Mathematical modeling for Fluid Flows originating in the Atmosphere

Abstract : Our Earth is surrounded by multiple layers of gases - collectively known as the Atmosphere. The Atmosphere is not only important because it gives us the necessary gases for survival, but it is also important as it helps in the circulation of heat and moisture - without which our Earth will be as barren as the other planets of our Solar system. We all know heat is distributed in a fluid mainly due to the convection currents. For the Atmosphere also, the convection currents play the vital role. But, the weather at any place depends on the geographical locations, topographic structures, rotation and revolution of the Earth. These factors forces the Atmosphere to behave differently at different places. We all know how ruthless and dangerous could be a cyclone or torrential rains! But, to forecast such events we need to understand the fluid motions in the Atmosphere that give rise to such events. Observational studies of the Atmosphere have been made from the ancient times but these observations are not sufficient to understand it or forecast its behaviors. This is where Mathematics is needed. To understand these phenomena we need to model them using the laws of Physics and to formulate and solve these models we need our Mathematical techniques - analytical or numerical. In this lecture I will give an introduction to the type of fluid flows occurring in the Atmosphere and how we can develop mathematical models for them. I will also present a brief example of a few mathematical models.