Models for Wave-Bottom Interaction and the Formation of Sand Bars and Sand Ridges

该项目的总体技术目标是开发三维地形模型，描述波浪主导的近岸带和陆架地区的海底动力学，其中单个和多个沙洲或沙脊形成了中心形态特征。研究者模拟并分析了波浪和洋流对海岸动力学的影响。这是具有挑战性的，因为存在两个自由表面，水面和可移动的底部，两者都随着时间的推移而变化，并通过复杂的非线性过程相互作用。该模型采用非线性、色散、耗散偏微分方程来描述从深水进入海岸的波浪的演变。这些Boussinesq型方程与海岸线上升和反射的模型相结合。一旦大致知道了水面的演变，就可以用势理论来确定大部分流体的速度场。然后，这个速度场被认为驱动了一个粘性的、含沙的边界层，在这个边界层中，沉积物的输运发生了。这一层的速度分布是用类似朗格-希金斯开创的思想来确定的。通过应用无限小形式的泥沙质量守恒，从而推导出一个用于确定底部变形的微分方程。因此，整个模型是比较复杂的，它包括一个非线性的波动初边值问题，以非局部的方式耦合到底部运动的守恒律。对该模型进行了详细的开发、分析并以计算机代码的形式实现。将模型预测结果与现场数据进行比较。还建议将计算机代码与地理信息系统的输入连接起来，以便在实际情况下更容易地部署模型。这个项目的潜在动机是双重的。首先，人们希望定性和定量地了解导致沿海地区和大陆架底部结构形成和维持的一些基本过程。这包括对波浪环境和海床动力学的全面了解，因为它受到波浪和水流的影响。其次，同样重要的是，该项目响应了对新的和更复杂的工具的需求，以帮助制定处理实际海岸工程问题的策略。该项目有可能有助于研究一些重要的科学和环境问题。北美的海洋边缘辽阔，而且在许多地方都很混乱。事实上，对松散海岸线的侵蚀是一种世界范围内的现象，人们对这种现象还没有很好的理解。全球变暖将使海平面上升，从而导致海岸后退，并为与海浪活动相关的冲刷和侵蚀提供更好的基础，从而加剧这些问题。脆弱的北极海岸和低海拔地区已经显示出由这些全球变化引起的明显恶化迹象。在接下来的半个世纪里，严重的侵蚀很可能会蔓延到其他沿海地区，因此人们对有效的预防方法的兴趣将会增加。除了诸如建造海堤之类的“硬”保护方案外，对利用自然过程的“软”保护策略的需求将会增加。

Bona9974116 The overall technical objective of the project is to developthree-dimensional topographical models that describe seabeddynamics in wave-dominated near-shore zones and shelf regionswhere single and multiple sand bars or sand ridges form a centralmorphological feature. The investigator models and analyses theeffects of waves and currents on coastal dynamics. This ischallenging because of the presence of two free surfaces, thewater surface and the movable bottom, both of which change overtime, and which interact with each other through complex,nonlinear processes. The model features nonlinear, dispersive,dissipative partial differential equations to describe theevolution of waves coming in to the shore from deep water. Theseequations, which are of Boussinesq type, are coupled to a modelfor run-up and reflection at the shoreline. Once the evolution ofthe water surface is approximately known, the velocity field inthe bulk of the fluid may then be determined via potentialtheory. This velocity field is then viewed as driving a viscous,sediment-laden boundary layer in which the sediment transport istaking place. The velocity distribution in this layer isdetermined using ideas similar to those pioneered byLonguet-Higgins. By applying conservation of sediment mass in aninfinitesimal form, a differential equation is thereby inferredthat serves to determine the bottom deformation. Thus the entiremodel is somewhat complicated, consisting of a nonlinearinitial-boundary-value problem for the wave motion coupled in anonlocal way to a conservation law for the bottom movement. Thismodel is developed in detail, analysed and implemented as acomputer code. Model predictions are compared with field data.It is also proposed to link the computer code with input from aGeographical Information System, to allow easier deployment ofthe model in real situations. The underlying motivation for the project is two-fold.First, there is a desire to understand both qualitatively andquantitatively some of the fundamental processes that lead to theformation and maintenance of bottom structure in coastal zonesand on continental shelves. This involves a thorough knowledgeof both the wave environment and the dynamics of the bed as it isinfluenced by waves and by currents. Second, and not lessimportant, the project responds to the need for new and moresophisticated tools to aid in the development of strategies todeal with real coastal engineering problems. The project has thepotential to contribute to the study of a number of importantscientific and environmental issues. The ocean margins in NorthAmerica are vast and in many places, troubled. Indeed, erosionof unconsolidated coastlines is a world-wide phenomenon that isnot well understood. Global warming will aggravate theseproblems by increasing sea levels, thus causing shore retreat andproviding a better base for the scour and erosion associated withwave activity. Fragile Arctic coasts and low-altitude regionsare already displaying unmistakable signs of deterioration causedby these global changes. Severe erosion may well spread to othercoast regions within the next half century, and thus there willbe an increased interest in effective prevention methods. Inaddition to "hard" protection schemes such as the construction ofseawalls and the like, there will be an increased demand for"soft" protection strategies that take advantage of naturalprocesses.