The Research Of Variation And Mode For Instabilities Of Longshore Currents In Time-spatial Domain Based On Wavelet Theory And Bottom Friction

Coastal region or its nearest place is often the most complex area becauseof its exposing to various environmental factors, which means that both theevolution and break of wave can result in a extremely complex law of motionfor instabilities of alongshore currents and the law of dissipation of pollutionalong the seashore. Since the discovery of the instabilities of alongshore currents,researchers have been widely studying the movement of alongshore currents andits phenomenon, finding that the instabilities of alongshore currents has a greatsignificance for the research of transportation law of the pollution anddepositions in the coastal region. The complex problems in the coastal regioncan be resolved smoothly if we deeply understand the theory of instabilities ofalongshore currents.In order to directly, clearly, comprehensively understand the characteristicsof the instabilities of alongshore currents, this paper researches its characteristicsin time-spatial domain and the changes of mode by using the wavelet analysisand the numerical model of instabilities of alongshore currents that considers thebottom friction. First, the research of instabilities of irregular waves induced alongshorecurrent in time and spatial domain proceeds, if the wavelet spectrum of timeseries can be calculated by using wavelet analysis. According to the analysis ofthe wavelet spectrum, we can analyze the characteristics of instabilities ofalongshore currents under two plane-beach slopes in detail and its relations andinfluences to the edge waves.Second, for the research of instabilities of alongshore currents under theplane-beach slope1:100, we can get growth rate and propagation speed that arerelated to the wave numbers and the coastline distribution of perturbationvelocity by building a linear instability model of alongshore currents whichadopted the velocity profiles(n=3and n=6) and the different bottom frictions.Lastly, for the research of instabilities of alongshore currents under the sandbar slopes1:100and1:40, we can get growth rate and propagation speed that arerelated to the wave numbers and the coastline distribution of perturbationvelocity by building a linear instability model of alongshore currents whichadopted bimodal velocity profiles we simulated beforehand.According to the research of instabilities of alongshore currents by usingwavelet analysis, we found that after the instabilities taking place, it cancontinuously exist in the time series; The energy transfer hardly occurredbetween the instabilities of alongshore currents and the low frequency waves;and the instabilities developed stronger in the alongshore direction than thecross-shore direction; and grew earlier with the increase of distance from theshore line and occurred earliest at the position of maximum mean alongshorecurrents, and developed stronger in both cross-shore and alongshore directionswith the increase of slope; The instabilities and the edge waves occursimultaneously in the cross-shore and alongshore direction; The instability ofalongshore currents can occur repeatedly under the same experimental condition. The research of growth rate of instabilities of alongshore currents whichconsidered bottom frictions under the plane-beach slopes and two velocityprofiles showed that bottom friction can affect the instabilities, which means thatlarger bottom friction can lead to a smaller growth rate; Under two velocityprofiles, there are same wave numbers that are responding to the maximum ofgrowth rate for different bottom frictions; the analysis of perturbation velocitythat was calculated by the instability model of alongshore currents showed thatthe perturbation velocity of alongshore currents presented a periodicalfluctuations under two velocity profiles whether the bottom frictions wereconsidered or not. The research of growth rate of instabilities of alongshorecurrents under six bimodal velocity profiles and sand bar slopes1:40and1:100in this paper shows that the instabilities had two growth modes whether therewere bottom frictions or not and these two growth modes are induced by frontshear and back shear in the alongshore currents; There were periodicalfluctuations in the field of perturbation velocity which is calculated byinstability model of alongshore currents; The slope can affect the growth rate ofinstabilities and the position of wave-breaking points. The increase of slope canmake growth rate of instabilities of alongshore currents larger, and also make theposition of wave-breaking points closer to the coastline.