turbulence, measured by the Taylor micro-scale Reynolds number $R_{\lambda }$. Here we report first experimental results on the dependence of the amplitude of the bottleneck as a function of $R_{\lambda }$ in a wind-tunnel flow. We used an active grid in the Variable Density Turbulence Tunnel (VDTT) (see Bodenschatz et al. (2014)) to reach $R_{\lambda }$ > 5000, which is unmatched in laboratory flows of decaying turbulence. The VDTT with the active grid permitted us to measure energy spectra from flows of different $R_{\lambda }$, with the small-scale features appearing always at the same frequencies. We relate those spectra recorded to a common reference spectrum, largely eliminating systematic errors which plague hotwire measurements at high frequencies. The data are consistent with a power law for the decrease of the bottleneck strength for the finite range of $R_{\lambda }$ in the experiment.

13 pages; 11 figures v2: clarified tick labels in Figs 6 and 7

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