Abstract
Following V.I. Arnold and A.M. Obukhov, we consider the similarities between the Lie structure of the Navier-Stokes equations of hydrodynamic turbulence and the Euler equations of a gyroscope. We show that indeed a certain type of direct interaction yields a quite closer analogy than previously considered. Furthermore, the interactions built up dynamically on it yield a dynamical space-time cascade, the cascade of scaling gyroscopes, which should preserve most of the properties of the Navier-Stokes equations. We point out that it corresponds to a non-trivial tree-decomposition of the non-simple Lie structure of turbulence. We show how this cascade model can help to clarify fundamental questions of turbulence by investigating the possible multifractal universality and multifractal phase transitions to Self Organized Criticality.
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Chigirinskaya, Y., Schertzer, D. (1997). Cascade of Scaling Gyroscopes: Lie Structure, Universal Multifractals and Self-Organized Criticality in Turbulence. In: Molchanov, S.A., Woyczynski, W.A. (eds) Stochastic Models in Geosystems. The IMA Volumes in Mathematics and its Applications, vol 85. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8500-4_3
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DOI: https://doi.org/10.1007/978-1-4613-8500-4_3
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