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 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-ω 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, i.e. 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.

International society for soil mechanics and geotechnical engineering

The equilibrium width of alongshore shoreline undul ations is studied using an integrated numerical sho reline model where the shape of the shoreline undulations is pre scribed and only the amplitude of the undulations e volves in the model. The waves, currents and sediment transport f ields are calculated using a 2DH area model and the shoreline evolution is computed using a one-line model. The r esults from the integrated shoreline model are comp ared with results from a detailed numerical shoreline model whe re the shoreline is completely free to move in any direction.

Width of shoreline undulations: integrated and full approach

Basic concepts of potential wave theory

/pdf/influence-of-clay-content-on-residual-liquefaction-in-waves-3cq5fc5ab5.pdf

Jørgen Fredsøe

Papers

International society for soil mechanics and geotechnical engineering

Width of shoreline undulations: integrated and full approach

Basic concepts of potential wave theory

Influence of clay content on residual liquefaction in waves