海岸动力学迭代法1

海岸动力学复习资料海岸动力学复习资料第一章1.海岸带宽度按从海岸线向内陆扩展10KM,向外海延伸到-15~-20m水深计算。

2.海岸类型：基岩海岸，砂质海岸，淤泥质海岸，生物海岸。

3.海岸的基本概念：海岸是海洋和陆地相互接触和相互作用的地带，包括遭受波浪为主的海水动力作用的广阔范围，即从波浪所能作用到的海底，向陆延伸至暴风浪所能到达的地带。

4.海岸动力因素：波浪的作用、海岸波生流、潮流的作用、径流的作用、海流的作用、风暴潮和海啸、风的作用、海平面上升。

5.波浪是引起海岸变化的主要因素。

6.近岸波生流——波浪传至近岸地区发生变形、折射与破碎，不仅其尺度改变了，同时还形成的一定水体流.7.沿岸流——斜向入射的波浪进入海滨地带后，在破波带引起一股与海岸平行的平均流。

8.裂流流速很高，会带动强烈的向外海输移的泥沙运动。

9.潮流对海岸的作用：影响海岸带波浪的作用范围及作用强度；影响海岸带地貌类型的发育；潮流流速影响海岸带的侵蚀与淤积。

10.河流径流挟带着大量的泥沙在河口外扩散和沉积，是海岸淤涨的主要物质来源之一，导致在河口外发育着河口三角洲或三角港。

第二章1.风浪的大小取决于风速、风时和风距的大小。

由于风速风向复杂多变，风所引起的海浪在形式上也极为复杂，波形极不规则，传播方向变化不定，不可能用简单的确定性数学公式来描述，所以经常把风浪称为不规则波。

2.波浪的分类:1）按形态分类：规则波和不规则波2）按传播海域的水深分类：深水波、有限水深波、潜水波（深水波与有限水深波界限为h/L=1/2，潜水波与有限水深波界限为h/L=1/20）。

3）按运动状态分类：震荡波、推进波、推移波4）按破碎与否分类：破碎波、未破碎波、破后波5）按运动学和动力学的处理方法：微幅波和有限振幅波3.波浪运动控制方程4.定解条件：1）海底表面设为固壁，因此水质点垂直速度为零。

z=-h2）在波面z=处，应满足动力学边界条件运动学边界条件。

动力学边界条件为水面上压力为常数，因此取z=，并令p=0，得到自由表面动力学边界条件。

海岸动力学复习资料.docx1.微幅波波能流:波浪在传播过程中存在能量传递，通过单宽波峰线长度的平均的能量传递率称为波能流。

2.驻波:当两个波波向相反，波高周期相等的行进波相遇时，形成驻波。

3.海岸:海岸是海洋和陆地相互接触相互作用的地带，包括遭受波浪为主的海水动力作用的广阔范围，即从波浪所能作用到的海底，向陆沿至波风浪所能到达的地带。

4.海岸侵蚀:指海水动力作用的冲击造成海岸线的海岸线的后退和海滩的下蚀。

5.海岸波生流:波浪传至近岸地区发生变形，不仅其尺度改变了，同时还形成一定水体——近岸波生流。

6.微幅波理论:为了把水波问题线性化，假设运动是缓慢的，波动的振幅远小于波长或水深。

7.漂流:净水平位移造成一种水平流动，称为漂移或质量输移。

8.波频谱:波能密度相对于组成波频率的分布函数。

9.浅水变形:波浪进入浅水区后，波高会产生变化，这种变化称为浅水变形。

浅水变形系数ks＝Hi／H0＝，波高H在有限水深范围内随水深减小而略有减小，进入浅水区后，则随水深增大而迅速增大。

10.波浪折射:随着水深变浅，如果波向与海底等深线斜交，波向将发生变化，即产生折射。

①折射波向线变化，斯奈尔定律:sinα／c＝sinα0／c0②折射引起波高变化，波浪折射系数kr＝根号(conαo／conαi)11.波浪绕射:波浪在传播过程中遇到障碍物如防波堤，岛屿或大型墩柱时，除可能在障碍物前产生波浪反射外，还将绕过障碍物继续传播，并在掩避区内发生波浪扩散，这是由于掩避区内波能横向传播所引起的。

