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

Document Type : Research Article


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


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.


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