Conservation law-based models for overturning circulations

该奖项将开发流体混合概念建模的数学和计算工具，并将其应用于尚未完全了解的与气候有关的过程的表示。新工具涉及使用非标准的守恒定律，以表示在破碎波时流体夹带的混合。这些将应用于两层情景，翻转环流的最简单模型，以及连续分层剪切流。前者为研究重力流、海洋混合层的夹带以及与海风、沿海上升流和热带对流的哈德利单元有关的环流提供了有用的环境。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，以及楼梯分层剖面形成背后的机制。在其地球物理应用方面，该奖项将加强我们对许多尺度上的混合和翻转环流的理解，包括风暴驱动的水从温跃层进入海洋混合层的卷带，以及对决定热带范围的主要因素的阐明。这是特别相关的，因为最近人们对确定在全球变暖的情况下，哈德利细胞是否会扩大，产生诸如高纬度荒漠化等气候变化非常感兴趣。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捕获了日波，这使得这种扩张变得不那么可信。在数学方面，偏微分方程中的新问题将得到解决，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。该项目将为本科生和研究生创造机会，在应用数学、计算科学、应用物理和地球科学的交叉领域进行跨学科研究。

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.