Coordination Funds

湍流是科学界公认的最具挑战性的经典科学问题之一。人们普遍认为湍流是由纳维-斯托克斯方程控制的。在海洋和大气动力学中，Navier-Stokes方程是由密度和温度变化引起的浮力驱动的，因为它是由Boussinesq近似模拟的。在海洋动力学中，盐度和温度的动态变化是造成这种密度变化的主要原因。在大气中，水分的存在意味着对水和蒸汽之间相变动力学的热力学建模的额外挑战，以及它影响和受温度场演变影响的方式。实际上，大气和海洋也是通过分离它们的界面上的应力交换和热传递而耦合在一起的。因此，综合的全球气候模式除了考虑海冰动力学等其他影响外，还必须考虑这种耦合。这里建议发展严格的数学分析和数值/计算工具来研究各种海洋和大气模式及其耦合。此外，该小组旨在推进一种系统的渐近方法，用于推导在相关尺度上捕获潜在地球物理现象的简化模型，并严格证明这种简化模型的合理性。因此，这个数学研究单位是由重要的现实应用驱动的。在开展其项目的过程中，它旨在证明地球物理流体动力学中严谨的数学研究和面向应用的理论发展可以联合起来，实现互利：虽然地球物理流动的正式理论发展在经过验证的数学定理的支持下获得了可信度，但实际应用会引发偏微分方程和相关领域数学的重要进步。正是这种在抽象数学和具体应用之间建立的建设性桥梁，是本研究单位在地球物理流体动力学领域内培育和建立的。所使用的方法从尺度分析、演化方程、凸积分和偏微分方程分析到地球物理模型（如ICON模型）的数值处理。拟议项目的目标和广度超出了单个提案的范围，需要一个独特的团队和密切的交流与合作。目前的团队在地球物理建模，数学和数值分析以及科学计算方面拥有广泛的专业知识，似乎处于实现既定雄心勃勃的目标的绝佳位置。

Turbulence is identified by the scientific community to be one of the most challenging classical scientific problems. It is commonly believed that turbulent flows are governed by the Navier-Stokes equations. In oceanic and atmospheric dynamics the Navier-Stokes equations are driven by buoyancy forces due variations in density and temperature as it is modeled by the Boussinesq approximation. The dynamical changes in the salinity and temperature are the main causes for such variations of density in oceanic dynamics. In the atmosphere, the presence of moisture implies the additional challenge of modeling the thermodynamics of the phase change dynamics between water and vapour and the way it affects, and is affected by, the evolution of the temperature field. Realistically, the atmosphere and oceans are also coupled through the exchange of stress forces and heat transfer at the interfaces that separate them. Therefore, comprehensive global climate models must take this coupling into account in addition to other effects such as sea-ice dynamics. It is proposed here to develop rigorous mathematical analytical and numerical/computational tools to investigate the various oceanic and atmospheric models and their coupling. In addition, the group aims to advance a systematic asymptotic methodology for the derivation of reduced models that capture underlying geophysical phenomena at the relevant scales and to rigorously justify such reduced models. This mathematical Research Unit is thus motivated by important real-life applications. In pursuing its projects, it aims to demonstrate that rigorous mathematical research and application-oriented theoretical developments in geophysical fluid dynamics can join forces to their mutual benefit: While formal theoretical developments in geophysical flows gain credibility when underpinned by proven mathematical theorems, real-life applications trigger important advances in the mathematics of partial differential equations and associated fields. It is this kind of constructive bridge-building between abstract mathematics, and concrete applications, which this Research Unit is to foster and establish within the field of geophysical fluid dynamics. The methods used range from scale analysis, evolution equations, convex integration and PDE analysis to the numerical treatment of geophysical models such as the ICON model. The aims and breadth of the proposed projects are beyond the reach of individual proposals requiring a unique team and intense exchange and cooperation. The present team, with its wide range of expertise in geophysical modeling, mathematical and numerical analysis and scientific computing, seems in an excellent position to accomplish the stated ambitious goals.