Numerical Verification of Log-Law in Flows with Pressure Gradient
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.
KeywordsRoughness Element Roughness Height Open Channel Flow Relative Roughness Total Shear Stress
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.
- Cordoso A (1989) Spacially accelerated flow in an smooth open channel. These No.813, Ecolé Polytechnique Federale de Lausanne.Google Scholar
- Clauser FH (1954) Turbulent boundary layers in adverse pressure gradients. J Aero Sci 21:91–108Google Scholar
- Czernuszenko W, Rylov AA (2003) A Modeling of shear and normal turbulent stresses. In: Open channel flows. XXX Congress IAHR Thessaloniki, Greece. Proceedings Theme C, vol 1:135–142Google Scholar
- Gimenez-Curto LA, Corniero Lera MAC (1996) Oscillating turbulent flow over rough surfaces. J Geophys Res 101(C9):20, 745–20, 758.Google Scholar
- Guo J, Julien PY, Meroney RN (2005) Modified log-wake law for zero-pressure-gradient turbulent boundary layers 43(4):421–430Google Scholar
- Mansour-Tehrani M (1992) Spatial distribution and scaling of bursting events in boundary layer turbulence over smooth and rough surfaces. University of London, Ph.D. Dissertation.Google Scholar
- McLean S, Dittrich A, Aberle J (2002) Zero-plane displacement for rough-bed open-channel flows. In: Proceedings of the international conference on fluvial hydraulics river flow 2002, Louvain-la-Neuve, Belgium, pp 83–92.Google Scholar
- Rastogi AK, Rodi W (1978) Predictions of heat and mass transfer in open channels. J Hydr Div 104(HY3):397–420.Google Scholar
- Tu H (1991) Velocity distribution in unsteady flow over gravel beds. These No. 911, Ecolé Polytechnique Federale de Lausanne, Lausanne EPFL.Google Scholar
- Yalin MS (1977) Mechanics of sediment transport. Pergamon Press, OxfordGoogle Scholar