Environmental Fluid Mechanics

, Volume 5, Issue 4, pp 373–386 | Cite as

Simple Analytical Model for Entire Turbulent Boundary Layer over Flat Plane

From Viscous and Mixing Layers to Turbulent Logarithmic Region
  • Victor S. L’vov
  • Anna Pomyalov
  • Vasil Tiberkevich


We discuss a simple analytical model of the turbulent boundary layer (TBL) over flat plane. The model offers an analytical description of the profiles of mean velocity and turbulent activity in the entire boundary region, from the viscous sub-layer, through the buffer layer further into the log-law turbulent region. In contrast to various existing interpolation formulas the model allows one to generalize the description of simple TBL of a Newtonian fluid for more complicated flows of turbulent suspensions laden with heavy particles, bubbles, long-chain polymers, to include the gravity acceleration, etc.

Key words

analytical model mean velocity turbulent activity profile turbulent boundary layer wall bounded turbulence 



planetary boundary layer


turbulent boundary layer


Navier–Stokes equation


direct numerical simulations


left-hand side


right-hand side


root mean square


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  1. 1.
    L’vov, V.S., Pomyalov, A., Procaccia, I., Tiberkevich, V. 2004Drag reduction by polymers in wall bounded turbulencePhys. Rev. Lett.68046308Google Scholar
  2. 2.
    Pope, S.B. 2000Turbulent FlowsUniversity PressCambridgeGoogle Scholar
  3. 3.
    Moser, R.G., Kim, J. and Mansour, N.N.: 1999, Direct numerical simulation of turbulent channel flow up to Reτ=590, Phys. Fluids 11, 943; DNS data at Scholar
  4. 4.
    Zagarola, M.V., Smits, A.J. 1997Scaling of the mean velocity profile for turbulent pipe flowPhys. Rev. Lett.78239CrossRefGoogle Scholar
  5. 5.
    Angelis, E., Casciola, C., L’vov, V.S., Pomyalov, A., Procaccia, I., Tiberkevich, V. 2004Phys. Rev. E70055301(R)Google Scholar
  6. 6.
    Benzi, R., L’vov, V.S., Procaccia, I., Tiberkevich, V. 2004Saturation of turbulent drag reduction in dilute polymer solutionsEuro Phys. Lett.68825Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Victor S. L’vov
    • 1
  • Anna Pomyalov
    • 1
  • Vasil Tiberkevich
    • 1
  1. 1.Department of Chemical PhysicsThe Weizmann Institute of ScienceRehovotIsrael

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