On helical multiscale characterization of homogeneous turbulence

Abstract

The helical properties of five prototypical homogeneous turbulent flows are investigated: statistically steady forced isotropic turbulence, decaying isotropic turbulence, decaying rotating turbulence, growing sheared turbulence, and growing rotating sheared turbulence with a rotation ratio f/S=+0.5. The five turbulent flows were originally studied using direct numerical simulations, and well-developed flow fields are chosen for this analysis. For comparison, a solenoidal uncorrelated Gaussian random field is included in the analysis as a sixth case. An orthogonal wavelet decomposition is used to study the scale-dependent properties of the cases. It is found that flows with growing turbulent kinetic energy and turbulent motion at large scales show a maximum in the relative kinetic helicity probability distribution functions (PDFs) at zero, corresponding to a trend to local two-dimensionalization of the flow with vorticity and velocity tending to be perpendicular. Flows with decaying turbulent kinetic energy and turbulent motion at small scales, however, show maxima of the relative kinetic helicity PDFs at plus and minus one, indicating a preference for helical motion with a trend to alignment or anti-alignment of vorticity and velocity. The PDFs of relative super-helicity always assume maxima at plus and minus one for all flows. The helical properties of statistically steady forced isotropic turbulence follow those of flows with decaying turbulent kinetic energy and a small asymmetry in the relative helicity PDFs is observed. Joint PDFs of relative kinetic helicity and relative super-helicity show that the quantities tend to have the same sign for all flows, including the random field, indicating that super-helicity dissipates kinetic helicity.

Keywords:

• helicity
• homogeneous isotropic and anisotropic turbulence
• scale-dependent statistics
• direct numerical simulation

Acknowledgements

We would like to thank Claude Cambon, Fabien Godeferd, Lukas Liechtenstein, Carlos da Silva, and P.K. Yeung for the use of their direct numerical simulation results. We are thankful for many fruitful discussions with Claude Cambon. F.G.J. acknowledges hospitality and support from the Laboratoire de Mécanique, Modélisation & Procédés Propres at Aix-Marseille Université, Marseille, France, as well as an International Opportunity Grant from the University of San Diego, San Diego, California. M.F. and K.S. acknowledge financial support from the Association CEA-Euratom and the French Research Federation for Fusion Studies within the framework of the European Fusion Development Agreement under contract V.3258.001. W.B. and K.S. acknowledge financial support from the French Research Agency (ANR), project SiCoMHD, contract ANR-11-BLAN-045.