Validation of Spatially Averaging Method for Using the Law of the Wall over Concave Bed Form (pool)

Document Type : Research Article

Authors

1 Graduate Student of Water Structures, Department of Water Engineering, Isfahan University of Technology

2 Assoc. Prof., Department of Water Engineering, Isfahan University of Technology

Abstract

Investigation of bedform development is one of important challenges in river engineering. Pools are one of existing bed forms in gravel and cobble bed rivers.  Variations in pressure gradients due to bedform development and the flow non-uniformity over it play the major role on the spatially and temporal distribution of velocity and estimation of shear velocity for determining roughness coefficient and sediment transport in gravel-bed rivers.  This paper introduces one of the applications of the double averaged velocity method to estimate shear velocity over the pools with different crest slopes. This method uses the law of the wall (the log law) and the boundary layer characteristics methods to evaluate shear velocity and von Karman constant. Reduction of shear velocity at the exit slope of pool due to the favorable pressure gradient and its augmentation at the pool entry indicate that the estimation of hydraulic parameters such as roughness coefficient and sediment transport cannot be described using a local velocity profile. Therefore, it is necessary to apply spatial and temporal averaged velocities (the double averaged method) over the bedform for estimating hydraulic parameters precisely. Results show that the double-averaged velocity distribution follow the trend of the local velocity distributions in the inner and the outer regions of the boundary layer along the pool as well as the application of log law for various crest slopes 5, 10, 15 and 20 degree. The velocity data deviate from the log law in the outer region of the boundary layer. However, the larger the crest slopes, the thinner the inner region. Also, application of the boundary layer characteristics method for estimating shear velocity using the double averaged velocity profile reveals that the larger the crest slope, the higher the shear velocity. For the crest slopes of 15 and 20 degree, considerable increase in the universal constant of von Karman (0.4) is observed.

Keywords

References

Afzalimehr, H.( 2010). “Effect of non-uniformity of flow on velocity and turbulence intensities over a cobble-bed”, J. Hydrological Processes, 24, pp. 331-341.
Afzalimehr, H. and Anctil. H. (2000). “Accelerating shear velocity in gravel bed channels”, Journal of Hydrological Science, IAHS, 45(1), pp. 143-155.
Afzalimehr H. and Anctil F. (2001). “Vitesse de frottement associée a un écoulement non uniforme et une rugosité relative intermédiaire”, Journal of Hydraulic Research, IAHR, 39(2), pp. 181-186.
Afzalimehr H. and Rennie, C.D. (2009). “Determination of bed shear stress using boundary layer parameters in a gravel-bed river”, Hydrological Sciences Journal, 54(1), pp. 147-159.
Afzalimehr H. and Dey S. (2009). “Influence of Bank Vegetation and Gravel Bed on velocity and Reynolds stress distributions”, International Journal of Sediment Research, Vol. 24. 2, pp. 236-246.
Emadzadeh. A Chiew Y. M. and Afzalimehr H (2010). “Effect of accelerating flow on incipient motion in a gravel-bed stream”, Journal of Advances in Water Resources, 33, pp. 1094-1104.
Finnigan, J.J. and Shaw, R.H.( 2008). “Double-averaging methodology and its application to turbulent flow in and above vegetation canopies”, Acta Geophysica 56, pp. 534–561.
Finnigan, J.J. (2000). “Turbulence in plant canopies”, Annual Review of Fluid Mechanics 32, pp. 519–571.
Franca, M.J., Ferreira, R.M.L. and Lemmin, U. (2008). “Parameterization of the logarithmic layer of double-averaged streamwise velocity profiles in gravel-bed river flows”, Advances in Water Resources 31, pp. 915–925.
Franca, M.J., Ferreira, R.M.L., Cardoso, A.H. and Lemmin U. (2010). “Double-average methodology applied to turbulent gravel-bed river flows”, J. River Flow 2010, pp. 59-65.
Goring, D.G. and Nikora, V.I. (2002). “Despiking acoustic Doppler velocimeter data”, Journal of Hydraulic Engineering, ASCE, 128(1), pp. 117-126.
Guo G and Julien P.Y. (2001). “Turbulent velocity profiles in sediment-laden flows”, Journal of Hydraulic Research, 39(1), pp. 11-23.
Kironoto, B. A. and Graf, W. H. (1995). “Turbulence characteristics in rough non-uniform open channel flow”, Proc. Institution of Civil Engineers-Water Maritime and Energy, United Kingdom. 112, pp. 316-348.
McLean, S. R. and Nikora, V. I. (2006). “Characteristics of turbulent unidirectional flow over rough beds: Double-averaging perspective with particular focus on sand dunes and gravel beds”, Water Resources Research, AGU, 2006, 42, W10409, doi:10.1029/2005WR004708.
 
Nikora, V.I., Goring, D.G., McEwan, I.K. and Griffiths, G. (2001). “Spatially averaged open-channel flow over rough bed”, J Hydr. Eng., 127(2), pp. 123-133.
Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D. and Walters, R. (2007). “Double-averaging concepts forrough-bed open-channel and overland flows: Theoretical background”, J Hydr. Eng. 133(8), pp. 873–883.
Raupach, M.R., Antonia, R.A. and Rajagopalan, S. (1991). “Rough-wall turbulent boundary layers”, Appl. Mech. Rev. 44(1), pp. 1–25.
Smith, J. D. and Mclean S. R. (1977). “Spatially averaged flow over a wavy surface”, Geoph. Res. Vol. 82, No. 12. pp. 1735-1746.
Vanoni V.A. (1975). “Sedimentation Engineering”, ASCE Manual and Reports on Engineering Practice, No. 54, p. 745.
Yalin S. M (1972). “Mechanics of sediment transport”, Pergamon Press, Oxford; New York: p. 290.
Journal of Hydraulics
Volume 8, Issue 2 - Serial Number 82
December 2014
Pages 19-28

Files

History

  • Receive Date: 15 December 2014
  • Accept Date: 15 December 2014

Share

How to cite

Statistics