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

Numerical simulations are presented for the flow and the dynamics of noncohesive sediment over 2D ripples in waves and current. For this purpose, a model based on a discrete vortex approach using the "cloud-in-cell" concept has been applied. The hydrodynamic model drives a Lagrangian model for the suspended sediment. The characteristic vorticity structures prevailing in the vicinity of ripples are accurately replicated and sediment suspension mechanisms are successfully described. Thus, the sediment transport resulting from asymmetrical waves and combined waves and current can be predicted. Especially, the wave-related component of the transport opposes the maximum free stream velocity and contributes significantly to the total transport. In the present work, the effect of the wave-induced drift is not included.

/pdf/sediment-transport-over-ripples-in-waves-and-current-2cdq2m7u5i.pdf

Sediment transport over ripples in waves and current

This paper summarizes the results of an experimental investigation of turbulent solitary wave boundary layers. The wave induced flow has been simulated by a solitary motion in an oscillating tunnel. The experiments show that the boundary layer flow remains laminar for Re numbers smaller than Re=5x10. The experiments further show that the bed shear stress reverses during the deceleration stage of the freestream flow. In a narrow sub-range of Re number (2x10 ≤ Re < 5x10) in the laminar regime, the boundary layer flow experiences a regular array of vortices near the bed over a short period of time during the deceleration stage. The transition-to-turbulence at Re=5x10 is associated with the emergence of turbulent spots, revealed by single/multiple, or, sometimes, quite dense spikes in the bed shear stress variations. Flow resistance in terms of wave friction coefficient including the phase information has also been worked out for both the acceleration and deceleration stages of the free-stream flow of the wave.

Turbulent solitary wave boundary layer

This 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...

Flow and edge scour in current adjacent to stone covers

/pdf/modelling-of-sand-dunes-in-steady-and-tidal-flow-1uvongp2yn.pdf

Modelling of Sand Dunes in Steady and Tidal Flow

The formation of ripples and dunes (lower range bed waves) is assumed to be related to the transport of sediment as bed load From the present theory it is concluded that the formation of the upper range bed configurations (standing waves, antidunes) may be explained on the assumption that the predominant part of the sediment transport is in suspension The paper presents a mathematical model of the formation of double-periodic antidunes, first-order potential flow theory being applied It differs from previous models in taking account of the non-uniform distribution of the suspended load The theory predicts regions of stability and instability Results are compared with measurements made by different observers

/pdf/three-dimensional-stability-analysis-of-open-channel-flow-10eyk3kgsk.pdf

Jørgen Fredsøe

Papers

Sediment transport over ripples in waves and current

Turbulent solitary wave boundary layer

Flow and edge scour in current adjacent to stone covers

Modelling of Sand Dunes in Steady and Tidal Flow

Three-dimensional stability analysis of open channel flow over an erodible bed