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 study presents the results of an experimental work with a spring‐supported cylinder exposed to irregular oscillatory flow. The steady current and regular‐oscillatory‐flow cases are also included for reference purpose. The oscillatory‐flow conditions are created by the so‐called carriage technique. The cross‐flow response of the cylinder has been investigated for the Keulegan‐Carpenter numbers equal to 10, 20, and 36, and for the reduced velocity from 0 to 11.5. The effect of the width of the flow‐velocity spectrum on the cylinder response was studied. The results show that the cylinder vibrations under irregular‐oscillatory‐flow conditions differ considerably from the response in the regular oscillatory flow. First of all, the cylinder responds mostly with its natural frequency. Second, vibration amplitudes are considerably reduced. Third, the vibrations are initiated earlier (i.e., at smaller values of the reduced velocity) than in regular oscillatory flow.

Cross-flow vibrations of cylinder in irregular oscillatory flow

In the present paper the vertical distribution of turbulent kinetic energy k under broken waves is calculated by application of a one-equation turbulence model. The contributions to the energy level originate partly from the production in the wave boundary layer, partly from the production in the roller. Further on, the findings for k are used to calculate the vertical distribution of suspended sediment in broken waves.

https://icce-ojs-tamu.tdl.org/icce/index.php/icce/article/download/4091/3773

The bottleneck problem for turbulence in relation to suspended sediment in the surf zone

AbstractThis paper presents the results of an experimental investigation on edge scour adjacent to a stone cover laid on a sandy bed. The three-dimensional flow over the edge of the stone layer has been investigated by the use of particle image velocimetry. The flow measurements show a significant amount of turbulence in the primary flow near the junction between the stone layer and the sand bed and the formation of complex secondary-flow structures. The results show that the flow and the edge scour process in a steady current are governed by the size of the roughness elements and to some extent the side slope of the berm. The edge scour is caused by the combined action of the primary flow and the secondary flow. The primary flow stirs up the sediment and puts it into suspension, and the secondary flow carries it away from the junction between the stone layer and the sand bed, resulting in a scour hole forming adjacent to the toe of the stone layer. The measured scour depth attained a constant level of ap...

Edge scour in current adjacent to stone covers

The shear instability of a uniform longshore current and the fully developed shear waves are studied in the numerical hydrodynamic model MIKE-21. The effect of the shear waves on the sediment transport, the cross-shore momentum transfer and mean velocity profile and the dispersion of suspended or dissolved matter is studied. The strength of the shear waves is calculated for a varying flow resistance and a varying momentum exchange coefficient. The formation of shear waves can be suppressed by modest rip channels in a longshore bar.

/pdf/numerical-simulation-of-finite-amplitude-shear-waves-and-2olj1jzxsq.pdf

Jørgen Fredsøe

Papers

Cross-flow vibrations of cylinder in irregular oscillatory flow

The bottleneck problem for turbulence in relation to suspended sediment in the surf zone

Edge scour in current adjacent to stone covers

Numerical simulation of finite amplitude shear waves and sediment transport

Investigation of bed shear stresses subject to external turbulence