Nonlinear Waves in Fluids

流体中的非线性波

• 批准号: 1908947
• 负责人: John Hunter
• 金额: $ 30万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1908947&HistoricalAwards=false
• 关键词: Nonlinear; Waves; Fluids

Fluids, such as air or water, support many different kinds of waves. For example, sound waves propagate through compressible fluids, water waves propagate on the surface of an ocean, and large-scale atmospheric waves affect the earth's weather and climate. At sufficiently low intensities, waves are modeled by linear systems of equations, which are relatively well-understood; but at higher intensities, the equations become nonlinear. Nonlinearity introduces fundamental mathematical difficulties and leads to new physical phenomena, such as the shock waves generated by supersonic aircraft, the solitons (particle-like waves) that propagate on shallow water, and nonlinear wave interactions that generate additional waves. The aim of this project is to study the dynamics of waves in fluids and uncover new nonlinear phenomena in the context of specific physical applications. This award will also provide support for the involvement of one graduate student in the project. This project addresses the mathematical modeling and analysis of nonlinear wave propagation in a variety of fluid systems. It focuses on the asymptotic analysis of nonlinear, nondispersive and dispersive waves, including waves that propagate on boundaries, free surfaces, or interfaces. A unifying framework is provided by Hamiltonian dynamics, which is an essential structure for the waves considered in the proposed research. Physical applications include waves on vorticity discontinuities in incompressible fluids, temperature fronts in surface quasi-geostrophic flows, current-vortex sheets in plasmas, shock wave reflection, and the resonant interaction of sound and entropy waves. A number of these problems lead to common mathematical themes, such as degenerate dispersive shocks, normal form transformations for quasilinear wave equations, and the formation and propagation of singularities.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.

流体，如空气或水，支持许多不同类型的波。例如，声波通过可压缩流体传播，水波在海洋表面传播，大规模大气波影响地球的天气和气候。在足够低的强度下，波由相对容易理解的线性方程组来模拟；但在较高的强度下，这些方程变成非线性的。非线性带来了基本的数学困难，并导致了新的物理现象，如超音速飞机产生的冲击波，在浅水中传播的孤子(类粒子波)，以及产生额外波的非线性波相互作用。这个项目的目的是研究流体中波的动力学，并在特定物理应用的背景下发现新的非线性现象。该奖项还将为一名研究生参与该项目提供支持。该项目致力于对各种流体系统中的非线性波传播进行数学建模和分析。它侧重于非线性、非色散波和色散波的渐近分析，包括在边界、自由面或界面上传播的波。哈密顿动力学提供了一个统一的框架，它是拟议研究中所考虑的波的基本结构。物理应用包括不可压缩流体中涡度间断上的波、地表准地转流中的温度锋、等离子体中的涡流片、激波反射以及声波和熵波的共振相互作用。许多这样的问题导致了共同的数学主题，如简并的色散激波，拟线性波动方程的范式变换，以及奇点的形成和传播。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Two-front solutions of the SQG equation and its generalizations

• DOI: 10.4310/cms.2020.v18.n6.a8
• 发表时间: 2019-04
• 期刊: arXiv: Analysis of PDEs
• 作者: J. K. Hunter;Jingyang Shu;Qingtian Zhang

Global solutions of a surface quasigeostrophic front equation

• DOI: 10.2140/paa.2021.3.403
• 发表时间: 2018-08
• 期刊: Pure and Applied Analysis
• 作者: J. K. Hunter;Jingyang Shu;Qingtian Zhang

On the approximation of vorticity fronts by the Burgers–Hilbert equation

用 Burgers-Hilbert 方程逼近涡度锋面

• DOI: 10.3233/asy-211724
• 发表时间: 2022
• 期刊: Asymptotic Analysis
• 影响因子: 1.4
• 作者: Hunter, John K.;Moreno-Vasquez, Ryan C.;Shu, Jingyang;Zhang, Qingtian
• 通讯作者: Zhang, Qingtian

Contour dynamics for surface quasi-geostrophic fronts

• DOI: 10.1088/1361-6544/ab8d16
• 发表时间: 2019-07
• 期刊: Nonlinearity
• 影响因子: 1.7
• 作者: J. K. Hunter;Jingyang Shu;Qingtian Zhang