绕射系数kd12.波浪破碎的原因:1.运动学原因:波峰处流体质点水平速度大于波峰移动速度;2.动力学原因:波峰处质点离心力大于重力加速度。

13.极限波陡:深水波浪的最大波高受波形能保持稳定的最大波陡所限制，达到极限波陡时，波浪就行将破碎。

14.破波角:破碎点处的波向线与岸线的外法线间的夹角称为破碎角。

15.破波带:波浪破碎点至岸边这一地带称为破波带。

第一章1.▲按波浪形态可分为规则波和不规则波。

2.按波浪破碎与否波浪可分为：破碎波，未破碎波和破后波3.★根据波浪传播海域的水深分类：①h/L=0.5深水波与有限水深波界限②h/L=0.05有限水深波和浅水波的界限，0.5>h/L>0.05为有限水深；h/L≤0.05为浅水波。

4.波浪运动描述方法：欧拉法和拉格朗日法；描述理论：微幅波理论和斯托克斯理论5.微幅波理论的假设：①假设运动是缓慢的u远小于0，w远小于0②波动的振幅a远小于波长L或水深h，即H或a远小于L和h。

6.(1)基本参数：①空间尺度参数：波高H:波谷底至波峰顶的垂直距离；振幅a:波浪中心至波峰顶的垂直距离；波面η=η(x,t):波面至静水面的垂直位移；波长L:两个相邻波峰顶之间的水平距离；水深h:静水面至海底的垂直距离②时间尺度参数：波周期T：波浪推进一个波长所需的时间；波频率f：单位时间波动次数f=1/T；波速c：波浪传播速度c=L/T(2)复合参数：①波动角(圆)频率σ=2π/T②波数k=2π/L③波陡δ=H/L④相对水深h/L或kh7.(1)势波运动的控制方程（拉普拉斯方程）：(2)伯努利方程：8.定解条件（边界条件）：①在海底表面水质点垂直速度为零，②在波面z=η处，应满足两个边界条件：动力边界条件：自由水面水压力为0；运动边界条件：波面的上升速度与水质点上升速度相同。

自由水面运动边界条件：③波场上、下两端面边界条件：对于简单波动，常认为它在空间和时间上呈周期性。

9.①自由水面的波面曲线：η=cos(kx-σt)*H/2②弥散方程：σ2=gktanh(kh)③弥散方程推得的几个等价关系式：L=tanh(kh)*gT2/(2π),c=tanh(kh)*gT/(2π),c2=tanh(kh)*g/k10.★弥散（色散）现象：水深给定时，波周期愈长，波长愈长，波速愈大，这样使不同波长的波在传播过程中逐渐分离。

这种不同波长（或周期）的波以不同速度进行传播最后导致波的分散现象称为波的弥散（或色散）现象。

牛顿迭代法解动力学方程不收敛摘要：1.引言2.牛顿迭代法简介3.动力学方程及其收敛性问题4.牛顿迭代法在解动力学方程中的应用5.牛顿迭代法在解动力学方程中的不收敛问题6.结论正文：1.引言在物理学中，动力学方程是描述物体运动状态的数学模型，广泛应用于各种实际问题中。

