Physics Colloquium - Spring 2020

Speaker: Mike Sitko, University of Cincinnati

Abstract: The discovery over the past two decades of thousands of planetary systems that do not look like our own begs the question "Why?". From planet-disk migration to the "Nice Model" and "Grand Tack", it appears that the planetary system architectures found today do not necessarily show how these systems looked in their youth. Today, high angular resolution astronomical techniques are the key to investigating the signposts of exoprotoplanet formation, and in some cases, the exoprotoplanets themselves. These include single-telescope adaptive optics coronagraphic imaging, multi-telescope interferometric observations, and non-redundant sparse aperture masking interferometry. Coming in as an "outsider" to the field high spatial resolution revolution, I will describe a few of the programs that I have wandered into over the past few years.

Speaker:  Timothy Dowling, University of Louisville, Department of Physics & Astronomy

Jupiter has dozens of alternating jet streams that have now been extensively observed by the two Voyager flybys, the Galileo entry probe, the Cassini flyby, and the Juno proximity orbiter. This has revealed that the analogue of the Mach number for vorticity waves, ‘Ma’, is central to understanding the long-mysterious properties of shear instability. The results have far-reaching consequences for large, fluid systems involving shear, including the meandering of jet streams, the formation of planets in protoplanetary disks, and the enhancement of magnetic confinement of hot plasmas in fusion reactors. We will examine how the concept of ‘Ma’ clarifies the physics and makes specific predictions, including about Jupiter’s deep jets and Saturn’s length of day. The lessons from Jupiter have taken most of the guesswork out of the prediction and control of shear instability.

Speaker:  Gung-Min Gie, University of Louisville, Department of Mathematics

Abstract: Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view, singular perturbations generate thin layers near the boundary of a domain, called boundary layers, where many important physical phenomena occur. In fluid mechanics, the Navier-Stokes equations, which describe the behavior of viscous flows, appear as a singular perturbation of the Euler equations for inviscid flows, where the small perturbation parameter is the viscosity. In general, verifying the convergence of the Navier-Stokes solutions to the Euler solution (known as the vanishing viscosity limit problem) remains an outstanding open question in mathematical physics. Up to now, it is not known if this vanishing viscosity limit holds true or not, even in 2D for which the existence, uniqueness, and regularity of solutions for all time are known for both the Navier-Stokes and Euler. In this talk, we discuss a recent result on the boundary layer analysis for the Navier-Stokes equations under a certain symmetry where the complete structure of boundary layers, vanishing viscosity limit, and vorticity accumulation on the boundary are investigated by using the method of correctors. We also discuss how to implement effective numerical schemes for slightly viscous fluid equations where the boundary layer correctors play essential roles.