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On the role of helicity in the three-dimensional Navier-Stokes equations

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By introducing an helical-decimated version of the three-dimensional Navier-Stokes equations (dNS) we show that all flows in nature posses a subset of triadic interactions leading to a split cascade regime, with energy going toward large scales and helicity toward small scales even in a fully periodic and isotropic statistical ensemble [1, 2]. Results concerning the statisical properties of the velocity field in both the direct-helicity and the inverse-energy regimes are studied. Finally, global (for all times and for all intial data) existence, uniqueness and continuos dependence on the initial data of solutions for such a model are rigorously proved.

Author(s):

Luca Biferale    
Dept. Physics and INFN University of Rome 'Tor Vergata'
Italy

Stefano Musacchio    
CNRS, Lab. J.A. Dieudonné
France

Titi S. Edriss    
Weizmann Institute of Science
Israel

Federico Toschi    
Eindhoven University of Technology
Netherlands