CAM Seminar—Mathematics of Rainfall and Cloud Dynamics: Asymptotics and New PDEs

Sam Stechmann
UW-Madison

2018-05-08 ~ 2018-05-08

13:30-14:30

Room 1303, Sciences Building No. 1

Abstract

The partial differential equations (PDEs) of weather forecasting are very complicated.  In light of these complications, how can we gain a better mathematical understanding of rainfall and clouds?  In this talk, first it will be shown that the basic features of rainfall and cloud dynamics can be described by a set of PDEs that are much simpler than typical weather forecasting PDEs.  Next, these simpler PDEs allow the possibility for mathematical analysis of atmospheric fluid dynamics with rainfall and clouds.  Some first steps in this direction will be described, including asymptotic limits that lead to precipitating versions of the quasi-geostrophic equations.  New PDEs arise with interesting nonlinearities, which physically represent phase changes of water between vapor and liquid, and which account for the dynamics of clouds.