Collaborative Research: Nonlinear Waves and Vorticity in Oceanic Flows

1715082，Oliveras 1715089，柯蒂斯研究人员研究涡度在与海洋中的自由表面水波有关的三个问题中的作用。涡度是流体局部旋转的量度。研究人员研究了流体中的涡流如何驱动表面波动力学，以及随深度变化的水下水流如何影响非线性波。他们还研究风力驱动的海浪和阵风的影响。第一个问题与海啸在水下漩涡存在时的浅滩行为有关。第二种方法有助于更好地理解水下洋流表面波的高度和速度，并有助于理解污染物和微生物如何沿着水下洋流传播。第三个有助于解释风是如何在海洋表面形成波浪的。本科生参与了这项研究，两名调查人员都有从代表性不足的池中吸引学生的记录。关于涡度对自由表面水波的影响，研究人员研究了三个不同的主题：(1)水下涡流如何影响表面波动力学，(2)在完全非线性区域中，随深度变化的水流如何在密度分层层之间交换能量，以及(3)风浪产生模型的发展。这些主题是通过使用统一变换法的修改版本来探讨的，统一变换法是由于Ablowitz、Fokas和Musslimani对欧拉运动方程的重新表述。这里开发的方法能够解决流体动力学和海洋学界感兴趣的一系列与涡度和深度变化流有关的未探索问题。例如，更好地了解界面波在变深度切变上的稳定性，可以更好地从数学上深入了解线性区域以外的风、流和波浪之间的能量交换。本科生参与了这项研究，两名调查人员都有从代表性不足的群体中聘请学生的记录。

1715082, Oliveras1715089, Curtis The investigators study the role of vorticity in three problems related to free-surface water waves in the ocean. Vorticity is a measure of the local rotation of a fluid. The investigators examine how eddies in fluids drive surface wave dynamics and how underwater currents that vary with depth affect nonlinear waves. They also study wind-driven waves and the effects of wind gusts. The first problem is related to the behavior of shoaling tsunamis in the presence of submerged eddies. The second leads to better understanding of the heights and velocities of surface waves over underwater currents, and can contribute to understanding how pollutants and micro-organisms propagate along underwater currents. The third helps explain how wind causes the formation of waves on the ocean surface. Undergraduate students participate in the research, and both investigators have records of engaging students from under-represented pools. The investigators study three separate topics regarding the influence of vorticity on free-surface water-waves: (1) how underwater eddies influence surface-wave dynamics, (2) how depth-varying currents exchange energy between density-stratified layers in the fully nonlinear regime, and (3) the development of a wind-wave generation model. These topics are approached through use of modified versions of the Unified Transform Method, a reformulation of Euler's equations of motion due to Ablowitz, Fokas, and Musslimani. The methods developed here are able to address a range of unexplored problems related to vorticity and depth-varying currents that are of interest to the fluid dynamics and oceanographic communities. For example, better understanding the stability of interfacial waves over depth-varying shear provides greater mathematical insight into the energy exchange between wind, currents, and waves beyond the linear regime. Undergraduate students participate in the research, and both investigators have records of engaging students from under-represented groups.