1995/08/31 by Luca Biferale, L. Biferale, Robert M. Kerr +1 · 3 citations
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Cascade #Classical mechanics #Energy cascade #Fluid Dynamics and Turbulent Flows #Geometry #Helicity #Invariant (physics) #Inviscid flow #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Meteorological Phenomena and Simulations #Physics #Quadratic equation #Quantum mechanics #Shell (structure) #Solar and Space Plasma Dynamics #Statistical physics #Turbulence #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physreve.52.6113
7 figures not included, available upon request from the author or on WWW in: http://www.mmm.ucar.edu/blt/kerr_shells.html
arxiv created 1995/09/01 · openalex publication_date 1995/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Nonpositive definite, global inviscid invariants similar to helicity are discussed for two types of shell models, and evidence for an alternate role for helicity in Navier-Stokes turbulence is presented. It is suggested that the extra invariants play the role of triggering an intermittent cascade of energy to small scales characterized by pulses. These invariants also determine where a transition to chaos appears. An analysis of numerical experiments with existing models is suggested and a class of shell models where the dynamical interactions of a second quadratic invariant are closer to those of helicity in the Navier-Stokes equations is introduced. The place of the popular Gledzer-Ohkitani-Yamada model within this class is discussed. (c) 1995 The American Physical Society