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The Stagnation Point Structure of Wall-Turbulence and the Law of the Wall in Turbulent Channel Flow

  • Vassilios Dallas
  • J. Christos Vassilicos
Part of the ERCOFTAC Series book series (ERCO, volume 14)

Abstract

DNS of turbulent channel flows propose the following picture. (a) The Taylor microscale λ(y) is proportional to s (y), the average distance between stagnation points of the fluctuating velocity field, i.e. λ(y)=B 1 s (y) where B 1 is constant, for δ νy<δ. (b) The number density of stagnation points n s varies with height as \(n_{s}=C_{s}y_{+}^{-1}/\delta_{\nu}^{3}\) with C s constant in the range δ νy<δ. (c) In that same range, the kinetic energy dissipation rate per unit mass, \(\epsilon=\frac{2}{3}E_{+}u_{\tau}^{3}/(\kappa_{s}y)\) where \(E_{+}=E/u_{\tau}^{2}\) is the normalised total kinetic energy per unit mass and \(\kappa_{s}=B_{1}^{2}/C_{s}\) is the stagnation point von Kármán coefficient. (d) For Re τ ≫1, large enough for the production to balance dissipation locally and for \(-\langle{uv}\rangle \sim u_{\tau}^{2}\) in the range δ νyδ, \(d\langle{u}\rangle /dy\simeq\frac{2}{3}E_{+}u_{\tau}/(\kappa_{s}y)\) in that same range. (e) The von Kármán coefficient κ is a meaningful and well-defined coefficient and the log-law holds only if E + is independent of y + and Re τ in that range, in which case κκ s . The universality of \(\kappa_{s}=B_{1}^{2}/C_{s}\) depends on the universality of the stagnation point structure of the turbulence via B 1 and C s , which are conceivably not universal.

Notes

Acknowledgements

We are grateful to Dr. Sylvain Laizet for providing the Navier–Stokes solver and to Halliburton for the financial support.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute for Mathematical Sciences & Department of AeronauticsImperial College LondonLondonUK

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