Validation of 3D semi-geostrophic equation as the vanishing Froude/Rossby number limit of the 3D Euler equation, in the class of smooth solutions

半地转方程是众所周知的大尺度地球物理流体动力学偏微分方程模型。通过研究其有效性，特别是严格量化其作为欧拉方程近似值的准确性，我们对SG捕获的地球天气的“主要特征”（如天气锋面和潮湿对流）有了重要的了解。这一理论研究也为新气象代码的数值模拟和试验提供了指导。英国气象局（Met Office）和雷丁大学（University of Reading）的研究人员都参与了这个项目，这有助于它产生更广泛的影响

Semi-geostrophic (SG) equation is a well-known partial differential equation model of large scale geophysical fluid dynamics. By studying its validation and especially rigorously quantifying its accuracy as an approximation of the Euler equation, we gain important insight into the *main features* of the Earth weather that are captured by SG, such as weather fronts and moist convection. This theoretical study also provides guidance for numerical simulation and testing of new weather code. Researchers from the Met Office and University of Reading are connected to this project, which facilitates its wider impact