Dual non-Kolmogorov cascades in a von Kármán flow

¹ SPHYNX, Service de Physique de l'État Condensé - DSM, CEA Saclay, CNRS URA 2464 91191 Gif-sur-Yvette, France, EU
² Mathematics Institute, University of Warwick - Coventry CV4 7AL, UK, EU
³ Laboratoire de Mécanique des Fluides et d'Acoustique - CNRS UMR 5509, École Centrale de Lyon, Université de Lyon - Lyon, France, EU

Received: 5 November 2012
Accepted: 5 November 2012

Abstract

The experimental spatial power spectrum of the velocity fluctuations in a von Kármán flow is measured, in a wide range of Reynolds numbers, 10² < Re < 10⁶, for the first time without using the Taylor hypothesis. At high enough Reynolds numbers, the spectra display a clear dual (direct and inverse) cascade. For any Re, the scaling of the direct cascade is steeper than the classical Kolmogorov −5/3 exponent of homogeneous and isotropic 3D turbulence. We then discuss the possibility of dual local and non-local cascades in a 3D turbulent Beltrami (a property satisfied by the von Kármán flow at large scale) flow, with inverse energy cascade and direct helicity cascade, by analogy with 2D turbulence. The corresponding energy spectra are computed in both local and non-local cases, and compared with our experimental results. The inverse cascade scaling is found to be in agreement with the non-local scenario. The direct cascade scaling is close to the non-local scenario for Re ≲ 4.10⁴, and switches towards the local scenario at Re > 10⁵.