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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.

本研究项目致力于研究不同运动流体之间的界面或流体表面产生的表面动力学。表面动力学包括水波的破裂和白浪，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组成部分。这些都是强烈的非线性现象，需要求解完全非线性的流体动力学方程。异常波是另一种强烈非线性的大表面波，它在海洋中自发发生。流体的相对运动（水面上的风）引起了它们共同界面的不稳定性，如开尔文-亥姆霍兹不稳定性（KHI）。这种不稳定性最近成为实验科学家在不同组分超流氦之间的界面背景下关注的焦点，也将在这个项目中得到解决。本研究的重点是开发一种新型的保角映射和新的工具，以有效地描述自由表面和界面的强非线性表面动力学。是斯托克斯在19世纪第一个使用保角映射作为工具来研究具有自由表面的流体的稳定流动。在这种方法中，流体占据的区域被保角映射到更简单的区域，如较低的复半平面。然后将表面的动力学简化为保角映射的动力学。它允许通过复杂区域中复杂分支切割和极点的运动来恢复流体动力学，从而为表面动力学的分析和高精度模拟提供了巨大的优势。本项目旨在推进地表动力学和可积性领域的发展，并开发实用工具来确定影响全球气候动力学的地表重力波耗散的简化模式。本研究将包括通过分支切割运动分析异常波和破碎波动力学，以及探索不同实验情况下超流体界面动力学的可积性。为了解决高振幅水波的统计问题，将采用分析方法以及开发高性能计算工具。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。