Transportation of sediment is an important and frequent phenomenon in rivers. Sediment is mobilized as bed-load with particles sliding, saltating, and rolling over the river bed, or as a suspended-load, where particles move with the turbulent water flow away from the bed.

Sediment Transport and Movable Bed s

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Table Of Integrals Series And Products

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

The Analysis of Time Series: An Introduction, 4th edn. By C. Chatfield. ISBN 0 412 31820 2. Chapman and Hall, London, 1989. 242 pp. £13.50.

The Analysis of Time Series: An Introduction

The flow of homogeneous fluids through porous media: analogies with other physical problems

Introduction.- Hydrodynamic Principles.- Turbulence in Open Channel Flows.- Sediment Threshold.- Bed-Load Transport.- Suspended-Load Transport.- Total-Load Transport.- Bedforms.- River Processes: Meandering and Braiding.- Scour.- Dimensional Analysis and Similitude.

Fluvial Hydrodynamics: Hydrodynamic and Sediment Transport Phenomena

The outcome of an experimental study on the turbulent horseshoe vortex flow within the developing (intermediate stages and equilibrium) scour holes at cylindrical piers measured by an acoustic Doppler velocimeter (ADV) are presented. Since the primary objective was to analyze the evolution of the turbulent flow characteristics of a horseshoe vortex within a developing scour hole, the flow zone downstream of the pier was beyond the scope of the investigation. Experiments were conducted for the approaching flow having undisturbed flow depth (=0.25 m) greater than twice the pier diameter and the depth-averaged approaching flow velocity (=0.357 m/s) about 95% of the critical velocity of the uniform bed sand that had a median diameter of 0.81 mm. The flow measurements by the ADV were taken within the intermediate (having depths of 0.25, 0.5, and 0.75 times the equilibrium scour depth) and equilibrium scour holes (frozen by spraying glue) at a circular pier of diameter 0.12 m. In order to have a comparative study, the ADV measurements within an equilibrium scour hole at a square pier (side facing the approaching flow) of sides equaling the diameter of the circular pier were also taken. The contours of the time-averaged velocities, turbulence intensities, and Reynolds stresses at different azimuthal planes (0, 45, and 90°) are presented. Vector plots of the flow field at azimuthal planes reveal the evolution of the characteristics of the horseshoe vortex flow associated with a downflow from intermediate stages to equilibrium condition of scour holes. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics of the horseshoe vortex are discussed from the point of view of the similarity with the velocity and turbulence characteristic scales. The imperative observation is that the flow and turbulence intensities in the horseshoe vortex flow in a developing scour hole are reasonably similar.

Characteristics of Horseshoe Vortex in Developing Scour Holes at Piers

The three-dimensional quasi-steady vortex flow field around circular piers in a quasi-equilibrium scour hole under a clear water regime has been investigated experimentally. The main characteristic features of the flow, to be modeled, are a relatively large secondary vortex flow within the scour hole and skewed velocity distributions along the circumference of the pier. The flow field has been divided into a number of parts according to the flow characteristics. The components of quasi-steady velocity for different parts have been theoretically expressed in the form of equations satisfying the continuity equation and the requirements of fitting an individual profile of the measured velocity components. Using the suitable functions, the equations of the velocity components derived for different parts have been combined and matched at the junctions of these parts to get a single equation for each velocity component. The measured data have been utilized to determine the coefficients and exponents used in these equations through curve fittings. The proposed flow model, which corresponds closely with the observations, can be utilized to simulate the flow field in prototype.

Clear water scour at circular piers : a model

The results of an experimental investigation on scour of noncohesive sediment beds (uniform and nonuniform sediments) downstream of an apron due to a submerged horizontal jet issuing from a sluice opening are presented. Attempts are made to explain the similarity existing in the scour process and profiles (including dune in the downstream of the scour hole). The scour profiles at different times follow a particular geometrical similarity and can be expressed by the combination of two polynomials. Using experimental scour depth at different times, the time variation of scour depth is scaled by an exponential law, where time scale increases linearly with densimetric Froude number. The equilibrium scour depth, related to the sediment size relative to the sluice opening, decreases with increase in sediment size and sluice opening. On the other hand, the equilibrium scour depth increases with increase in densimetric Froude number. The variation of equilibrium scour depth with tailwater depth indicates a critical tailwater depth corresponding to a minimum equilibrium scour depth. The effect of sediment gradation on scour depth is pronounced for nonuniform sediments, which reduce scour depth significantly due to formation of an armor layer, and therefore prompted study of the reduction of scour depth by a launching apron placed downstream of the rigid apron. The results show that the average reduction of scour depth by placing a launching apron was 39%, having a maximum of 57.3% and a minimum of 16.2%. The characteristic parameters affecting maximum equilibrium scour depth are identified based on the physical reasoning and dimensional analysis. Equation of maximum equilibrium scour depth obtained empirically agrees well with the experimental data.

Scour Downstream of an Apron Due to Submerged Horizontal Jets

A semiempirical model is presented to compute the time variation of scour depth in an evolving scour hole at short abutments (abutment length/flow depth 1), namely the vertical wall, 45° wing wall, and semicircular, in uniform and nonuniform sediments under a clear water scour condition. The methodology developed for computing the time variation of scour depth is based on the concept of the conservation of the mass of sediment, considering the primary vortex system as the main agent of scouring, and assuming a layer-by-layer scouring process. For an equilibrium scour hole, the characteristic parameters affecting the nondimensional equilibrium scour depth (scour depth/abutment length), identified based on the physical reasoning and dimensional analysis, are excess abutment Froude number, flow depth—abutment length ratio, and abutment length—sediment diameter ratio. Experiments were conducted for time variation and equi- librium scour depths at different sizes of vertical walls, 45° wing walls and semicircular abutments in uniform and nonuniform sediments under limiting clear water scour conditions (approaching flow velocity nearly equal to the critical velocity for bed sediments ). The present model corresponds closely with the data of time variation of scour depth in uniform and nonuniform sediments obtained from the present experiments and reported by different investigators.

Subhasish Dey

Papers

Fluvial Hydrodynamics: Hydrodynamic and Sediment Transport Phenomena

Characteristics of Horseshoe Vortex in Developing Scour Holes at Piers

Clear water scour at circular piers : a model

Scour Downstream of an Apron Due to Submerged Horizontal Jets

Time Variation of Scour at Abutments