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Multifractality in a nested velocity gradient model for intermittent turbulence

Yuan Luo1, Yipeng Shi1,2, and Charles Meneveau3

  • 1State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, People's Republic of China
  • 2Center for Applied Physics and Technology, HEDPS, and College of Engineering, Peking University, Beijing 100871, People's Republic of China
  • 3Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA

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Phys. Rev. Fluids 7, 014609 – Published 25 January, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.014609

Abstract

Small-scale intermittency is an omnipresent feature of turbulent flows, and the velocity gradient tensor in three dimensions provides a rich characterization of its salient statistical and geometric features. A recent model for isotropic turbulence involving a set of stochastic differential equations was derived for the Lagrangian time evolution of the velocity gradient tensor at multiple scales. Dominant terms in the model could be derived directly from the Navier-Stokes equations while also requiring phenomenological models for unclosed pressure and viscous terms. In this work we show that instead of having to integrate this stochastic model in time at multiple levels and scales, the same predictions can be obtained based on a single level that recursively modulates the model terms interpreted at arbitrarily higher levels. The equivalence is explored based on actual realizations of the modeled stochastic process and then extended to probability densities and moments at all levels and scales. Statistical properties compare very well to direct numerical simulation and experimental data at different Reynolds numbers. The proposed formalism represents a new type of multifractal intermittency model that can be connected directly to terms in the Navier-Stokes equation and is capable of predicting many intricate statistical and geometric features of turbulent flows over a wide range of Reynolds numbers.

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Phys. Rev. Fluids 7, 014609– Published 25 January, 2022
  • Received 5 July 2021
  • Accepted 21 December 2021
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