Hidden scale invariance of intermittent turbulence in a shell model

  title={Hidden scale invariance of intermittent turbulence in a shell model},
  author={Alexei A. Mailybaev},
  journal={arXiv: Fluid Dynamics},
  • A. Mailybaev
  • Published 1 May 2020
  • Engineering
  • arXiv: Fluid Dynamics
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… 

Figures from this paper

Hidden spatiotemporal symmetries and intermittency in turbulence

We consider general infinite-dimensional dynamical systems with the Galilean and spatiotemporal scaling symmetry groups. Introducing the equivalence relation with respect to temporal scalings and

Shell model intermittency is the hidden self-similarity

We show that the intermittent dynamics observed in the inertial interval of Sabra shell model of turbulence can be rigorously related to the property of scaling self-similarity. In this connection,

Dyadic models for fluid equations: a survey

. Over the centuries mathematicians have been challenged by the partial differential equations (PDEs) that describe the motion of fluids in many physical contexts. Important and beautiful results were

Emerging scale invariance in a model of turbulence of vortices and waves

It is put forward the hypothesis that the invariance of multipliers is due to an extreme non-locality of their interactions (similar to the appearance of mean-field properties in the thermodynamic limit for systems with long-range interaction) and provides a unique opportunity for an analytic study of emerging scale invariance in a system with strong interactions.

Hidden scale invariance in Navier–Stokes intermittency

It is shown that hidden symmetry accounts for the scale-invariance of a certain class of observables, in particular, the Kolmogorov multipliers, and repairs the scale invariance, which is broken by intermittency in the original formulation.

Solvable Intermittent Shell Model of Turbulence

  • A. Mailybaev
  • Physics
    Communications in Mathematical Physics
  • 2021
We introduce a shell model of turbulence featuring intermittent behaviour with anomalous power-law scaling of structure functions. This model is solved analytically with the explicit derivation of

Fibonacci Turbulence

Never is the difference between thermal equilibrium and turbulence so dramatic, as when a quadratic invariant makes the equilibrium statistics exactly Gaussian with independently fluctuating modes.




▪ Abstract We review the most important theoretical and numerical results obtained in the realm of shell models for the energy-turbulent cascade. We mainly focus here on those results that had or

Gibbsian Hypothesis in Turbulence

We show that Kolmogorov multipliers in turbulence cannot be statistically independent of others at adjacent scales (or even a finite range apart) by numerical simulation of a shell model and by

Improved shell model of turbulence

We introduce a shell model of turbulence that exhibits improved properties in comparison to the standard (and very popular) Gledzer, Ohkitani, and Yamada (GOY) model. The nonlinear coupling is chosen

Symmetries of the turbulent state

The emphasis of this review is on fundamental properties, degree of universality and symmetries of the turbulent state. The central questions are which symmetries remain broken even when the

Conformal invariance in two-dimensional turbulence

The simplicity of fundamental physical laws manifests itself in fundamental symmetries. Although systems with an infinite number of strongly interacting degrees of freedom (in particle physics and

A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number

The hypotheses concerning the local structure of turbulence at high Reynolds number, developed in the years 1939-41 by myself and Oboukhov (Kolmogorov 1941 a,b,c; Oboukhov 1941 a,b) were based

Optimal subgrid scheme for shell models of turbulence.

We discuss a theoretical framework to define an optimal subgrid closure for shell models of turbulence. The closure is based on the ansatz that consecutive shell multipliers are short-range

Description of a Turbulent Cascade by a Fokker-Planck Equation

Fully developed turbulence is still regarded to be one of the main unsolved problems of classical physics. Great efforts have been made towards an understanding of small scale turbulent velocity

Kolmogorov's third hypothesis and turbulent sign statistics.

It is shown that the multipliers at adjacent scales are not independent but that their correlations decay rapidly in scale separation, and new scaling laws are predicted and verified for both roughness and sign of turbulent velocity increments.

Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics

Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena