Jørgen Fredsøe

Mechanics of coastal sediment transport

The main objective of the book is to describe from a deterministic point of view the sediment transport in the general wave-current situation. For this purpose, the book is divided into two major parts. The first part of the book is related to flow and turbulence in combined wave-current. This part covers the turbulent wave boundary layer, bed friction in combined wave-current motion, turbulence in the surf zone, and wave-driven currents in the long- and cross-shore direction. The second part treats the sediment transport as a result of the wave-current action. This part includes an introduction to basic sediment transport concepts, distribution of suspended sediment in the sheet flow regime, description of bedforms formed by current and waves, and their influence on sediment transport pattern. Finally, the modelling of cross- and long-shore sediment transport is described. This book is useful for students with a background in basic hydrodynamics.

Turbulent oscillatory boundary layers at high Reynolds numbers

This study deals with turbulent oscillatory boundary-layer flows over both smooth and rough beds. The free-stream flow is a purely oscillating flow with sinusoidal velocity variation. Mean and turbulence properties were measured mainly in two directions, namely in the streamwise direction and in the direction perpendicular to the bed. Some measurements were made also in the transverse direction. The measurements were carried out up to Re = 6 x lo6 over a mirror-shine smooth bed and over rough beds with various values of the parameter alk, covering the range from approximately 400 to 3700, a being the amplitude of the oscillatory free-stream flow and k, the Nikuradses equivalent sand roughness. For smooth-bed boundarylayer flows, the effect of Re is discussed in greater detail. It is demonstrated that the boundary-layer properties change markedly with Re. For rough-bed boundary-layer flows, the effect of the parameter alk, is examined, at large values (0(103)) in combination with large Re.

On the development of dunes in erodible channels

A two-dimensional stability analysis of the flow in a straight alluvial channel has been carried out, using the vorticity transport equation. In the analysis an attempt has been made to account for the influence of gravity on bed-load transport, and this turned out to change the stability quite significantly. In the case of instability, the further growth of the dunes has been investigated using a second-order approximation, This nonlinear theory explains the experimental fact that the dunes very soon become asymmetric.

Meandering and braiding of rivers

The origin of meandering and braiding of alluvial rivers is re-analysed in terms of stability theory. The flow is described by a two-dimensional model, and the transportation of sediment is separated into bed-load transport and transport of suspended sediment, by use of the improved knowledge of sediment transport mechanisms achieved in recent years. The paper explains why it is important to distinguish between the sediment transported as bed load and that in suspension. The analysis is able to predict whether a river remains stable or tends to meander or braid. The results of the stability analysis are compared with laboratory experiments and data from natural rivers, and the agreement is satisfactory.

Wave plus current over a ripple-covered bed

Abstract This paper concerns the combined wave and current boundary layer flow over a ripple-covered bed. The study comprises experiments as well as a numerical modelling study: the experimental part comprises laser Doppler anemometry (LDA) velocity and turbulence measurements, and a flow-visualization study in the laboratory with ripples, 22 cm in length, and 3.5 cm in height. One wave-alone, three current-alone, and three combined waves and current tests were conducted. The wave-velocity-to-current-velocity ratio ranges from 1 to 2.4. The orbital-amplitude-to-ripple-length ratio (at the bed) is 0.41. The effect of superimposing waves on a current is to displace the velocity profile to higher elevations. The velocity profiles exhibit two “logarithmic layers”, one associated with the actual roughness of the bed (the actual ripple roughness), and the other with the apparent roughness induced by the waves. The apparent roughness is, for the tested cases, found an order of magnitude larger than the actual bed roughness. The turbulence near the bottom increases markedly during the time when the lee-wake vortices are washed over the ripples. The numerical part of the study gives a detailed numerical description of the flow around fixed ripples by use of a k−ω model to calculate the roughness, and friction of a rippled bed.

Onset of scour below pipelines and self-burial

Abstract This paper summarizes the results of an experimental study on the onset of scour below and self-burial of pipelines in currents/waves. Pressure was measured on the surface of a slightly buried pipe at two points, one at the upstream side and the other at the downstream side of the pipe, both in the sand bed. The latter enabled the pressure gradient (which drives a seepage flow underneath the pipe) to be calculated. The results indicated that the excessive seepage flow and the resulting piping are the major factor to cause the onset of scour below the pipeline. The onset of scour occurred always locally (but not along the length of the pipeline as a two-dimensional process). The critical condition corresponding to the onset of scour was determined both in the case of currents and in the case of waves. Once the scour breaks out, it will propagate along the length of the pipeline, scour holes being interrupted with stretches of soil (span shoulders) supporting the pipeline. As the span shoulder gets shorter and shorter, more and more weight of the pipeline is exerted on the soil. In this process, a critical point is reached where the bearing capacity of the soil is exceeded (general shear failure). At this point, the pipe begins to sink at the span shoulder (self-burial). It was found that the self-burial depth is governed mainly by the Keulegan–Carpenter number. The time scale of the self-burial process, on the other hand, is governed by the Keulegan–Carpenter number and the Shields parameter. Diagrams are given for the self-burial depth and the time scale of the self-burial process.