然而，在求解动力学方程时，常常会遇到收敛性问题。

牛顿迭代法作为一种求解非线性方程的数值方法，被广泛应用于解动力学方程。

本文将探讨牛顿迭代法在解动力学方程中的不收敛问题。

2.牛顿迭代法简介牛顿迭代法是一种求解非线性方程的数值方法，其基本思想是通过迭代使得函数值逐步逼近零。

对于非线性方程F(x) = 0，牛顿迭代法的迭代公式为：x[n+1] = x[n] - F(x[n])/F"(x[n])，其中F"(x) 表示F(x) 的导数。

牛顿迭代法具有二阶收敛性，即当迭代步长足够小，且初始值足够接近真实解时，可以通过有限次迭代得到精确解。

3.动力学方程及其收敛性问题动力学方程描述了物体在给定力的作用下的运动状态，通常包括质量、速度、加速度等物理量。

求解动力学方程时，通常需要采用数值方法，因为解析解往往难以求得。

然而，在数值求解过程中，可能会遇到收敛性问题。

例如，在迭代过程中，如果迭代步长过大或者初始值与真实解差距过大，可能导致迭代结果发散，无法得到精确解。

4.牛顿迭代法在解动力学方程中的应用由于牛顿迭代法具有二阶收敛性，因此在求解动力学方程时，可以得到较好的数值解。

在实际应用中，可以根据动力学方程的特点，选择合适的牛顿迭代法求解。

例如，对于具有显式解的动力学方程，可以直接使用牛顿迭代法求解；对于具有隐式解的动力学方程，可以通过拟合等方法得到显式解，然后使用牛顿迭代法求解。

5.牛顿迭代法在解动力学方程中的不收敛问题尽管牛顿迭代法具有二阶收敛性，但在求解动力学方程时，仍然可能出现不收敛的情况。

这主要是因为动力学方程的非线性特性和迭代过程中的误差累积。

海岸动力学上海海事大学2007106130041. 波浪分类：1按形态分布分规则波和不规则波2按波浪是否破碎分破碎波、未破碎波和破后波3按水深分h/l<0.05为浅水波；0.05≤h/l ≤0.5为有限水深波；h/l>0.5为深水波2. 波浪运动的描述方法：欧拉法、拉格朗日法3. 波理论的简单描述：微幅波理论和斯托克斯波理论（有限水深波理论）4. 波浪描述的参数：（基本参数）空间尺度包括波高H ，振幅a ，波面η，波长L ，水深h ；时间尺度包括波周期T ，波频率f=1/T ，波速c=L/T 。

（复合参数）波动角频率σ=2π/T ，波数k=2π/L ，波陡δ=H/L ，相对水深h/L 或kh5. 波理论假设：1流体是均质和不可压缩的，其密度为常数2流体是无粘性的理想流体3自由水面的压力是均匀的且为常数4水流运动是无旋的5海底水平不透水6流体上的质量力仅为重力，表面张力和柯氏力可忽略不计7波浪属于水平运动，即在xy 平面内做6. 波动方程：拉普拉斯方程 伯努利方程边界条件7. 微服波控制方程： 自由水面波面曲线：η=2H cos(kx-σt)；自由表面边界条件：σ2=gktanh(kh)弥散方程 弥散方程：表面波浪运动中角频率σ、波数k ，水深h 之间的相互关系推导：L= π2gT 2tanh(kh)；c=π2gT tanh(kh)；c 2=kg tanh(kh)——σ=2π/T ；k=2π/L ；c=L/T 8. 迭代法求波长9. 名词解释：弥散（色散）现象：当水深给定是，波的周期越长，波长也越长，这样就使不同波长的波在传播过程中逐渐分散开来。

这种不同波长或周期的波以不同速度进行传播最后导致波的分散现象称为波的弥散（或色散）现象10. 深水波和浅水波：根据双曲函数图像深水波：潜水波：11. 水质点运动方程：12. 轨迹为一个封闭的圆，在水底处b=0，说明水质点沿水滴只作水平运动。

在深水情况下，运动轨迹为一个圆，随着指点距水面的深度增大，轨迹圆的半径以指数形式迅速减小。

第一章 波浪理论1.波浪分类（1）按波浪形态：分为规则波和不规则波（2）按波浪传播海域的水深：h/L ≥1/2 为深水波；1/2>h/L>1/20 为有限水深波；h/L ≤1/2 为浅水波（3）按波浪破碎与否：分为破碎波、未破碎波和破后波2.波浪运动控制方程 （1）描述一般水流运动方法有两种：一种叫欧拉法，亦称局部法，另一种叫拉格朗日法，亦称全面法（2）描述简单波浪运动的理论： 一个是艾利（Airy ）提出的为微幅波理论，另一个是斯托克斯（Stokes ）提出的有限振幅波理论3.参数（1）波高H ：两个相邻波峰顶之间的水平距离（2）振幅a ：波浪中心至波峰顶的垂直距离，H=2A （3）波周期T ： 波浪推进一个波长所需的时间（4）波面升高 ）t , x （ηη= ：波面至静水面的垂直位移（5）函数表达式： ）t -kx （Acos ση=（6）圆频率：T 2πσ= （7）波速c ： 波形传播速度，即同相位点传播速度，又称相速度4.建立简单波理论的假设：流体是均质和不可压缩的，其密度为一常数；流体是无粘性的理想流体；自由水面的压力是均匀的且为常数；水流运动是无旋的；海底水平、不透水；流体上的质量力仅为重力，表面张力和柯氏力忽略不计；波浪属于平面运动，即在xz 平面内作二维运动。

