Collaborative Research: A Lagrangian Description of Breaking Ocean Surface Waves from Laboratory Measurements and Stochastic Parameterizations.

波浪破碎效应在大气和海洋科学的许多领域都很重要，包括海气相互作用和动量、能量和生物地球化学通量、飓风动力学和热力学、污染物的传输和扩散、气溶胶产生和海洋声学等等。这项合作研究的目标是建立一个随机拉格朗日参数的表面波破碎，随后可以应用于波浪和海洋模拟。受雇于该项目的学生和博士后研究人员将获得科学、技术、工程和数学(STEM)学科的经验。这里发展的数据和破裂参数化将直接应用于大气和海洋模拟。海洋模式的保真度和分辨率的提高，特别是那些专注于次中尺度的海洋模式，需要改进对面波过程的表示。除了在波流相互作用动力学中的重要性外，它还在质量传输中起着重要作用，而不是经典的斯托克斯漂移理论；在朗缪尔湍流的动力学和运动学中；更广泛地说，在示踪剂和污染物的传输和扩散中。这项研究涉及测量破碎波中流体颗粒的拉格朗日位移和速度的实验室实验。然后，这些数据将被用来开发和参数化朗之万方程类中的随机常微分方程式，以描述流体元件的拉格朗日运动。与获得(欧拉)随机偏微分方程的n点结构函数相比，实验获得的粒子路径的n点结构函数将约束参数化，该n点结构函数相对容易获得并且与随机常(拉格朗日)微分方程相关联。给出了拉格朗日模型，利用到欧拉标架的投影，得到了波流相互作用和其他混合层过程的破裂的动力学表示。

Wave breaking effects are important in many areas of atmospheric and ocean sciences, including air-sea interaction and momentum, energy and biogeochemical fluxes; hurricane dynamics and thermodynamics; pollutant transport and dispersion; aerosol production and ocean acoustics, to name a few. The goal of this collaborative research is to build a stochastic Lagrangian parameterization of surface wave breaking that can subsequently be applied to wave and ocean modeling. The students and postdoctoral researchers employed in this project will gain experience in the disciplines of science, technology, engineering and mathematics (STEM). The data and breaking parameterization developed here will subsequently find direct application in atmosphere and ocean modeling.Increases in the fidelity and resolution of ocean models, specifically those focused on the sub-mesoscales, require improved representation of surface wave processes. In addition to the importance of wave breaking in the dynamics of wave-current interaction, it also plays an important role in mass transport beyond that represented in classical theories of Stokes drift; in the dynamics and kinematics of Langmuir turbulence; and, more generally, in the transport and dispersion of tracers and pollutants. This research involves laboratory experiments to measure the Lagrangian displacement and velocity of fluid particles in breaking waves. The data will then be used to develop and parameterize a stochastic ordinary differential equation, within the class of Langevin equations, to describe the Lagrangian motion of the fluid elements. The parameterization will be constrained by the n-point structure functions for the experimentally obtained particle paths, which are comparatively easier to obtain and to relate to a stochastic ordinary (Lagrangian) differential equation, when compared to obtaining the n-point structure function of an (Eulerian) stochastic partial differential equation. Given the Lagrangian model, a projection to the Eulerian frame will be used to obtain the dynamical representation of breaking for wave-current interaction and other mixed-layer processes.