AMC-SS: Stochastic Waves and Wave-Mean Interactions

AMC-SS：随机波和波均值相互作用

• 批准号: 0604519
• 负责人: Oliver Buhler
• 金额: $ 33.61万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-15 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604519&HistoricalAwards=false
• 关键词: AMC; SS; Stochastic; Waves; Wave

BuhlerDMS-0604519 The investigator undertakes a theoretical and numericalstudy of strong stochastic effects in mathematical fluiddynamics, specifically in the area of wave-mean interactiontheory. Here "strong" refers to effects that substantially changethe overall dynamics of the fluid system when compared to thestandard deterministic setting. In general, wave-meaninteraction theory describes the nonlinear interactions betweensmall-scale waves and the large-scale mean flows on which thewaves are propagating. There exists a substantial body ofclassical wave-mean interaction that is based on deterministicwaves, but very little has been done on the stochastic version ofthe problem. The present work combines a number of projectsaimed at extending the classical theory in this direction. Examples include the use of stochastic theory for wave dynamicsand nonlinear wave breaking, for two-dimensional wave-vortexturbulence, and for the derivation of effective mean-flowequations for stratified flows subject to high-frequencyoscillatory forcing. Interactions between waves and mean currents include thedriving of long-shore currents and vortical motions such as ripcurrents by breaking waves on a beach (important for civilengineering and naval operations), the creation of clear-airturbulence by breaking waves in the stratosphere (important foraviation and the environment), and the driving of the global aircirculation by breaking waves in the mesosphere, above 60kmaltitude or so (important for climate evolution). Theseprocesses are far too small in spatial scale to be resolvable innumerical models for atmosphere-ocean dynamics, which means thatin these models their impact must be put in by hand based ontheory and observations. This is called the "parametrization"problem for unresolvable processes, and even on the biggestsupercomputers it will remain a bottleneck problem for decades tocome. Now, in the classical "deterministic" theory in this area,the prevailing conditions are assumed to be simple and perfectlyknown. However, in reality, the prevailing conditions are oftencomplex and poorly known. Stochastic theory addresses this byallowing for uncertain, or random, components of the situation. This project brings modern stochastic theory to bear on the kindof wave-mean interaction problems that are relevant toatmosphere-ocean science. There are two principal project aims:first, finding new effects that are missed by the deterministictheory; and second, laying the foundation for a more realisticrepresentation of wave-mean interactions in numerical models foruse in climate prediction, aviation, and near-shore civilengineering.

BuhlerDMS-0604519 调查员承担了数学流体动力学中强随机效应的理论和数值研究，特别是在波平均相互作用理论领域。这里的“强”是指与标准确定性设置相比，显著改变流体系统整体动力学的影响。 一般来说，波平均相互作用理论描述的是小尺度波与波在其上传播的大尺度平均流之间的非线性相互作用。 存在大量的经典波-平均相互作用是基于确定性波，但很少有人做了随机版本的问题。 目前的工作结合了一些projectsaimed在这个方向上扩展的经典理论。例子包括使用随机理论的波动动力学和非线性波破碎，二维波涡湍流，并推导出有效的平均流量方程的分层流受到高频振荡强迫。 波浪和平均流之间的相互作用包括驱动沿岸流和旋涡运动，如在海滩上破碎的波浪引起的激流（对土木工程和海军作战很重要），在同温层中打破波浪而产生的晴空湍流（对航空和环境很重要），以及通过中间层的碎波驱动全球空气循环，海拔60公里以上（对气候演变很重要）。 这些过程在空间尺度上太小，无法在大气-海洋动力学数值模型中解析，这意味着在这些模型中，它们的影响必须根据理论和观测手工计算。 这就是所谓的“参数化“问题，对于无法解决的过程，即使在最大的超级计算机上，它也将是未来几十年的瓶颈问题。 现在，在这一领域的经典“确定性”理论中，普遍的条件被假定为简单和完全已知的。 然而，在现实中，主要的条件往往是复杂的，知之甚少。 随机理论通过考虑不确定或随机的情况来解决这个问题。这个项目将现代随机理论应用于与大气-海洋科学相关的波-平均相互作用问题。 有两个主要的项目目标：第一，发现新的影响，被遗漏的决定论;第二，奠定基础，一个更现实的表示波平均相互作用的数值模式，用于气候预测，航空，和近岸土木工程。