5.速度φ的控制方程（拉普拉斯方程）： 02222=∂∂+∂∂z x φφ 就是势运动的控制方程。

6.拉普拉斯方程的边界条件：（1）海底表面边界条件：海底水平不透水 0z=∂∂φ ，h z -= 处（2）自由水面动力学边界条件： 0])()[(21t 22=+∂∂+∂∂+∂∂==ηφφφηηg zx z z （3）自由水面的运动边界条件：自由水面上个点的运动速度等于位于水面上个水质点的运动速度0zx x t =∂∂-∂∂∂∂+∂∂φφηη ，η=z 处（4）二维推进波，流场上、下两端面边界条件可写为：）z ,ct -x （）t ,z ,x （φφ=7.微幅波理论假设：假设运动是缓慢的，波动的振幅A 远小于波长L 或水深h7.微幅波波面方程：）t -kx （cos 2σηH =弥散方程）kh （gktanh 2=σ 波长：）kh （tanh 2gT L 2π= 波速：）kh （tanh 2gT c π= 深水波长：π2gT L 2o = 深水波速：π2gT c o = 浅水波长：gh T L s = 浅水波速gh c s =8.色散（弥散）现象：不同波长（或周期）的波以不同速度进行传播最后导致波的分散现象称为波的色散现象。

richardson迭代法
Richardson迭代法（也称为Richardson外推）是一种数值计算方法，用于计算连续函数的导数或求解微分方程。

该方法的基本思想是通过迭代，以逐步逼近目标函数的导数或微分方程的解。

具体步骤如下：
1. 选择一个适当的步长h和初始值x0。

2. 计算函数在x0和x0+h点的函数值f(x0)和f(x0+h)。

3. 使用以下公式计算导数的近似值：
f'(x0) ≈ (f(x0+h) - f(x0)) / h
4. 通过不断缩小步长h，重复步骤2和步骤3，直到达到所需的精度或满足其他终止条件。

