Motion of Complex Singularities and Integrability in Surface Dynamics

表面动力学中复杂奇点的运动和可积性

基本信息

批准号：
1814619
负责人：
Pavel Lushnikov
金额：
$ 30.6万
依托单位：
University of New Mexico
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1814619&HistoricalAwards=false
关键词：
Motion Complex Singularities Integrability Surface

项目摘要

This research project is devoted to a study of surface dynamics that arise either at the interface between different moving fluids or at the fluid's surface. Surface dynamics include breaking of water waves and whitecapping, which are the primary mechanisms for the exchange of energy between the ocean and atmosphere making them a crucial ingredient of the global climate dynamics. These are strongly nonlinear phenomena which require to solve fully nonlinear hydrodynamics equations. Rogue waves are another example of strongly nonlinear large surface waves, which occur spontaneously in the ocean. Relative motion of fluids (wind over the water) induces instability of their common interface such as Kelvin-Helmholtz instability (KHI). This instability that recently became a focus of attention of experimental scientists in the context of the interface between different components superfluid Helium, will also be addressed in this project. This research will focus on development a new type of conformal map and new tools for the efficient description of the strongly nonlinear surface dynamics both for free surface and interfaces. It was Stokes who in the 19th century first used conformal mapping as a tool for studying of the steady flow of the fluid with a free surface. In this approach domains occupied by fluids are conformally mapped into simpler domains such as a lower complex half plane. The dynamics of the surface is then reduced to the dynamics of the conformal map. It gives an enormous advantage for both the analysis and high precision simulations of surface dynamics by allowing to recover the fluid dynamics through the motion of the complex branch cuts and poles in the complex domain. This project is aimed towards advancing the fields of surface dynamics and integrability as well as developing practical tools to identify the reduced models for dissipation of surface gravity waves, affecting global climate dynamics. The research will include an analysis of rogue and breaking waves dynamics through the motion of branch cuts as well as an exploration of integrability of interface dynamics of superfluids in different experimental situations. To address statistics of high amplitude water waves, analytical methods will be employed as well as development of high-performance computing tools.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该研究项目致力于研究表面动力学的研究，该研究要么在不同移动的流体之间或流体表面之间的界面上产生。表面动力学包括打破水波和白蛋白，这是海洋和大气之间能量交换的主要机制，使其成为全球气候动力学的重要成分。这些是强烈的非线性现象，需要解决完全非线性流体动力学方程。流氓波是强烈非线性大型表面波的另一个例子，它们在海洋中自发发生。流体的相对运动（水上的风）会引起其常见界面的不稳定性，例如开尔文 - 霍尔莫尔兹不稳定性（KHI）。在本项目中，这种不稳定在不同组件超级氦的界面之间成为实验科学家的关注焦点。这项研究将着重于开发一种新型的保形图和新工具，以有效描述自由表面和界面的强烈非线性表面动力学。正是斯托克斯在19世纪首次使用保形映射作为研究自由表面稳定流动的工具。在这种方法中，流体占据的域被共形映射到较简单的域，例如较低的复合半平面。然后将表面的动力学降低到保形图的动力学。它通过允许通过复杂域中的复杂分支切割和极点的运动来恢复表面动力学的分析和高精度模拟，从而为表面动力学提供了巨大优势。该项目旨在推进表面动态和集成性领域，并开发实用工具，以识别减少的模型以耗散表面重力波，从而影响全球气候动态。这项研究将包括通过分支切割的运动进行流氓和破坏波动力学的分析，以及在不同实验情况下对超流体界面动力学的整合性的探索。为了解决高振幅水波的统计数据，将采用分析方法以及开发高性能计算工具。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子和更广泛的影响来通过评估来支持的。