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Universal Reynolds Number of Transition and Derivation of Turbulent Models

  • V. YakhotEmail author
  • C. Bartlett
  • H. Chen
  • R. Shock
  • I. Staroselsky
  • J. Wanderer
Conference paper
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 130)

Abstract

Renormalization or coarse-graining applied to basic equations governing multi -scale phenomena, leading to effective equations for large-scale properties is often called model-building. Unlike fluids in thermodynamic equilibrium, in case of high-Reynolds number turbulent flows the procedure leads to generation of an infinite number relevant high-order nonlinearities which are hard to deal with. In this paper, based on the recently discovered universality of transition to strongly non-Gaussian (anomalous) statistics of velocity derivatives, we show that in the infrared limit \(k\rightarrow 2\pi /L\), where \(L\) is the integral scale corresponding to the top of inertial range, the lowest-order contributions to the renormalized perturbation expansion give asymptotically exact equations for the large-scale features of the flow. The quality of the derived models is demonstrated on a few examples of complex flows. At the small scales \(\varDelta < L\), an infinite number of \(O(1)\) non-linear terms, generated by the procedure invalidate low-order models widely used for Large-Eddy-Simulations (LES) of turbulent flows.

Keywords

Reynolds Number Dissipation Rate Direct Numerical Simulation Effective Viscosity Inertial Range 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • V. Yakhot
    • 1
    Email author
  • C. Bartlett
    • 1
  • H. Chen
    • 2
  • R. Shock
    • 2
  • I. Staroselsky
    • 2
  • J. Wanderer
    • 2
  1. 1.Department of Mechanical EngineeringBoston UniversityBostonUSA
  2. 2.EXABurlingtonUSA

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