A morphological stability analysis for a long straight barred coast

A morphological stability analysis is carried out for a long straight coast with a longshore bar. The situation with oblique wave incidence and a wave-driven longshore current is considered. The flow and sediment transport are described by a numerical modelling system. The models comprise: (i) a wave model with depth refraction, shoaling and wave breaking, (ii) a depth integrated model for wave driven currents and (iii) a sediment transport model for the bed load transport and the suspended load transport in combined waves and current. The direction of the sediment transport is taken to be parallel to the depth integrated mean current velocity, neglecting the effects of a bed slope and secondary currents. An instability is found to develop around the bar crest. The instability is periodic in the alongshore direction, and tends to form rip channels and to steepen the offshore face of the bar between the rip channels. The alongshore wave length of the most unstable perturbation is determined for different combinations of the wave conditions and the geometry of the profile.

Shear stress distribution in dissipative water waves

Abstract The exchange of energy and the mean shear stress distribution are analyzed for dissipative water waves. The cases of energy dissipation in an oscillatory bottom boundary layer and of spilling breakers or broken waves are considered. The wave motion is assumed to be described by linear shallow water wave theory. It is described how energy is extracted from the wave motion and transported to the location of dissipation. For the case of breaking waves this requires a dynamic model for the surface roller. In the case of a wave boundary layer, the energy exchange is associated with the secondary water motions caused by displacement in the boundary layer. The shear stress distribution depends on the location of the energy dissipation. In case of no dissipation or dissipation near the bed, the near surface shear stress is zero, whereas in case of dissipation near the surface, the near surface shear stress is determined from the gradient in the wave energy flux. In non-uniform waves the vertical and the horizontal orbital motion are not completely out of phase, and the organized wave motion gives a significant contribution to the vertical momentum transfer, which is important for determining the shear stress distribution.

Turbulent combined oscillatory flow and current in a pipe

This work concerns the combined oscillatory flow and current in a circular, smooth pipe. The study comprises wall shear stress measurements, and laser-Doppler-anemometer velocity and turbulence measurements. Three kinds of pipes were used, with diameters D =19 cm, 9 cm, and 1.1 cm, enabling the influence of the parameter R /δ to be studied in the investigation ( R /δ ranging from about 3 to 53), where R is the radius of the pipe, and δ is the Stokes layer thickness. The ranges of the two other parameters of the combined flow processes, namely the current Reynolds number, Re c , and the oscillatory-flow boundary-layer (i.e. the wave–boundary layer) Reynolds number, Re w , are: Re c =0−1.6×10 5 , and Re w =0−7×10 6 . The transition to turbulence in the combined flow case occurs at a current Reynolds number larger than the conventional value, ca. 2×10 3 , depending on Re w , and R /δ. A turbulent current can be laminarized by superimposing an oscillatory flow. The overall average value of the wall shear stress (the mean wall shear stress) may retain its steady-current value, it may decrease, or it may increase, depending on the flow regime. The increase (which can be as much as a factor of 4) occurs when the combined flow is in the wave-dominated regime, while the oscillatory-flow component of the flow is in the turbulent regime. The component of the wall shear stress oscillating around the mean wall shear stress can also increase with respect to its oscillatory-flow-alone value. For this to occur, the originally laminar oscillatory boundary layer needs to become a fully developed turbulent boundary layer, when a turbulent current is superimposed. This increase can be as much as O (3–4). The velocity profiles across the cross-section of the pipe change near the wall when an oscillatory flow is superimposed on a current, in agreement with the results of the wall shear stress measurements. The period-averaged turbulence profiles across the cross-section of the pipe behave differently for different flow regimes. When the two components of the flow are equally significant, the turbulence profile appears to be different from those corresponding to the fundamental cases; the level of turbulence increases (only slightly) with respect to those experienced in the fundamental cases.

Sinking/floatation of pipelines and other objects in liquefied soil under waves

Abstract This paper presents the results of an experimental study where the sinking and floatation of a pipeline and other objects (namely, a sphere and a cube) in a silt bed was investigated. The bed was exposed to progressive waves. Two kinds of experiments were made: The undisturbed-flow experiments, and the experiments with the structure model (a pipeline, a sphere, and a cube). In the former experiments, the pore-water pressure was measured across the soil depth. The pore-water pressure built up, as the waves progressed. The soil was liquefied for wave heights larger than a critical value. Regarding the experiments with the structure model, the displacement of the structure (sinking or floatation) was measured simultaneously with the pore-water pressure. The influence of various parameters (such as the initial position of the object, the specific gravity, the soil layer thickness, and the wave height) was investigated. It was found that while the pipe sank in the soil to a depth of 2–3 times the pipe diameter, the sphere sank to even larger depths. The pipe with a relatively small specific gravity, initially buried, floated to the surface of the soil. The drag coefficients for the objects sinking in the liquefied soil were obtained.