Frontiers in Mathematics Lecture Series

Date: March 21, 2019

Time: 4:00PM - 5:00PM

Location: Blocker 117

Speaker: Rupert Klein, Freie Universität Berlin

Title: Multi-scale regimes of atmospheric motions

Abstract:

Flows of the Earth’s atmosphere cover a very wide range of scales, from micrometer-sized raindrops to planetary-scale climate phenomena. The range of relevant time scales is equally broad. A central task of theoretical meteorology is to identify specific weather- or climate-related flow phenomena that are associated with particular length and time scales, and to construct simplified models describing these phenomena in terms of some reduced set of effective degrees of freedom.

Textbooks on theoretical meteorology offer derivations of such reduced models from more comprehensive fluid dynamical governing equations through scale analysis, which involves often ingenious combinations of physical intuition and skillful mathematical derivations. Nevertheless, keeping track of how these models relate to each other and what were the underlying assumptions in their derivations is a formidable task. If one is interested, however, in how phenomena associated with different length and/or time scales interact, then knowing how to consistently couple or synchronize the individual reduced models becomes crucial.

In the first part of the lecture I will introduce a systematization of reduced model equations of theoretical meteorology that is based on the principles of dimensional and asymptotic analysis. This approach allows one to re-derive a large number of reduced models of theoretical meteorology in a unified fashion from the full compressible flow equations via classical single-scale asymptotics.More importantly, this unified approach lends itself naturally to multiple scales analyses, i.e., to studies of how scale-dependent phenomena described by different reduced model equations are coupled across the scales. The second part of this lecture will cover examples of such multiscale interaction theories selecting from an asymptotic model for tropical storm intensification, the derivation and justification of sound-proof atmospheric flow models involving a non-standard asymptotic three