The Turbulent Wave Boundary Layer

Abstract

Close to the bottom the no-slip condition will retard the flow and cause a boundary layer to develop. In nature this boundary layer will for most practical purposes be turbulent and the bed will be rough. Usually the boundary layer is confined to a thin layer close to the bed having a typical thickness of 0.2 m under surface gravity waves. The turbulence intensity in this rather thin layer can be very high and strongly unsteady. The understanding of the hydrodynamics of this flow is not only of great academic/scientific interest. but it has also a wide range of applications in practical engineering. The object of this study is to investigate the use of turbulence modellinq in connection with the turbulent wave boundary layer. Two theoretical models are established and their results are checked against available measurements. A third model is constructed but not implemented so no results are thus being presented for this model. Finally, the effects of a refined flow model in connection with sediment transport computations are considered through a few examples. First , the mixing-length theory was used to construct the zero-equation model BL0BAK. Modelling of the turbulent kinetic energy budget was improved by, inclusion of a transport equation for turbulent kinetic energy which gave the one-equation model BL1PJ. Finally a two-equation model BL2PJ for which also a transport equation for the dissipation rate has been outlined but it has not been implemented. It can he concluded that the description of the velocity field in an oscillatory boundary layer can be obtained from BL0BAK or BL1PJ as well as from a constant eddy viscosity model like that of Myrhaug. The latter model requires, however, that the boundary layer thickness is knows a priory, whereas the present models do not have this limitation. In the theoretical models it has been possible to determine the energy loss factor. A good agreement with experimental data is observed. This applies to BL0BAK as well as to BL1PJ, the latter model yielding slightly better results. Perhaps the most important topic in this report is the calculation of the turbulent kinetic energy conditions in the boundary layer. Using the model BL1PJ it has been investigated how energy is produced, diffused, dissipated, and preserved from times with a production surplus to later times where dissipation is high. The calculations show that the production is very high just before the maximum ambient velocity culminates. This surplus of energy is then preserved in the turbulent motions and is spread towards areas in which the energy level is lower. The turbulent motions are of course sustained throughout the period of oscillation. The model shows that this effect is most pronounced for low values of a/kN. The time scale for the decay of turbulent energy is then comparable with the period of oscillation. Unfortunately we have not been able to check the theoretical findings against measurements duo to the lack of experimental data.