Feature Of The Vertical Distribution Of Wave Induced Currents With Experimental And Numerical Simulations

Based on the recorded longshore and cross-shore velocity time series, the feature of the vertical distribution of wave induced currents were analyzed using the logarithmic fitting method and the variation of the friction velocity in cross-shore direction are analyzed. According to the incomplete self-similarity assumption, a power type formula is advised to predict the vertical distribution of longshore currents. The formula is applied to calculate the vertical distribution of longshore currents which were observed in field or laboratory experiements. The vertical distribution of undertow observed on plane and barred beaches was given. The three dimensional nearshore circulation models and three dimensional radiation stress formulations given by Mellor(2003,2008), Xia et.al.(2004), Lin and Zhang(2005) are reviewed. Based on the pressure sheet, a new three dimentional radiation stress formula is derived. In shallow water, Solutions for the undertow driven by Mellor(2003)’s, Svendsen(1984)’s and present three dimensional radiation stresses are given. An extension of the Princeton Ocean Model (POM) is used to simulate undertow and vertical distribution of longshore currents observed from present and relavent experimentsFirstly, the important meanings of the vertical distribution of wave induced currents to investigate transportaion of coastal pollutant, sendiment were explained. And it is pointed out that the experimental study of the vertical distribution of longshore currents is few. Hence, it is helpful to investigate the vertical distribution of longshore currents by the experimental study intuitively, deeply and all-around, and provide empirical parameters for the numerical modeling of the vertical structure of longshore current and other related studies with them.The experiment of the vertical distribution of wave induced currents over plane and barred beaches including the experimental set-up, instruments deployment are introduced in detail. The longshore uniformity and repeatability of wave height, set-up and longshore currents over plane and barred beaches generated by the passive system are discussed. At last, the recorded velocity time series of the vertical distribution of longshore currents and cross-shore mean flow are given. The vertical distribution of longshore currents is analyzed briefly.In chapter3, logarithmic law and power type law are applied to fit the measured vertical current profiles. The results indicate that the logarithmic law fits the data well for plane and barred beaches. Since friction velocity and apparent roughness height can not be obtained accurately, the logarithmic law is hardly applied to predict vertical profile of longshore currents. Based on the analysis of the measured data, a power type formula is proposed to describe the vertical profile of longshore currents. The formula can give good prediction with o=1/10for plane beach. But for barred beach different values of exponent a need to be taken for different region. For the region from the bar trough to the offshore side of bar crest, a=1/10and a=1/7can give good fitting and for the data over the trough region of cross-shore distribution curve of the mean longshore current, using a=1/3can give good fitting. The formula with a=1/10and1/7is examined using published data from four sources covering laboratory and field experiments. The results indicate that the power-law fits the data well for the laboratory and field data with a=1/10. The present model is easily applied to predict the vertical profile of longshore currents. At last, the observed cross-shore mean flow on plane and barred beaches is given.In chapter4, a briefing to the POM model is given. Three dimensional radiation stress expressions have been derived by other researchers and applied POM to simulate nearshore circulation. The shortcomings of their radiation stress formulas and the rationality of the numerical results are reviewed. A new formulation of local radiation stresses is presented by taking the local radiation stresses as the vertical spatial rate of momentum flux below pressure reference sheet.In chapter5, analytical solutions for undertow driven by pressure sheet radiation stress are given, and comparisons with the other undertow profiles driven by different three dimensional radiation stress are performed. Parabolic eddy viscosity, linear eddy viscosity and vertical constant eddy viscosity are adopted to derive analytical solutions for undertow and the effect of eddy viscosity is investigated. A vertical2d nearshore circulation model for application to the nearshore surf zone is developed. The three dimensional radiation stress developed by present study has been included in the model. The model is applied to relavent undertow experiments. Model results are compared to observations from these experiments.In chapter6, two three dimensional nearshore circulation model is proposed in present study, one of them is coupled model and another is semi-coupled. The effect of the vertical eddy viscosity and the bottom shear stress on the longshore currents is discussed. The vertical distribution of longshore currents observed from present experiments, Visser(1991) and Hamilton and Ebersole (2001) are simulated. Besides, the cross-shore mean flow profiles observed in present experiment are also simulated by the model. The comparison shows that the numerical results agree with measurements well.To the end, the conclusions and prospect about the present study are given.