Cascades of energy and helicity in the GOY shell model of turbulence

P. D. Ditlevsen

doi:10.1063/1.869270

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arXiv · chao-dyn/9811009

Cascades of energy and helicity in the GOY shell model of turbulence

P. D. Ditlevsen

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Abstract

The effect of extreme hyperviscous damping, $νk_n^p, p=\infty$ is studied numerically in the GOY shell model of turbulence. It has resently been demonstrated [Leveque and She, Phys. Rev. Lett, 75,2690 (1995)] that the inertial range scaling in the GOY model is non-universal and depending on the viscous damping. The present study shows that the deviation from Kolmogorov scaling is due to the cascade of the second inviscid invariant. This invariant is non-positive definite and in this sense analogous to the helicity of 3D turbulent flow.

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P. D. Ditlevsen. 1998-11-04. Cascades of energy and helicity in the GOY shell model of turbulence. https://doi.org/10.1063/1.869270

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