A Laboratory Study And Theoretical Analysis On The Instabilities Of Alongshore Currents

Based on the recorded cross-shore and longshore velocity time series and collected images of dye patch movement,the variations of dominant periods of shear instabilities of longshore currents,oscillation amplitudes(u',v') in cross-shore direction and propagation speed with incident wave height,wave period and bottom topography were analyzed using the maximum entropy method,regression method of trigonometric function and linear fit;the observations were investigated using the linear shear instability model.The longshore currents methemetical model is built.And the influences of the instability of longshore currents on the mean longshore currents are studied.At last,the effects of velocity profiles on the growth mode are analyzed numerically.Firstly,the important meanings of the shear instabilities of longshore current to investigate transportaion of coastal pollutant,sendiment were explained.And it is pointed out that the experimental study of shear instabilities of longshore currents is few.Hence,it is helpful to investigate the shear instabilities of longshore currents by the experimental study intuitively,deeply and all-around,and provide empirical parameters for the numerical modeling of the shear instabilities and other related studies with them.The experiment of the shear instabilities including the experimental set-up,instruments deployment and the release of dye are introduced in detail and the recorded cross-shore and longshore velocity time series and collected images of dye patch movement are given.The characteristics of the observations are analyzed in detail.Especially,whether the oscillation with long period occurs under all cases is analyzed,and the results show that this kind of oscillation occurs under all cases.The wavy dye patches are also observed in the collected images.And we analyze the effects of mass transport currents,alongshore currents,large vorticities and the instabilities of alongshore currents on the movement of the dye patch.And the spatial structures of shear instabilities are analyzed using these collected photos.In chapter 3,the maximum entropy method,regression method of trigonometric function and measurement method are introduced.In chapter 4,the results about the frequency,variations of amplitude in cross-shore direction and propagation speed of the instabilities of longshore currents under regular waves and random waves are given detailed. In chapter 5,the linear shear instability model is formulated.And the model is discretized using the second order centered finite difference scheme.The obtained matrix equation after discretizing is solved using the modified QZ algrorithm.Putrevu and Svendsen solved the instability equation using fourth order finite difference scheme.The comparison between Putrevu and Svendsen' and the present scheme is conducted.The comparison shows that the present scheme has enough accuracy.The shear instability modes of longshore currents in present experiment are calculated using the present numerical model.And we make the comparison between numerical results and measurements.And the growth modes of shear instabilities under present laboratory are calculated using the built linear instability model.In chapter 6,the effects of slope on the growth mode are analyzed using nondimensional linear instability model,and we investigate the effects of frontshear and backshear on the shear instability mode.Because the shear wave periods are different under regular waves and irregular waves,we discuss the reason.In chapter 7,the multi-mode cases are analyzed numerically using analytical velocity profiles.And we investigate the effects of distance of maximum of mean longshore currents on the instability mode.In chapter 8,two dimensional longshore currents numerical model is built.The governing equations are two dimensional shallow water equations.The variations of wave height are calculated using the conservasion equation of wave energy.And the comparison between the numerical results and measurements is made.The comparison shows that the numerical results agree with measurements well.The influences of the instability of longshore currents on the mean longshore currents are studied numerically.And the lateral mixing coefficient due to the instability of longshore currents is estimated.To the end,the conclusions and prospect about the present study are given.