Richardson迭代法的优点是简单易实现，但缺点是需要进行多次迭代，且步长的选择对结果的准确性有较大影响。

在实际应用中，通常需要根据函数的性质和所需精度进行调优。

此外，Richardson迭代法还可以应用于求解微分方程。

通过将微分方程离散化为差分形式，然后使用该方法进行迭代，可以逼近微分方程的解。

与求解导数类似，需要根据微分方程的特性和所需精度进行调优。

总之，Richardson迭代法是一种重要的数值计算方法，适用于求解导数和微分方程，但在实际应用中需要注意参数选择和精度控制。

“Bilingual Course”精品课程C t l H d d i Coastal HydrodynamicsHOHAI UNIVERSITYAifeng April 2013 / TAO AifengZHENGZHENG JinhaiJinhai/ TAOChapter 6 COASTAL PROCESSESCh t 6 COASTAL PROCESSESStating beach nomenclatureStating beach profileStating coastal change1/32In the treatment of coastal sediment transport, In the treatment of coastal sediment transport it is quite common to consider separately sediment movement perpendicular to the shoreline and that parallel to it. The sedimenth li d th t ll l t it Th di tp pmovement perpendicular to the shoreline is considered to be the more significant one for the short--term variation of coastal processes, th h t t i ti f t lthe shortpwhile that parallel to the shoreline is the more significant one for the longsignificant one for the long--term variation of the coast.2/3261General Beach Nomenclature §6.16.1 General Beach NomenclatureGeneral Beach Nomenclaturenearshore zoneoffshore zonei h f h backshorecoastline inshore foreshore backshorecliffbeachscarp3/32longshore bar longshore trough beach face berm crest bermsThe beach is an accumulation of unconsolidated The is an accumulation of unconsolidated sediment (sand, shingle, cobbles, and so forth) di h d f h l id extending shoreward from the mean low--tide extending shoreward from the mean lowline to some physiographic change such as ap y g p gsea cliff or dune field, or to the point where permanent vegetation is established. permanent vegetation is establishedWe require a more inclusive term, one that will encompass this underwater portion of the environment, since that is where the more environment,since that is where the more important processes occur which are responsible for the beach formation.i f f i4/32The term littoral is used to denote this entire Th t litt l i d t d t thi ti,environment, which extends across the beach and into the water to a depth at which the sediment is less actively transported by surface waves. This depth varies, of course, but is waves This depth varies of course but is generally considered to be some 10 to 20g ymeters. In the actual practice the term beach commonly is almost synonymous with the above definition of littoral zoneabove definition of littoral zone.5/32The littoral zone（沿岸带）is composed of four li l i f f portions: backshore, foreshore, inshore, and portions:backshore foreshore inshore and offshore.offshore.The nearshore zone extends seaward from the shoreline to just beyond the region in which the waves break, so that this term is particularly useful when discussing waves and currents within this environment.ithi thi i t6/32The comparatively flat Offshore（离岸区）: : The comparatively flat Off h Th ti l fl tp p gportion of the beach profile extending seaward from beyond the breaker zone to the edge of the continental shelf. This term is also used to refer to the water and waves seaward of the refer to the water and waves seaward of thegnearshore zone. The interesting feature in this region is the generation of sand ripples, which seem to have a strong influence on sediment movement.movement7/32Inshore（外滩）: : The zone of the beach profileThe zone of the beach profile:The zone of the beach profile extending seaward from the shoreline at mean low tide to just beyond the breaker zone.Th i h i i th l hThe inshore region is the place whereg pp distinguishable sediment movement appears, and where longshore bars are generated by breaking waves. In this region, breaking wave b ki I thi i b kip yaction predominates to intensify the turbulent intensity of fluid motion, thus putting a large amount of sediment in suspension.8/32A longshore bar（沿岸沙坝）is a ridge of sand A l h b i id f d running roughly parallel to the shoreline. It running roughly parallel to the shoreline.It may become exposed at low tide. At times there may be a series of such ridges parallel to one another but at different water depths.A longshore trough（槽）is elongatedA l h t h i l t d depression extending parallel to the shoreline depression extending parallel to the shoreline and any longshore bars that are present.9/32The sloping portion of the前滩Foreshore（前滩）: : The sloping portion of the beach profile lying between a berm crest (or in beach profile lying between a berm crest(or in,ppthe absence of a berm crest, the upper limit of wave swash at high tide) and the lower--water wave swash at high tide) and the lowermark of the backrush of the wave swash at low tide. In this region, either suspended movement or bed load movement is dominant depending or bed load movement is dominant, dependinggon the breaking wave characteristics.10/32The term foreshore is often nearly synonymouswith the beach face but is commonly more with the beach face but is commonly more,ginclusive, containing also some of the flatportion of the beach profile below the beachface. A beach face（滩面）is the slopingsection of the beach profile below the bermwhich is normally exposed to the action of the which is normally exposed to the action of the wave swash.11/32The zone of the beach Backshore（后滩）: : The zone of the beachprofile extending landward from the sloping foreshore to the point of development offoreshore to the point of development ofvegetation or change in the physiography(sea cliff, dune field, and so on).(sea cliff dune field and so on)A beach berm（滩肩）is a nearly horizontalportion of the beach formed by the deposition ti f th b h f d b th d iti of sediment by the receding waves.A beach scarp（滩坎）is an almost verticalp p y escarpment notched into the beach profile by wave erosion.The seaward limit of a berm is named aThe seaward limit of a berm is named a bermcrest（滩肩缘）.12/32Beach Profile6.2 Beach Profile§6.262Beach Profile1.Equilibrium beach profile1Equilibrium beach profile2. 2. Beach profile changesBeach profile changes2.Beach profile changes13/321.1. Equilibrium beach profileEquilibrium beach profile During the progress of the experiment inq pg p g pwhich a constant wave input is maintained, the beach profile will reach a steady statecondition, that is, the beach profile in theflume will approach a particular one,which is named the equilibrium beach profile which is named the equilibrium beach profile.