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

A theory has been developed that predicts the rate of natural backfilling of pipeline trenches through the action of waves and currents. The theory claims that even if the amount of suspended load is much larger than the bed load, the gravity infill of the bed load normally will be the dominant resedimentation mechanism. This occurs because the relatively small width of the trench keeps the suspended grains from settling in it; instead, they are carried by the current across the trench. Experiments with waves confirm the theory of gravity infill of bed load and further support the conclusion that no scour occurs near the pipeline when the pipe is placed in a trench in the seabed, rather than on the seabed itself.

Natural Backfilling of Pipeline Trenches

A 3D investigation of flow across long, straight channels aligned obliquely to the flow direction has been conducted. The applied mathematical model solves the Reynolds-averaged Navier-Stokes equat...

Oblique Flow over Dredged Channels. I: Flow Description

This paper treats the numerical prediction of initial and long-term morphology of small pipeline trenches. For this purpose a refined flow and sediment transport description is applied such that the entire mathematical problem is formulated and solved on a curvilinear grid using a k — e turbulence-closure. The backfilling process of trenches exposed to either waves or a steady current is of importance in relation to the implementation of pipelines in the marine environment. With respect to the sedimentation of trenches, the non-dimensional Trench-Keulegan- Carpenter number, KC = a/L, where a is the excursion length of a particle in waves and L the trench length, is investigated in detail, and an optimal KC-numher for the backfilling rate is found. Coherent structures in the non-uniform unsteady trench-flow are shown to dominate the deposition rate when present. The importance of a detailed description of the flow is further justified by comparing predictions of a very simple flow-model neglecting convective terms with the sophisticated flow-model.

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Backfilling of trenches exposed to waves

Influence of turbulence on bedload sediment transport

By means of detailed mathematical modeling the processes responsible for the morphological evolution of small-scale excavations exposed to wave-induced flow are investigated. The problem is relevant when assessing rates of sedimentation of trenches dredged for the purpose of laying out pipelines or cables in the marine environment. A flow and sediment transport model formulated in curvilinear coordinates is applied. The unsteady Reynolds-averaged Navier-Stokes equations along with a standard k-e turbulence model and the equation of continuity constitute the flow model. The action of waves is simulated by an oscillating pressure gradient imposed on the horizontal momentum equation. The sediment transport is composed of bed and suspended load taking into account the effect of gravity on the former. The convection-diffusion concept is applied to calculate the distribution of suspended sediment concentration. Intraperiod flow and sediment transport processes are resolved, and the effect of these on the backfi...

Jørgen Fredsøe

Papers

Natural Backfilling of Pipeline Trenches

Oblique Flow over Dredged Channels. I: Flow Description

Backfilling of trenches exposed to waves

Influence of turbulence on bedload sediment transport

Sediment Transport and Backfilling of Trenches in Oscillatory Flow