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

The circulation over a longshore bar with rip channels

A 3-D flow code, EllipSys3D, tested and validated, has been implemented along with a morphologic model to simulate the scour process around a vertical circular pile in a steady current in the case of non-cohesive sediment The k-omega turbulence model has been used for closure The morphologic model includes (1) a two-dimensional bed load sediment transport description, and (2) a description of surface-layer sand slides for bed slopes exceeding the angle of repose The simulation captured all the bed features, ie, the scour hole and the formation of a downstream dune at the initial stage, and the truncated cone-shaped scour hole in the equilibrium stage The maximum equilibrium scour depth obtained from the simulation compares fairly well with the measurements

3-D Numerical modelling of flow and scour around a pile

A morphological modelling concept for long term nearshore morphology is proposed and examples of its application are presented and discussed. The model concept combines parameterised representations of the cross-shore morphology, with a 2DH area model for waves, currents and sediment transport in the surf zone. Two parameterization schemes are tested for two different morphological phenomena: 1) Shoreline changes due to the presence of coastal structures and 2) alongshore migration of a nearshore nourishment and a bar by-passing a harbour. In the case of the shoreline evolution calculations, a concept often used in one-line modelling of cross-shore shifting of an otherwise constant shape cross-shore profile is applied for the case of a groyne and a detached breakwater. In the case of alongshore bar/nourishment migration an alternative parameterization is adopted. All examples are presented, analysed and discussed with respect to the question of realistic representation, time scale and general applicability of the model concept.

/pdf/long-term-morphological-modelling-4rtecsv2gd.pdf

Long term morphological modelling

The free surface simulation of breaking waves is studied using a combination of VOF and RANS closures. Further, a numerical model for the detailed study of sediment transport and morphological development is presented. In the present study it is applied to the case of sediment transport in the surf zone. The temporal change of a cross shore beach profile under both regular and bichromatic waves is considered. The dependency on the morphological time scale on the regularity of the incident waves is discussed. The feedback onto the hydrodynamics due to a changing bed level is discussed in the case of regular waves.

/pdf/a-full-hydrodynamic-modelling-of-2d-breaker-bar-development-3c5n8zndn5.pdf

A Full Hydrodynamic Modelling of 2D Breaker Bar Development

Rotational flow of an inviscid fluid over an irregularity in the bottom is investigated. The flow is regarded as a perturbed unidirectional flow, and the shape of the irregularity is described using Fourier transforms. The velocity profile in the unidirectional flow is determined using the eddy-viscosity concept and a finite wall slip velocity. Two different examples of irregularities are considered: ( a ) an infinitely long straight irregularity which forms an arbitrary angle with the direction of the basic flow and ( b ) a hump in a channel with impermeable walls. The influence of rotation on the two- and three-dimensional waves which are formed downstream of these irregularities is analysed and experimentally verified. Further, it is shown that the gradient of the basic velocity profile increases the transverse movement of the fluid particles at the bottom, while at the surface this transverse movement is decreased.

Jørgen Fredsøe

Papers

The circulation over a longshore bar with rip channels

3-D Numerical modelling of flow and scour around a pile

Long term morphological modelling

A Full Hydrodynamic Modelling of 2D Breaker Bar Development

Rotational channel flow over small three-dimensional bottom irregularities