Numerical Verification of Log-Law in Flows with Pressure Gradient

  • Włodzimierz Czernuszenko
  • Alexey Rylov
Part of the GeoPlanet: Earth and Planetary Sciences book series (GEPS)


The chapter deals with 3D rough turbulent flows with pressure gradient in a straight open channel with regular bed roughness. The bed of the channel is characterized by roughness elements which are supposed to be uniform in size and form a regular surface of the bed. Turbulence structure above viscous sub-layer for such a roughness type is assumed to be homogenous in horizontal plane. Due to numerous experiments, this type of flow with zero pressure gradient is known to match the logarithmic law (log-law). So a question arises if it can be extended to flows with non-zero pressure gradient, and second, what are parameters of the log-law. An open channel turbulent flow is described by the Reynolds equations with simple turbulent model, which has eddy viscosities described by an enhanced mixing length hypothesis. The Reynolds equations with the continuity equation for steady, parabolic 3D turbulent flow in an open channel are solved for accelerating and decelerating flows. For these types of flow the additive parameter \(B\) of the log-law is calculated and results are discussed.


Roughness Element Roughness Height Open Channel Flow Relative Roughness Total Shear Stress 
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.



This work was supported by grant No. N306 658140 from The National Science Centre Grant, Poland. Authors are grateful to Dr P. Rowinski for reviewing an early draft of the results and for his helpful criticism.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute of Geophysics Polish Academy of SciencesWarsawPoland
  2. 2.Trianon CoNovosibirskRussia

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