Conservation law-based models for overturning circulations

该奖项将为流体混合的概念建模开发数学和计算工具，并将它们应用于尚未完全理解的与气候有关的过程的表示。这些新颖的工具涉及到非标准守恒定律的使用，以便表示通过破碎波上的流体夹带进行混合。这些将应用于两层情景，最简单的颠覆环流模式，以及连续分层切变流。前者提供了有用的环境来研究重力流、海洋混合层的夹带和环流，如与海风、海岸上升流和热带对流的哈德利环流有关的环流。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层化，以及产生阶梯层结廓线背后的机制的问题。在地球物理应用方面，该奖项将加强我们对许多尺度上的混合和颠覆环流的理解，包括由风暴驱动的水从温跃层携带到海洋混合层的过程，以及决定热带范围的主要因素的阐明。这一点特别重要，因为最近有很大兴趣确定在全球变暖的情况下，哈德利环流是否会扩大，从而导致气候变化，如更高纬度的荒漠化。如果这里提出的一个模型是正确的，细胞的范围是由于科里奥利效应对昼夜波的捕获，这使得这种扩张变得不那么可信。在数学方面，将解决偏微分方程组中的新问题，包括连续分层介质中的非标准守恒定律和激波系统以及垂直不连续性。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点接受跨学科研究培训。

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.