Interactions between Turbulence and Waves: Kinetic Approach

湍流与波浪之间的相互作用：动力学方法

• 批准号: 2009418
• 负责人: Yuri Lvov
• 金额: $ 34万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-01 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2009418&HistoricalAwards=false
• 关键词: Interactions; between; Turbulence; Waves; Kinetic

The dynamics of the ocean is a fascinating and complex subject. There are many types of waves and flows in the ocean: surface gravity waves are the familiar waves that can be observed breaking rhythmically near the shore; internal waves are hidden beneath the surface and take the form of modulations between layers of different water density; ocean eddies are circular currents of water, and finally, turbulence includes myriad types of unsteady movements of water. These different flows span a wide range of length and time scales, ranging from centimeters to thousands of kilometers, and from a few seconds to several years. Crucially, all these flows interact with each other, creating a system of immense complexity whose study remains a major challenge. This project attempts to build a rigorous mathematical theory to characterize the interactions between internal waves and large scale, two-dimensional eddies. The motivation is recent data from physical oceanography, indicating that processes operating on small scales can significantly affect oceanic energy flows on the large scale. The project will contribute to the study of this phenomenon by analyzing how energy is transferred in the reverse direction, from large scale horizontal motions in eddies to small scale isotropic turbulence where the energy of the eddy is dissipated. Additionally, the project will provide research opportunities for postdoctoral scholars.The interaction of waves and turbulence within a rotating stratified fluid is of crucial importance for the understanding of the ocean and atmosphere dynamics. The project will examine this interaction by employing the hydrostatic rotating Boussinesq equations. The project aims to utilize ideas from the wave turbulence theory on a novel system of partial differential equations that is equivalent to the hydrostatic rotating Boussinesq equations but has the advantage of explicitly separating wave motions from vorticity effects. This PDE system will be used to derive kinetic-like equations that describe the flow of spectral energy density between large scale vortices and internal waves. The mathematical predictions will be compared to oceanographic data of internal waves as well as to high resolution direct numerical simulations of rotating stratified turbulence.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.

海洋动力学是一个迷人而复杂的课题。海洋中有许多类型的波浪和流动：表面重力波是我们熟悉的波浪，可以观察到它在海岸附近有节奏地破碎;内波隐藏在表面之下，并以不同水密度层之间的调制形式出现;海洋漩涡是水流的循环，最后，湍流包括无数类型的水的不稳定运动。这些不同的流动跨越了广泛的长度和时间尺度，从厘米到数千公里，从几秒钟到几年。至关重要的是，所有这些流动相互作用，创造了一个极其复杂的系统，其研究仍然是一个重大挑战。本计画试图建立一个严谨的数学理论来描述内波与大尺度二维涡旋之间的相互作用。其动机是物理海洋学的最新数据，表明在小尺度上运行的过程可以显著影响大尺度上的海洋能量流。该项目将通过分析能量如何在相反方向上转移，从涡流中的大尺度水平运动到小尺度各向同性湍流，在那里涡流的能量被耗散，从而有助于研究这一现象。此外，该项目还将为博士后学者提供研究机会。旋转分层流体中波浪和湍流的相互作用对于理解海洋和大气动力学至关重要。该项目将采用流体静力旋转Boussinesq方程来研究这种相互作用。该项目的目的是利用波动湍流理论的思想，建立一个新的偏微分方程系统，该系统相当于流体静力旋转Boussinesq方程，但具有明确分离波浪运动和涡量效应的优点。这个偏微分方程系统将被用来推导出描述大尺度涡和内波之间的谱能量密度流动的类动力学方程。数学预测将与内波的海洋学数据以及旋转分层湍流的高分辨率直接数值模拟进行比较。该奖项反映了NSF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。

项目成果

Generalized Clebsch Variables for Compressible Ideal Fluids: Initial Conditions and Approximations of the Hamiltonian

可压缩理想流体的广义 Clebsch 变量：哈密顿量的初始条件和近似

• DOI: 10.3390/fluids7040122
• 发表时间: 2022
• 期刊: Fluids
• 影响因子: 1.9
• 作者: Rumpf, Benno;Lvov, Yuri V.
• 通讯作者: Lvov, Yuri V.

On the Origins of the Oceanic Ultraviolet Catastrophe

海洋紫外线灾难的起源

• DOI: 10.1175/jpo-d-21-0121.1
• 发表时间: 2022
• 期刊: Journal of Physical Oceanography
• 影响因子: 3.5
• 作者: Dematteis, Giovanni;Polzin, Kurt;Lvov, Yuri V.
• 通讯作者: Lvov, Yuri V.

Wave Turbulence and thermalization in one-dimensional chains

• DOI: 10.1016/j.physrep.2023.09.006
• 发表时间: 2023-05
• 期刊: Physics Reports
• 作者: M. Onorato;Y. Lvov;G. Dematteis;S. Chibbaro

Energy flux and high-order statistics of hydrodynamic turbulence

流体动力湍流的能量通量和高阶统计

• DOI: 10.1017/jfm.2023.662
• 发表时间: 2023
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Lvov, Yuri V.;L'vov, Victor S.
• 通讯作者: L'vov, Victor S.

The structure of energy fluxes in wave turbulence

波湍流中的能量通量结构

• DOI: 10.1017/jfm.2022.995
• 发表时间: 2023
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Dematteis, Giovanni;Lvov, Yuri V.
• 通讯作者: Lvov, Yuri V.