Role of inviscid invariants in shell models of turbulence

Abstract

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 DOI: http://dx.doi.org/10.1103/PhysRevE.52.6113 © 1995 The American Physical Society