How the viscous subrange determines inertial range properties in turbulence shell models

Abstract

We calculate static solutions of the 'GOY' shell model of turbulence and do a linear stability analysis. The asymptotic limit of large Reynolds numbers is analyzed. A phase diagram is presented which shows the range of stability of the static solution. We see an unexpected oscillatory dependence of the stability range upon $\lg \nu$, where $\nu$ is the viscosity. This effect depends upon the discrete structure of the shell model and goes to zero as the separation between the shells is brought to zero. These findings show how viscous effects play a role in determining inertial properties of shell models and give some hints for understanding the effects of viscous dissipation upon real turbulence.

Physica D, in press

References in corpus (5)

• Scaling and Dissipation in the GOY Shell Model
• Transition to Chaos in a Shell Model of Turbulence
• Scale resolved intermittency in turbulence
• Universality in fully developed turbulence
• The Breakdown of Dynamic Scaling and Intermittency in a Cascade Model of Turbulence

Cited by in corpus (12)

• An optimal shell model of turbulence
• Analytic Study of Shell Models of Turbulence
• Scaling and Linear Response in the GOY Turbulence model
• Response maxima in modulated turbulence Part II: Numerical simulations
• Links between dissipation, intermittency, and helicity in the GOY model revisited
• Dynamic Multiscaling in Turbulence
• Decaying and kicked turbulence in a shell model
• Singularities in cascade models of the Euler equation
• Pulses in the Zero-Spacing Limit of the GOY Model
• Dynamical Organization around Turbulent Bursts
• Chaotic Behavior in Shell Models and Shell Maps
• Fixed points, stability and intermittency in a shell model for advection of passive scalars