Multiple Scales Analyses for Atmospheric Flows
Asymptotic techniques generalize the classical approach of scale analysis in theoretical meteorology. Through, e.g., matched asymptotic and multiple scales expansions they allow us to systematically study interactions across separated length and times scales. This will be demonstrated drawing from recent work on hurricane-like concentrated vortices and on cloud--internal wave interactions.
Whereas the classical theory of anelastic mostions by Ogura and Phillips (1962) is naturally captured in an asymptotics-based framework, its subsequent extensions, e.g., by Dutton & Fichtl (1969), Lipps & Hemler (1982), Bannon (1996), as well as Durran's pseudo-incompressible model (1989,2008) pose a particular challenge. I will show that their systematic theoretical justification will require techniques that go beyond scale analysis and single or multiple scales expansions.
Rupert Klein, Potsdam Institute for Climate Impact Research and Free University of Berlin, Germany