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

Solution of pore presure buildup due to progressive waves

This paper reviews the results of an experimental investigation of the interaction between an erodible bed and a pipeline vibrating in the transverse direction to a current. A springsupported rigid...

Interaction Between Vibrating Pipe and Erodible Bed

This paper presents the results of an experimental investigation on scour around pile groups with different configurations exposed to steady current. Two kinds of tests were carried out: (1) Rigid-bed tests, and (2) Actual scour tests. In the former tests, the mean and turbulence properties of the flow were measured across the pile groups. The pile group configurations were such that the global scour was distinguished from the local scour. The results show that the global scour can be quite substantial.

Global and local scour at pile groups

[1] The shape and dimensions of dunes formed in an erodible bed and exposed to flowing water are investigated by using a numerical model. The flow is calculated using a curvilinear flow model, where we combine a k-ɛ turbulence closure scheme with a sediment-transport description and the equation of continuity for the sand bed. The complete flow description allows for a discussion about what determines the length of dunes: From the equation of continuity for sediment, it turns out that the sediment transport over dunes is proportional to the local height of the dune. This means that the maximum height of the sand wave occurs at the location of maximum sediment transport. We relate the dune length to the location of maximum sediment transport. It is demonstrated that the effect of streamline curvature is essential for determining the location of maximum sediment transport at low bed shear stresses, due to an overshoot in bed shear stress. For large dimensionless bed shear stresses the downstream decay of turbulence from the former dune is demonstrated to play a major role.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004JF000171

Calculation of dune morphology

A stability analysis is used to investigate the development of large-scale periodic bottom topographies on a straight uniform coast. The work is an extension of the work by Hino (1974) and (1976), and special attention is paid to improve and refine the description of the sediment transport. The effect of the bed slope on the bed load sediment transport turns out to be very important. Further, the behaviour of suspended sediment is described by introducing lag effects that modify the predictions of the wave length considerably.

https://icce-ojs-tamu.tdl.org/icce/index.php/icce/article/download/5078/4756

Jørgen Fredsøe

Papers

Solution of pore presure buildup due to progressive waves

Interaction Between Vibrating Pipe and Erodible Bed

Global and local scour at pile groups

Calculation of dune morphology

Sea bed stability on a long straight coast