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ON HELICAL PROPERTIES OF HOMOGENEOUS TURBULENCE

Frank G. Jacobitz
Mechanical Engineering Program University of San Diego 5998 Alcala Park San Diego, California 92110, USA

Kai Schneider
Laboratoire de Modélisation et Simulation Numérique en Mécanique, CNRS et Universités d'Aix-Marseille & CMI, Université de Provence, 39 rue Frédéric Joliot-Curie, 13453 Marseille, France

Wouter J. T. Bos
LMFA-CNRS Ecole Centrale de Lyon - University de Lyon 36 Avenue Guy de Collongues, 69134 Ecully Cedex, France

Marie Farge
LMD-IPSL-CNRS Ecole Normale Superieure 24 rue Lhomond, 75231 Paris Cedex 5, France

Abstract

The helical properties of five prototypical turbulent flows are investigated: statistically steady forced isotropic turbulence, growing sheared turbulence, growing rotating sheared turbulence with rotation ratio f/S = +0.5, decaying rotating sheared turbulence with f/S = +5, and decaying rotating turbulence. These five turbulent flows were originally studied using direct numerical simulations. It was found that flows with growing turbulent kinetic energy and turbulent motion at large scales show a maximum in the velocity helicity probability distribution functions (PDFs) at hu = 0, corresponding to a trend to two-dimensionalization of the flow with vorticity and velocity being perpendicular. Flows with decaying turbulent kinetic energy and turbulent motion at small scales, however, show a maximum in the velocity helicity PDFs at hu = ±1, indicating a preference for helical motion with alignment or anti-alignment of vorticity and velocity. The PDFs of vorticity helicity hω always assume a maximum at hω = ±1 for all cases. Joint PDFs of relative velocity helicity and relative vorticity helicity show that hu and hω tend to have the same sign for all flows considered here, indicating that vorticity helicity diminishes velocity helicity.