沿岸流不稳定运动的实验研究及理论分析
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摘要
本文以沿岸流不稳定实验采集的垂直岸线方向和沿岸方向的流速时间历程和墨水运动轨迹图片资料为基础,利用最大熵谱分析方法分析了实验室观测到的沿岸流不稳定运动的频率;利用测量的墨水运动轨迹分析了其传播速度;利用三角函数回归法分析了其波动幅值在垂直岸线方向的变化特征;并讨论了这些量随入射波波高、入射波周期、地形的变化。用线性剪切不稳定模型理论分析了实验观测到的结果,得到了对应实验情况的沿岸流不稳定运动的频率、波长和传播速度,并与实验结果进行了对比分析,发现了实验中两个不同坡度(1:40和1:100)海岸上所观察到的沿岸流不稳定运动分别对应两种不同的剪切流线性不稳定模式,即1:40坡度海岸的不稳定运动是由于沿岸流速度剖面后剪切所引起,而1:100坡度海岸的不稳定运动是由于沿岸流速度剖面前剪切所引起。讨论了平均沿岸流速度剖面对不稳定增长模式的影响,利用解析速度剖面分析了速度剖面对不稳定多模式的影响。以浅水方程为控制方程,基于波能守恒方程计算波浪辐射应力,建立了平均沿岸流数学模型。数值分析了沿岸流不稳定对平均沿岸流的影响。
文中首先阐述了沿岸流不稳定运动对研究近岸污染物、泥沙输移的重要意义,并指出目前沿岸流不稳定运动实验研究比较少,因此,通过实验来研究沿岸流不稳定运动有助于更加直观、深刻、全面的认识沿岸流不稳定运动的特性,并为沿岸流不稳定运动数值模拟的研究以及与沿岸流不稳定运动相关的其它方面提供实验结果。
第二章详细介绍了沿岸流不稳定运动的实验,具体包括该实验的物理模型布置,仪器布置以及墨水投放的实验,并给出了实验采集的30个波况垂直岸线方向、沿岸方向的流速时间历程以及用CCD系统采集的墨水运动轨迹的图片。基于采集的实验结果,本文就其不同波况下的流速时间历程和墨水运动特点作了详细分析,着重分析了在规则波和不规则波情况下是否出现了长周期波动,并分析了质量输移流、沿岸流、大尺度漩涡和沿岸流不稳定运动对墨水运动轨迹的影响;波高对沿岸流不稳定运动空间结构的影响。
第三章介绍了沿岸流不稳定运动实验结果分析方法。用最大熵谱方法确定沿岸流不稳定运动的频率;用三角函数回归法确定其波动幅值;用墨水运动轨迹来确定其传播速度。
第四章用第三章的方法分析了规则波和不规则波情况对应的两种坡度1:100和1:40地形条件下沿岸流不稳定运动的频域特性、幅值特性和传播速度特性。
第五章利用沿岸流线性不稳定运动理论模型对实验中观测到的不稳定进行了理论分析。首先用二阶中心差分格式对该模型进行离散,得到了计算不稳定增长模式的矩阵方程,并采用Garbow,Moler等提出算法基础上改进的QZ算法对矩阵方程进行了求解,通过与已有计算结果的对比对所用的数值格式进行了验证。利用本章的沿岸流线性不稳定的理论模型计算了30个实验波况下的沿岸流不稳定运动增长模式,并将计算结果与实验结果进行了比较。
第六章利用无因次的沿岸流线性不稳定模型,分析讨论了坡度对沿岸流增长模式的影响;分析了前剪切、后剪切对沿岸流增长模式的影响;分析讨论了规则波与不规则波情况不稳定周期不同的原因。
第七章利用Allen给出的解析速度分析了不稳定模式出现不连续的情况,即多模式情况。并分析了速度剖面最大值发生变化后对于不稳定的影响。
第八章建立了二维平均沿岸流的数学模型并分析了沿岸流不稳定对平均沿岸流的影响,并初步分析了沿岸流不稳定引起的侧混系数的范围。首先给出了平均沿岸流计算模型,该模型利用二维浅水方程为控制方程,其中波高变化利用波能守恒方程求得,从而计算出了波浪辐射应力。用交替方向隐式(ADI)法对该模型进行了数值求解,并将计算结果与实验结果进行了比较。然后数值分析了沿岸流不稳定对平均沿岸流的影响。
最后给出了本文的结论以及对于本研究的展望。
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.
文中首先阐述了沿岸流不稳定运动对研究近岸污染物、泥沙输移的重要意义,并指出目前沿岸流不稳定运动实验研究比较少,因此,通过实验来研究沿岸流不稳定运动有助于更加直观、深刻、全面的认识沿岸流不稳定运动的特性,并为沿岸流不稳定运动数值模拟的研究以及与沿岸流不稳定运动相关的其它方面提供实验结果。
第二章详细介绍了沿岸流不稳定运动的实验,具体包括该实验的物理模型布置,仪器布置以及墨水投放的实验,并给出了实验采集的30个波况垂直岸线方向、沿岸方向的流速时间历程以及用CCD系统采集的墨水运动轨迹的图片。基于采集的实验结果,本文就其不同波况下的流速时间历程和墨水运动特点作了详细分析,着重分析了在规则波和不规则波情况下是否出现了长周期波动,并分析了质量输移流、沿岸流、大尺度漩涡和沿岸流不稳定运动对墨水运动轨迹的影响;波高对沿岸流不稳定运动空间结构的影响。
第三章介绍了沿岸流不稳定运动实验结果分析方法。用最大熵谱方法确定沿岸流不稳定运动的频率;用三角函数回归法确定其波动幅值;用墨水运动轨迹来确定其传播速度。
第四章用第三章的方法分析了规则波和不规则波情况对应的两种坡度1:100和1:40地形条件下沿岸流不稳定运动的频域特性、幅值特性和传播速度特性。
第五章利用沿岸流线性不稳定运动理论模型对实验中观测到的不稳定进行了理论分析。首先用二阶中心差分格式对该模型进行离散,得到了计算不稳定增长模式的矩阵方程,并采用Garbow,Moler等提出算法基础上改进的QZ算法对矩阵方程进行了求解,通过与已有计算结果的对比对所用的数值格式进行了验证。利用本章的沿岸流线性不稳定的理论模型计算了30个实验波况下的沿岸流不稳定运动增长模式,并将计算结果与实验结果进行了比较。
第六章利用无因次的沿岸流线性不稳定模型,分析讨论了坡度对沿岸流增长模式的影响;分析了前剪切、后剪切对沿岸流增长模式的影响;分析讨论了规则波与不规则波情况不稳定周期不同的原因。
第七章利用Allen给出的解析速度分析了不稳定模式出现不连续的情况,即多模式情况。并分析了速度剖面最大值发生变化后对于不稳定的影响。
第八章建立了二维平均沿岸流的数学模型并分析了沿岸流不稳定对平均沿岸流的影响,并初步分析了沿岸流不稳定引起的侧混系数的范围。首先给出了平均沿岸流计算模型,该模型利用二维浅水方程为控制方程,其中波高变化利用波能守恒方程求得,从而计算出了波浪辐射应力。用交替方向隐式(ADI)法对该模型进行了数值求解,并将计算结果与实验结果进行了比较。然后数值分析了沿岸流不稳定对平均沿岸流的影响。
最后给出了本文的结论以及对于本研究的展望。
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.
引文
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