Conservation law-based models for overturning circulations

基于守恒定律的翻转环流模型

• 批准号: 1211298
• 负责人: Esteban Tabak
• 金额: $ 30.6万
• 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: 2012
• 资助国家: 美国
• 起止时间: 2012-08-15 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1211298&HistoricalAwards=false
• 关键词: Conservation; law; based; models; overturning

This award will develop mathematical and computational tools for the conceptual modeling of fluid mixing, and apply them to the representation of climate-related processes that are not yet fully understood. The novel tools involve the use of non-standard conservation laws, so as to represent mixing through fluid entrainment at breaking waves. These will be applied to two-layer scenarios, the simplest models for overturning circulations, and to continuously stratified shear flows. The former provides useful settings to study gravity currents, entrainment into the ocean's mixed layer and circulations such as those associated with the sea-breeze, coastal upwelling and the Hadley cells of tropical convection. The latter provides a sophisticated mathematical scenario to answer questions about the formation of mixed layers and their re-stratification, and the mechanisms behind the creation of staircase stratification profiles.In its geophysical applications, this award will enhance our understanding of mixing and overturning circulations at many scales, including the storm-driven entrainment of water from the thermocline into the ocean's mixed layer and the elucidation of the leading factors determining the extent of the tropics. This is particularly relevant, as there has been substantial recent interest in determining whether, under global warming scenarios, the Hadley cells would expand, yielding climatic changes such as higher-latitude desertification. If a model proposed here is correct, the extent of the cells is due to the trapping of diurnal waves by the Coriolis effect, which makes such an expansion much less plausible. On the mathematical side, new problems in partial differential equations will be addressed, including non-standard systems of conservation laws and shocks and vertical discontinuities in continuously stratified media. The project will create opportunities for undergraduate and graduate students to be trained in interdisciplinary research, at the intersection between applied mathematics, computational science, applied physics and the geosciences.

该奖项将为流体混合的概念建模开发数学和计算工具，并将其应用于尚未完全理解的气候相关过程的表示。这些新颖的工具涉及非标准守恒定律的使用，以便通过破碎波浪时的流体夹带来表示混合。这些将应用于两层场景、最简单的翻转环流模型以及连续分层剪切流。前者为研究重力流、海洋混合层夹带和环流（例如与海风、沿海上升流和热带对流哈德利环流相关的环流）提供了有用的设置。后者提供了一个复杂的数学场景来回答有关混合层的形成及其重新分层的问题，以及阶梯分层剖面创建背后的机制。在其地球物理应用中，该奖项将增强我们对许多尺度的混合和翻转环流的理解，包括风暴驱动的水从温跃层夹带到海洋混合层中，以及阐明决定混合层和翻转环流程度的主要因素。 热带地区。 这一点尤其重要，因为最近人们对确定在全球变暖的情况下哈德利环流是否会扩大、导致高纬度荒漠化等气候变化产生了浓厚的兴趣。如果这里提出的模型是正确的，那么细胞的范围是由于科里奥利效应对昼夜波的捕获造成的，这使得这种扩张不太可信。在数学方面，将解决偏微分方程中的新问题，包括守恒定律和冲击的非标准系统以及连续分层介质中的垂直不连续性。该项目将为本科生和研究生创造机会，接受应用数学、计算科学、应用物理学和地球科学交叉领域的跨学科研究培训。