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

Modelling of non-cohesive sediment transport processes in the marine environment

This paper summarizes the results of an experimental study on scour around spherical bodies and self-burial in steady current and in waves. The equilibrium scour depth below a fixed sphere in steady current for live-bed conditions was found to be S∕D=O (0.3) , D being the sphere diameter. The effect of the Shields parameter, θ , and that of the position of the sphere with respect to the bed, e , were investigated. It was found that, under live-bed conditions, the effect of θ is quite weak. It was also found that the effect of e is significant. No scour occurs when e∕D>0.8 . It was demonstrated that, in the case of waves, the Keulegan-Carpenter number, KC , is the main parameter that governs the equilibrium scour depth. S∕D is always smaller in waves than in steady currents. Regarding the self-burial, the equilibrium self-burial depth in steady current was found to be e∕D=O (0.5) . The self-burial depth in waves is governed by KC , similar to the scour depth for a fixed sphere. e∕D is always smaller in wav...

Scour around spherical bodies and self-burial

This paper presents the results of an experimental study of the influence of clay content (CC) on liquefaction of seabed beneath progressive waves. Experiments were, for the most part, conducted with silt and silt-clay mixtures; in supplementary tests, sand-clay mixtures were used. Two types of measurements were carried out: (1) pore-water pressure measurements across the soil depth and (2) water-surface elevation measurements. These measurements were synchronized with video recordings of the liquefaction process from the side. The ranges of the various quantities in the experiments were wave height H=7.6−18.3 cm, wave period T=1.6 s, and water depth h=55 cm. The experiments showed that the influence of CC on wave-induced liquefaction is very significant. Susceptibility of silt to liquefaction was increased with increasing CC up to CC≈30% (which is clay-specific), beyond which the mixture of silt and clay was not liquefied. Sand may become prone to liquefaction with the introduction of clay, contr...

Influence of Clay Content on Wave-Induced Liquefaction

The longitudinal current sorting of graded sediment is analysed by use of a sediment transport formula developed recently by Engelund and Fredsoe (1976). The analysis yields that for a given longitudinal profile of a river, the longitudinal variation in mean grain diameter and the grain distribution curve is unique determined by the sediment input and water discharge. No requirement concerning an ultimate equilibrium state of the bed elevation is introduced. The analysis yields that the mean grain size will decrease as the slope of the river decreases and further, that originally logarithmic normally distributed sand will tend to be logarithmic hyperbolic distributed after sorting.

Jørgen Fredsøe

Papers

Modelling of non-cohesive sediment transport processes in the marine environment

Scour around spherical bodies and self-burial

Influence of Clay Content on Wave-Induced Liquefaction

Longitudinal Grain Sorting by Current in Alluvial Streams

Wave scour around structures