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Conceptual dynamical models for turbulence.

Andrew J Majda1, Yoonsang Lee

  • 1Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012.

Proceedings of the National Academy of Sciences of the United States of America
|April 23, 2014
PubMed
Summary
This summary is machine-generated.

Simple conceptual models capture complex anisotropic turbulence, revealing intermittent energy transfer from small to large scales. These models aid in predicting and understanding chaotic fluid dynamics.

Keywords:
stochastic modelwave–mean interaction

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Area of Science:

  • Fluid Dynamics
  • Turbulence Theory
  • Computational Physics

Background:

  • Anisotropic turbulence in engineering and environmental flows presents significant challenges.
  • Energy transfer across scales in turbulent systems is complex and intermittent.
  • Existing models struggle to capture the full dynamics of anisotropic turbulence.

Purpose of the Study:

  • To introduce and develop simple conceptual dynamical models for anisotropic turbulence.
  • To capture key statistical features of complex turbulent systems using simplified models.
  • To provide a test bed for prediction, uncertainty quantification, and data assimilation algorithms.

Main Methods:

  • Development of conceptual dynamical models with large-scale mean flow and turbulent fluctuations.
  • Inclusion of energy-conserving wave-mean-flow interactions and stochastic forcing.
  • Numerical experiments using a six-dimensional conceptual dynamical model.

Main Results:

  • Models qualitatively capture key statistical features of complex anisotropic turbulent systems.
  • Observed chaotic statistical behavior in the mean flow with sub-Gaussian fluctuations.
  • Turbulent fluctuations showed decreasing energy and correlation times at smaller scales, with non-Gaussian probability distribution functions (PDFs) indicating intermittency.

Conclusions:

  • Conceptual dynamical models offer a simplified yet effective approach to studying anisotropic turbulence.
  • The models highlight the intermittent nature of small-scale fluctuations and their impact on the mean flow.
  • These models serve as a valuable tool for developing and testing algorithms for turbulent flow analysis.