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 研究人员对数学流体动力学中的强随机效应进行了理论和数值研究，特别是在波均相互作用理论领域。这里“强”是指与标准确定性设置相比，显着改变流体系统的整体动力学的效果。 一般来说，波均相互作用理论描述了小尺度波与波传播的大尺度平均流之间的非线性相互作用。 存在大量基于确定性波的经典波均值相互作用，但在该问题的随机版本上却做得很少。 目前的工作结合了许多旨在朝这个方向扩展经典理论的项目。例子包括使用随机理论来研究波浪动力学和非线性波破碎、二维波浪涡旋湍流，以及推导受高频振荡强迫作用的分层流的有效平均流动方程。 波浪与平均洋流之间的相互作用包括驱动长岸洋流和涡流，例如海滩上的波浪破碎产生的离岸流（对于土木工程和海军作业很重要），平流层中的破碎波浪产生晴空湍流（对于航空和航空业很重要）环境），以及通过海拔 60 公里左右的中层破碎波驱动全球空气循环（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，必须根据理论和观测手动计算它们的影响。 这被称为不可解析过程的“参数化”问题，即使在最大的超级计算机上，它也将在未来几十年内仍然是一个瓶颈问题。 现在，在该领域的经典“决定论”理论中，普遍的条件被假设为简单且众所周知的。 然而，实际上，普遍的情况往往很复杂且鲜为人知。 随机理论通过考虑情况的不确定或随机成分来解决这个问题。该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。 项目有两个主要目标：第一，寻找确定性理论遗漏的新效应；其次，为在气候预测、航空和近岸土木工程中使用的数值模型中更真实地表示波浪与平均相互作用奠定了基础。