Keith Julien, Department of Applied Mathematics, University of Colorado Boulder
Asymptotic strategies for modeling geophysical and astrophysical flows
Geophysical and astrophysical fluid flows occur on scales that are often strongly influenced by forces such as buoyancy, rotation, magnetic and shear. In many cases it is typical that one or more of these forces dominate and constrain the observed dynamics. Such situations are characterized by the extreme values of non-dimensional parameters measuring the relative magnitude of applied forces. Current models and simulations are conducted at parameters orders of magnitudes away from observed values and often in regimes where extrapolations are questionable. Improvements in computing power through Moore’s laws will produce minimal advances with present-day models. It is therefore clear that advances must occur through new model development and associated simulations utilizing extreme parameter values in an asymptotic manner. This will require a body of knowledge gained from large-scale direct numerical simulations, laboratory experiments and observations that explore the tendency towards extreme parameter values in controlled settings.
In this talk, an overview is given of recent advances utilizing asymptotic method to develop reduced partial differential equations that capture the relevant dynamics. Rotationally constrained flows will be used as case study illustrating how advancements are occurring through a confluence of asymptotic models, laboratory investigations and direct numerical simulations of the Navier-Stokes equations.
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Name: Ian Cunningham