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 (Donzis and Sreenivasan in J Fluid Mech 657:171–188, 2010; Falkovich in Phys Fluids 6:1411–1414, 1994; Frisch et al. in Phys Rev Lett 101:144501, 2008; Kurien et al. in Phys Rev E 69:066313, 2004; Verma and Donzis in Phys A: Math Theor 40:4401–4412, 2007). Based on direct numerical simulations of the incompressible Navier-Stokes equations, results from Donzis and Sreenivasan (657:171–188, 2010) pointed to a power-law 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 the 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 (Griffin et al. in Control of long-range correlations in turbulence, arXiv:1809.05126, 2019) in the variable density turbulence tunnel (VDTT) (Bodenschatz et al. in Rev Sci Instrum 85:093908, 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.