Events for 03/23/2021 from all calendars

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Sam Stechmann, University of Wisconsin - Madison

Title: Singular Limits of Atmospheric Dynamics with Clouds and Phase Changes

Abstract: Many systems involve the coupled nonlinear evolution of slow and fast components, where, for example, the fast waves might be acoustic (sound) waves with a small Mach number or inertio-gravity waves with small Froude and Rossby numbers. In the past, for some such systems, an interesting property has been shown: the slow component actually evolves independently of the fast waves, in a singular limit of fast wave oscillations. Here, a fast-wave averaging framework is developed for a moist Boussinesq system with additional complexity beyond past cases, now including phase changes between water vapor and liquid water. The main question is: Do phase changes induce coupling between the slow component and fast waves? Or does the slow component evolve independently, according to moist quasi-geostrophic equations? A formal asymptotic analysis is presented here. Compared to the dry dynamics, a substantial challenge is that the method needs to be adapted to a piecewise operator with variable coefficients, due to phase changes. Joint work with Leslie Smith and Yeyu Zhang.