Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1995-08-28
Nonlinear Sciences
Chaotic Dynamics
7 figures not included, available upon request from the author or on WWW in: http://www.mmm.ucar.edu/blt/kerr_shells.html
Scientific paper
10.1103/PhysRevE.52.6113
Non-positive definite, global inviscid invariants similar to helicity are discussed for two types of shell models and evidence for a new role for helicity in Navier-Stokes turbulence is presented. It is suggested that the extra invariants play the role of triggering the intermittent cascade of energy to small scales characterized by pulses. These invariants also determine where a transition to chaos appears. New analysis of numerical experiments with existing models is suggested and a new 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 GOY model within this class is discussed.
Biferale Luca
Kerr Robert
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