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A statistical state dynamics approach to wall turbulence.

B F Farrell1, D F Gayme2, P J Ioannou3

  • 1Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138, USA farrell@seas.harvard.edu.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|February 8, 2017
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Summary

Statistical state dynamics (SSD) simplifies turbulence analysis in wall-bounded shear flows. Restricted nonlinear (RNL) dynamics offer computationally efficient, self-sustaining turbulence models with insights into wall turbulence.

Keywords:
coherent structuresnonlinear dynamical systemstransition to turbulenceturbulent boundary layers

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Area of Science:

  • Fluid Dynamics
  • Turbulence Modeling
  • Computational Physics

Background:

  • Turbulence in wall-bounded shear flows remains a complex challenge.
  • Statistical State Dynamics (SSD) offers a novel perspective for analysis.
  • Existing models often struggle with computational cost and accuracy at high Reynolds numbers.

Purpose of the Study:

  • To review the benefits of the Statistical State Dynamics (SSD) approach for understanding wall-bounded shear flows.
  • To introduce and evaluate the Restricted Nonlinear (RNL) dynamics as a tractable approximation to SSD.
  • To demonstrate the potential of RNL systems for computationally efficient turbulence modeling.

Main Methods:

  • Utilizing a second-order closure within SSD, retaining specific interactions between mean flow and perturbation covariance.
  • Implementing Restricted Nonlinear (RNL) dynamics by removing explicit perturbation-perturbation nonlinearity.
  • Approximating SSD with finite ensemble RNL systems and comparing with infinite ensemble (stochastic structural stability theory) systems.

Main Results:

  • RNL systems provide computationally efficient approximations to SSD, capturing self-sustaining turbulence.
  • Qualitative features of RNL turbulence resemble those from direct numerical simulations.
  • Turbulence can be sustained by minimal components, and 'band-limiting' enhances quantitative accuracy.

Conclusions:

  • The SSD approach, particularly through RNL dynamics, offers new analytical and computational tools for wall turbulence.
  • RNL models provide valuable insights into turbulence mechanisms with reduced computational cost.
  • This framework facilitates the development of high-fidelity models for wall turbulence at large Reynolds numbers.