Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bayazit M (1976) Free surface flow in a channel of large relative roughness. J Hydr Res 14(2):115–126
Cordoso A (1989) Spacially accelerated flow in an smooth open channel. These No.813, Ecolé Polytechnique Federale de Lausanne.
Clauser FH (1954) Turbulent boundary layers in adverse pressure gradients. J Aero Sci 21:91–108
Czernuszenko W, Rylov AA (2000) A generalisation of Prandtl’s model for 3D open channel flows. J Hydraul Res 38(2):133–139
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 1:135–142
Gimenez-Curto LA, Corniero Lera MAC (1996) Oscillating turbulent flow over rough surfaces. J Geophys Res 101(C9):20, 745–20, 758.
Grass AJ, Stuart RJ, Mansour-Tehrani M (1993) Common vertical structure of trbulent flows over smooth and rough boundaries. AIAA J 31(5):837–847
Guo J, Julien PY, Meroney RN (2005) Modified log-wake law for zero-pressure-gradient turbulent boundary layers 43(4):421–430
Kamphuis JW (1974) Determination of sand roughness for fixed beds. J Hydr Res 12(2):193–203
Kirkgoz SM (1989) Turbulent velocity profiles for smooth and rough open channel flow. J Hydr Eng ASCE 15(11):1543–1561
Launder BE, Spalding DB (1974) The numerical computation of turbulent flows. Comput Meth Appl Mech Eng 3:269
Leschziner MA (1980) Practical evaluation of three finite difference schemes for the computation of steady-state recirculation flows. Comput Meth Appl Mech Eng 23:293–312
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.
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.
Nezu I, Rodi W (1986) Open-channel flow measurements with a laser doppler anemometer. J Hydr Eng 112(5):335–355
Nikora VI, Koll K, McLean S, McEwan I, Dittrich A (2004) Velocity distribution in the roughness layer of rough-bed flows. J Hydr Eng 130(10):1036–1042
Patankar SV, Spalding DB (1972) A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows. J Heat Mass Trans 15:1787–1806
Perry AE, Schofield WH, Joubert PN (1969) Rough Wall Turbulent Boundary Layers. J Fluid Mech 37:383–413
Rastogi AK, Rodi W (1978) Predictions of heat and mass transfer in open channels. J Hydr Div 104(HY3):397–420.
Raupach MR, Antonia RA, Rajagopalan S (1991) Rough-wall turbulent boundary layers. Appl Mech Rev 44(1):1–25
Tu H (1991) Velocity distribution in unsteady flow over gravel beds. These No. 911, Ecolé Polytechnique Federale de Lausanne, Lausanne EPFL.
Yaglom AM (1979) Similarity laws for constant-pressure and pressure-gradient turbulent wall flows. Ann Rev Fluid Mech 11:505–540
Yalin MS (1977) Mechanics of sediment transport. Pergamon Press, Oxford
Yang S-Q (2009) Veloicty distribution and wake-law in gradually decelerating flows. J Hydr Res 47(2):177–184
Acknowledgments
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Czernuszenko, W., Rylov, A. (2013). Numerical Verification of Log-Law in Flows with Pressure Gradient. In: Rowiński, P. (eds) Experimental and Computational Solutions of Hydraulic Problems. GeoPlanet: Earth and Planetary Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30209-1_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-30209-1_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30208-4
Online ISBN: 978-3-642-30209-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)