Hidden scale invariance of intermittent turbulence in a shell model

Abstract

It is known that scale invariance is broken in the developed hydrodynamic turbulence due to intermittency, substantiating complexity of turbulent flows. Here we challenge the concept of broken scale invariance by establishing a hidden self-similarity in intermittent turbulence. Using a simplified (shell) model, we derive a nonlinear spatiotemporal scaling symmetry of inviscid equations, which are reformulated in terms of intrinsic times introduced at different scales of motion. Numerical analysis persuasively confirms that this symmetry is restored in a statistical sense within the inertial interval. At the end, we discuss implications of this result for the Navier-Stokes system.

5 pages, 2 figures

References in corpus (1)

• The large deviation approach to statistical mechanics

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• Wavelet Conditional Renormalization Group
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• RG approach to the inviscid limit for shell models of turbulence
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• Turbulent cascade arrests and the formation of intermediate-scale condensates