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 deals with turbulent oscillatory boundary-layer flows over a plane bed with a sudden spatial change in roughness. Two kinds of ‘change in the roughness’ were investigated: in one, the roughness changed from a smooth-wall roughness to a roughness equal to 4.8 mm, and in the other, it changed from a roughness equal to 0.35 mm to the same roughness as in the previous experiment (4.8 mm). The free-stream flow was a purely oscillating flow with sinusoidal velocity variation. Mean flow and turbulence properties were measured. The Reynolds number was 6 × 106 for the major part of the experiments, with a maximum velocity of approximately 2 m/s and the stroke of the motion about 6 m. The response of the boundary layer to the sudden change in roughness was found to occur over a transitional length of the flow. The bed shear stress over this transitional length attains a peak value over the bed section with the larger roughness. It was found that the amplification in the bed shear stress due to this peak could be up to 2.5 times its asymptotic value. Also, it was found that the turbulence is quantitatively different in the two half periods; a much stronger turbulence is experienced in the half period where the flow is towards the less-rough section. The present experiments further showed that a constant streaming occurs near the bed in the neighbourhood of the junction between the two bed sections. This streaming is directed towards the section with the larger roughness.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112093003696

Experimental investigation of wave boundary layers with a sudden change in roughness

Impact of groyne fields on the littoral drift: A hybrid morphological modelling study

The sedimentation of navigation channels due to leveling of side slopes is investigated This leveling is caused by the deviation of the particle path from the direction of bed shear on a bed with transverse slope because of the action of gravity In the first part of the paper the variation in the rate of bed load with depth is neglected, and a simple solution of the problem (an error-function) has been obtained This solution has been compared with experiments, and the agreement between theory and experiments is satisfactory Taking into account a weak variation in the bed load with water depth, a second-order solution is presented, which describes in a more detailed manner the development in the form of the slope (U-formed); also this is experimentally verified /Author/

Sedimentation of River Navigation Channels

The scour process around monopiles caused by breaking waves is studied experimentally using regular waves. The use of regular waves is conservative, which made it possible to avoid scour phenomena caused by nonbreaking waves such as scour generation and backfilling. The waves were breaking on a flat sand section after shoaling on a mildly sloping ramp. Various monopiles were exposed to plunging breakers that were breaking at various distances from the pile. It was found that the scour was caused by turbulence generated by the breaking and was diverted toward the bottom by the pile. The maximum scour depth found was approximately 0.60D. This was smaller than the scour observed around piles exposed to current; however, in some cases it was an order of magnitude larger than the scour caused by nonbreaking waves. This is apparently especially true for larger piles.

Experimental Study on the Scour around a Monopile in Breaking Waves

When a stone/armor layer on a sand bed is exposed to flow, the sand underneath will be agitated by the flow turbulence. When the flow velocity reaches a critical value, the sand will be sucked (winnowed out) from between the armor blocks. In a previous investigation, we studied suction removal of sediment in steady currents. The present study is an extension of our previous investigation to waves. The critical condition for the onset of suction is determined. It is found that the onset of suction is governed by three parameters: (1) the sediment mobility number (based on the sediment size); (2) the ratio of sediment size to stone size, d∕D ; and (3) the Keulegan-Carpenter (KC) number, based on the armor block/stone size. The variation of the critical mobility number for suction as a function of d∕D and KC is determined for the ranges of the parameters 0.001<d∕D⩽1 and 1<KC<50 . The case of steady current is included as a reference case. The effect of waves superimposed on current, the effect of a multilaye...

Jørgen Fredsøe

Papers

Experimental investigation of wave boundary layers with a sudden change in roughness

Impact of groyne fields on the littoral drift: A hybrid morphological modelling study

Sedimentation of River Navigation Channels

Experimental Study on the Scour around a Monopile in Breaking Waves

Suction Removal of Sediment from between Armor Blocks. II: Waves