Conservation law-based models for overturning circulations

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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.