Analytic Methods in Hydrodynamic and Wave Turbulence

流体动力学和波浪湍流的分析方法

基本信息

批准号：
2242677
负责人：
Tristan Buckmaster
金额：
$ 20.07万
依托单位：
University of Maryland, College Park
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-07-01 至 2022-12-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2242677&HistoricalAwards=false
关键词：
Analytic Methods Hydrodynamic Wave Turbulence

项目摘要

Turbulence is ubiquitous in nature, playing a fundamental role in a multitude of physical theories, from atmospheric and oceanic dynamics to the birth of stars. This project is dedicated to an investigation into hydrodynamic and wave turbulence, both of which, at the core predict cascades of energy. The principal aim of this supported research is to better understand these energy cascades. The project is divided into two projects: a study of non-uniqueness of weak solutions to equations arising in hydrodynamics, and a rigorous approach to the derivation of the kinetic wave equation in wave turbulence theory. The focus of the first project will be to utilize the theoretical tool of convex integration to build theoretical energy cascades in order to resolve long standing open problems related to weak solutions to the Navier-Stokes equations. The overarching goal of the second project will be to rigorously determine the validity of the kinetic wave equation which is theorized to predict turbulence phenomena in a host settings such as water waves, plasma physics and climate science. The project will draw on a diverse set of mathematical tools from analysis, number theory and statistical physics.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.

湍流本质上是普遍存在的，从大气和海洋动力学到恒星的诞生，在多种物理理论中发挥了基本作用。该项目致力于研究流体动力和波浪湍流，这两者都在核心预测能量级联。这项支持的研究的主要目的是更好地了解这些能源级联。该项目分为两个项目：研究在流体动力学中产生的方程式弱解决方案的非唯一性，以及在波湍流理论中动态波方程的衍生方法的严格方法。第一个项目的重点将是利用凸集成的理论工具来构建理论能量级联，以解决与Navier-Stokes方程较弱的解决方案有关的长期开放问题。第二个项目的总体目标是严格确定动力波方程的有效性，该方程的有效性是从理论上预测宿主环境中的湍流现象（例如水波，等离子体物理学和气候科学）。该项目将从分析，数字理论和统计物理学中借鉴各种数学工具。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优点和更广泛的影响评估标准通过评估来支持的。