Numerical Algorithms for the Detection and Simulation of Surface Water Waves

海浪的产生、传播和能量传输在许多技术中起着至关重要的作用，包括近岸船舶导航、深海石油钻井平台的设计以及海啸的产生和传播。然而，远距离探测和测量非线性波的基本技术是基于线性声波或电磁辐射从流体表面或主体的散射。毫不奇怪，这两种不同的波动现象在理论、近似和数值模拟方面的最新水平是完全不同的。在这项提案中，首席调查员(PI)主张开发一种统一的计算方法来解决这两个问题，目标是产生一套高精度、稳定和误差可控的数值算法，用于探测、模拟和评估大型水体表面的波浪。在过去的十年里，PI发展了一套稳定的、高精度的边界摄动(BP)算法，用于研究行进海浪和不规则形状障碍物的散射回波。这些BP算法都包含一个独立的摄动参数，PI建议研究一种通过连接这些参数来耦合这两个不同算法的策略，从而实现巨大的计算量节省。此外，PI还建议显著扩展和改进现有的BP算法，用于模拟高频区域的线性波。简而言之，几何光学解决方案指出了解决Anatz的方法，它可以用与频率无关的未知数表示。PI与F.Reitich合作，展示了这种与经典BP方法相结合的ANSATZ如何用于计算浅表面的高频散射回波，并节省了大量计算。在这项建议中，国际海洋研究所主张进一步发展这些算法，以纳入多次反射的情景。海浪的产生和传播特性在许多技术中都是至关重要的，包括船舶导航、深海石油钻井平台的设计和海啸研究。然而，这些非线性海浪的测量方法是基于线性声波或电磁辐射的散射，这两种不同的海浪现象在理论和实践上都有很大的不同。在这项建议中，首席调查员(PI)主张发展一种统一的方法来计算这两个问题，目的是产生一套可靠和准确的海浪探测和模拟数值算法。这将涉及到PI将他的研究计划的两个独立的线索结合在一起，以实施这种统一的方法。此外，他将需要扩展他的算法的能力，以解释在这些应用中出现的线性波的高振荡特性。后一项任务将特别具有挑战性，是目前民事和军事机构大量研究的重点。

The generation, propagation, and energetic transport of ocean wavesplay a crucial role in many technologies including near-shorewatercraft navigation, the design of deep-sea oil-drilling rigs, andthe generation and propagation of tsunamis. However, the fundamentaltechnologies for the remote detection and measurement of thesenonlinear waves are based upon the scattering of linear acoustic orelectromagnetic radiation from the surface or bulk of the fluid. Notsurprisingly, the state-of-the-art in theory, approximation, andnumerical simulation of these two disparate wave phenomena is quitedifferent. In this proposal the Principal Investigator (PI) advocatesthe development of a unified computational approach to these twoproblems with the goal of producing a set of highly accurate, stable,and error-controllable numerical algorithms for the detection,simulation, and evaluation of waves on the surface of large bodies ofwater. Over the past ten years the PI has developed a set of stable,high-accuracy Boundary Perturbation (BP) algorithms for the study ofboth traveling ocean waves and scattering returns from irregularlyshaped obstacles. These BP algorithms each involve an independentperturbation parameter and the PI proposes to investigate a strategyof coupling these two disparate algorithms by linking theseparameters, thus realizing huge computational savings. Additionally,the PI proposes to significantly extend and improve existing BPalgorithms for the simulation of linear waves in the high-frequencyregime. In short, the Geometric Optics solution points the way to asolution Ansatz which can be represented with a frequency-independentnumber of unknowns. The PI, in collaboration with F. Reitich, hasdemonstrated how this Ansatz coupled to classical BP methods can beused to compute high-frequency scattering returns from shallowsurfaces with enormous computational savings. In this proposal the PIadvocates the further development of these algorithms to incorporatethe scenario of multiple reflections.The generation and propagation properties of ocean waves are crucialin many technologies including watercraft navigation, design ofdeep-sea oil-drilling rigs, and the study of tsunamis. However, themethods for the measurement of these nonlinear ocean waves are basedupon the scattering of linear acoustic or electromagnetic radiation.The state-of-the-art in both the theory and practice of these twodisparate wave phenomena is quite different. In this proposal thePrincipal Investigator (PI) advocates the development of a unifiedapproach to the computation of these two problems with the goal ofproducing a set of reliable and accurate numerical algorithms for thedetection and simulation of ocean waves. This will involve the PIbringing together two separate threads of his research program toimplement this unified approach. Additionally, he will need to expandthe capabilities of his algorithms to account for the highlyoscillatory character of the linear waves which arise in theseapplications. The latter task will be particularly challenging and isthe current focus of a great deal of research by both civilian andmilitary agencies.