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

A method is presented which enables the computation of the bed-load transport as the product of the saltation height, the particle velocity and the bed-load concentration. The equations of motions for a solitary particle are solved numerically to determine the saltation height and particle velocity. Experiments with gravel particles (transported as bed load) are selected to calibrate the mathematical model using the lift coefficient as a free parameter. The model is used to compute the saltation heights and lengths for a range of flow conditions. The computational results are used to determine simple relationships for the saltation characteristics. Measured transport rates of the bed load are used to compute the sediment concentration in the bed-load layer. A simple expression specifying the bed-load concentration as a function of the flow and sediment conditions is proposed. A verification analysis using about 600 (alternative) data shows that about 77% of the predicted bed-load-transport rates are within 0.5 and 2 times the observed values.

Sediment transport; Part I, Bed load transport

Development and validation of a three-dimensional morphological model

A method is presented which enables the computation of the suspended load as the depth-integration of the product of the local concentration and flow velocity. The method is based on the computation of the reference concentration from the bed-load transport. Measured concentration profiles have been used for calibration. New relationships are proposed to represent the size gradation of the bed material and the damping of the turbulence by the sediment particles. A verification analysis using about 800 data shows that about 76% of the predicted values are within 0.5 and 2 times the measured values.

Sediment Transport, Part II: Suspended Load Transport

A critical review of the intrinsic nature of vortex-induced vibrations

This paper presents the results of an experimental investigation on suction removal of sediment from between armor blocks/stones placed on a loose bed. The process of suction has been investigated. It was found that the vortices that form in the holes between the armor blocks are key to the process. The sediment swept into these vortices is entrained into the main body of the flow by these same vortices (the suction removal of sediment from between the armor blocks). The critical condition for the onset of suction was determined. It was found that the onset of suction is governed by two parameters: (1) the Shields parameter (based on the sediment size); and (2) the ratio of sediment size to stone size, d/D. The variation of the critical Shields parameter for suction as a function of d/D was determined for a broad range of the parameter d/D, namely, 0.001 & d/D # 1. The timescale of the suction process and the downward displacement of stones (the general lowering of the armor layer) have also been investigated.

Suction removal of sediment from between armor blocks

article i nfo In this work a detailed hydrodynamic model is presented, which is used for the study of cross-shore sediment trans- port and morphodynamics in two dimensions. The model is described in the framework of the generally unstruc- tured, finite volume method. Considerable emphasis is put on those subtleties in the morphological formulation, which are required to achieve mass conservation for the amount of sediment in the bed and in suspension. In this first part of two, the hydrodynamic description overthe cross-shore profile is presented. The model is val- idatedagainstanexperiment withdetailedmeasurementsofthefreesurface andturbulence over a fixedbreaker bar profile. A test matrix covering a large interval of the surf similarity parameter is simulated, and the phase lag between the breakpoint and the initiation of the setup is described. The relation of this phase lag to a cross-shore delay in dissipation of organised energy into turbulence is described. The relation of this phase lag to the distribution of the location of maxima in bed shear stresses and magnitude of the undertow is also described. Furthermore, processes in the hydrodynamics, which will have a smoothing effect on the mean cross-shore sediment transport and morphodynamic response are considered. All simulations are presented for regular waves and for values of the deep-water surf similarity parameter, ζ0 ,i n the range from 0.08 to 1.19, i.e. covering both spilling and plunging breakers. © 2013 Published by Elsevier B.V.

Formation and development of abreaker bar under regular waves. Part1: Model description and hydrodynamics

Scour at the head of a vertical-wall breakwater

[1] Two parallel experiments involving the evolution and runup induced by plunging regular waves near the shoreline of a sloping bed are considered: (1) a rigid-bed experiment, allowing direct (hot film) measurements of bed shear stresses and (2) a sediment-bed experiment, allowing for the measurement of pore-water pressures as well as observation of sediment suspension and bed morphological changes. Both experiments utilize the same initial bed profile and wave forcing. The experiments show that the mean bed shear stresses experienced onshore of incipient breaking are amplified by nearly a factor of 2 relative to prebreaking conditions, whereas their corresponding turbulent fluctuations are amplified even more strongly, by a factor of 5–6. The plunging processes lead to a series of vortices, whose formation may be explained as the result of shear layer instability. Measurements show that these vortices can significantly enhance peaks in the offshore-directed bed shear stresses. Moreover, near-bed pore pressure measurements indicate that these vortices cause large upward-directed pressure gradients, which in turn produce a corresponding series of suspended sediment plumes shoreward of the initial breaking event. These findings are related to the induced morphological changes over both short and long time scales. The present results are also compared and contrasted with previous experiments utilizing a similar methodology, but involving plunging solitary waves.

Jørgen Fredsøe

Papers

Suction removal of sediment from between armor blocks

Formation and development of abreaker bar under regular waves. Part1: Model description and hydrodynamics

Scour at the head of a vertical-wall breakwater

Laboratory observations of flow and sediment transport induced by plunging regular waves

Modelling the morphology of sandy spits