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)


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.


Reynolds Number Dissipation Rate Direct Numerical Simulation Effective Viscosity Inertial Range 
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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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