（海滩平衡剖面）.14/32On natural beaches the changing waves give rise to an ever--varying equilibrium whichrise to an everp pthe beach profile attempts to achieve butseldom does. One of the more importantaspects of a beach is its dynamic personality: aspects of a beach is its dynamic personality: the loose granular sediments continuouslyrespond to the ever changing waves andrespond to the ever--changing waves andrespond to the evercurrents imposed from the adjacent body of the water. However, the only way in whichbeach profiles can be understood is in terms of this equilibrium profile and how it isdetermined by wave conditions and thedetermined by wave conditions and thesediments which compose the beach.15/32It is still debated whether in reality there is It i till d b t d h th i lit th i an equilibrium beach profile in the fieldan equilibrium beach profile in the field where the tide and waves are continuously changing. Nevertheless, the concept of equilibrium beach profile is quite useful in understanding processes of coastal changed t di f t l hand in investigating the mechanisms ofand in investigating the mechanisms of erosion and deposition in the coastal region. 16/32Beach profile changes2. Beach profile changes2.¾Typical beach profiles¾Experimental study17/32There are two typical types of beach profile: Th t t i l t f b h fil one is the longshore bar type（沙坝剖面）, one is the longshore bar typewhile the other is the step type（滩肩剖面）.p ypThese different beaches are also found in the field. The former is also called a winter beach （冬季剖面）or stormy beach（风暴剖面）, and the latter a summer beach（夏季剖面）, ordinary beach or swell beachordinary beach or swell beach（常浪剖面）. 18/32storm profile swell profilep p常浪剖面bar trough sea cliffbermThe storm beach profile with barsversus the swell profile with a pronouncedberm that occurs under swell waves conditions 19/32The summer profile is characterized by a wideberm, the flat shoreward portion of the profile,and a smooth offshore profile without barsexcept perhaps in relatively deep water.The winter profile has almost no berm, thesand having shifted offshore to form a seriesof bars parallel to the shoreline. The overallprofile slope is smaller in the winter profilethan in the summer one. The volume of sandinvolved remains relatively constant. Thesediment shifts from the berm to bar and back20/32 again.Chapter 6Profile changes along Scripps Pier, California, showing the tendency to shift from a more evenly sloping swell (summer)profile to a storm (winter) profile and back again accordingto the season.21/32Chapter 6This accounts for the terminology---- summerand winter profiles. Such shifts in the profilewas first observed off the west coast of theUnite States, where storm waves are typical ofthe winter and long-period swell waves occurin the summer. Therefore, the shifts in theprofile corresponded with the winter andsummer. However, it is peculiar that thisterminology is sometimes used elsewhere inthe world where the seasonal connotations arenot 22/32 correct.Chapter 6winter profile under swell waves conditions in front of Nanri Sea dikeThe onshore-offshore shift of sand associated withprofile changes from storm to swell conditions isgenerally correlated with the wave steepness andthe grain size of the beach sediment.Johnson classified the stormy beach and theordinary beach by wave steepness parameter indeep water, H0/L0. He determined that with a wave steepness greater than 0.03 an offshore baralways forms, whereas if the steepness is less than0.025 an offshore bar is never formed.23/32Chapter 6Dean presented a model for the shift from a storm to a swell profile based on a consideration of the trajectory of a suspended sand particle during its fall to the bottom, acted upon at the same time by the horizontal water particle velocity of the wave.critical24/32Chapter 6In fact, our understanding of the critical wavesteepness which governs the shift from theswell profile to the storm profile is stillincomplete.This incompleteness is particularly true forfield studies. This is also due in part to thegreat irregularity of profile changes on realbeaches.25/32Chapter 6The development of a storm versus a swell profilecan be understood in terms of the directions ofsediment transport within the surf zone andbeyond the breaker zone. With storm waves thesand seaward of the breaker zone movesshoreward, while sand in the surf zone istransported in an offshore direction. Thisconvergence of the sand transport directions mustresult in an accumulation of sand at the breakerposition, forming a bar. With flatter swell waves,the sand is moved landward at all depths, withinthe surf zone as well as beyond the breaker zone,so that it accumulates on the berm.26/32Chapter 6The beach profile type is of importance to seacliff and coastal property erosion. With a swellprofile the sea cliffs are protected from thewave action by a wide berm and so experiencelittle or no erosion. During storm conditionsthe sand is shifted offshore and the berm lost,so that the more intense swash is able to reachand erode the sea cliffs. In other years thestorms are separated by quieter periods, andthe beach berm may not be entirely eliminated.27/32Chapter 6The beach changes from swell to storm profileinvolve principally onshore-offshore shifts ofsediment. Therefore, the profile changescannot be understood until we comprehendthe details of this transport normal to theshoreline. However, a complete comprehensionas is required is still very remote, so that onlythe broadest understanding is presentlypossible.28/32Chapter 6It is well known that storm waves transport beachmaterial offshore causing beach erosion and material offshore, causing beach erosion andforming a bar. Waves of gentle steepness betweensuccessive storms gradually move bar formingmaterial onshore,resulting in beach accretion material onshore, resulting in beach accretion and creation of a berm.According to their laboratory investigations, According to their laboratory investigations, Sunamura and Horikawa classified beach profiles from a different point of view.fil f diff i f iThey proposed the following semiy p p g p They proposed the following semi--empirical criterion on whether a beach will erode or accrete. This criterion is a function of three accrete This criterion is a function of three parameters, i.e., wave steepness, sediment grain size and bottom slope.The value for C is 4~8 to demarcate erosionTh l f i48t d t iand accretion of laboratory beaches.and accretion of laboratory beachesWhen C>8, beach erodes and the bar type,yp profile occurs.While C<4, beach accretes and the step typeprofile forms.When 4<C<8, the equilibrium profile is found. It was also found that=18for natural beaches It was also found that C=18 for natural beaches. 31/32“Coastal Hydrodynamics”——chapter 6ZHENG ZHENG Jinhai Jinhai / TAO / TAO Aifeng Aifeng Apr 2013THANK YOU。