Coordination Funds

湍流被科学界认为是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-斯托克斯方程支配的。在海洋和大气动力学中，由于密度和温度的变化，Navier-Stokes方程是由浮力驱动的，因为它是由Boussinesq近似模拟的。盐度和温度的动态变化是造成海洋动力学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的相变动力学及其影响和受温度场演变影响的方式的热力学建模方面的额外挑战。实际上，大气和海洋也是通过在分隔它们的界面上的应力交换和热传递来耦合的。因此，除了海冰动力学等其他影响外，全面的全球气候模型还必须考虑到这种耦合。这里建议开发严格的数学、分析和数值/计算工具，以研究各种海洋和大气模型及其耦合。此外，该小组的目标是提出一种系统的渐近方法，用于推导反映相关比例尺上潜在地球物理现象的简化模型，并严格证明这种简化模型是合理的。因此，这个数学研究单位的动机是重要的现实生活应用。在实施其项目时，它的目的是证明，地球物理流体动力学方面的严格数学研究和面向应用的理论发展可以相互促进：虽然地球物理流动的正式理论发展在得到证实的数学定理的支持下获得了可信度，但现实生活中的应用促进了偏微分方程组和相关领域的数学方面的重要进展。正是这种在抽象数学和具体应用之间的建设性桥梁，这个研究组将在地球物理流体动力学领域内培养和建立这种桥梁。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个别提案的范围，需要一个独特的团队和密切的交流与合作。目前的小组在地球物理建模、数学和数值分析以及科学计算方面拥有广泛的专业知识，似乎处于实现所述雄心勃勃的目标的绝佳地位。

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.