Special: Michael Calkins
Reduced Models and Fast Algorithms: A Synergistic Approach for Modeling Geophysical and Astrophysical Fluid Turbulence
This talk will be followed by an informal lunch with APPM faculty and graduate students
Applied Mathematics,Ìý
Date and time:Ìý
Thursday, November 7, 2013 - 12:15pm
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ECCR 257
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Fluid turbulence is ubiquitous in the universe.Ìý It is the primary driving mechanism for atmospheric and oceanic dynamics, magnetic field generation in planets and stars, and is thought to be a necessary ingredient for the formation of planets.Ìý A defining characteristic of fluid turbulence is a broad-band kinetic energy spectrum; a range of scales are
present within the flow that range from domain-size down to the scale where fluid motions are converted irreversibly to heat by the action of viscosity.Ìý This property represents the single biggest road-block for employing direct numerical simulations (DNS) of the full governing equations to study geophysical and astrophysical turbulence at realistic parameters (e.g. the Reynolds number); current computational constraints limit DNS to parameter values that are distant from those that characterize natural systems.Ìý Reduction of the governing equations is therefore necessary, both as a means to reduce the computational cost of numerical simulations, but also as a means of gaining an improved understanding of the physics through a simplified equation set.Ìý Often times, mathematically rigorous reduced equations can be derived by employing multiple scale asymptotics.Ìý Aided with computationally fast numerical algorithms, these new 91ÃÛÌÒ¸ó can interrogate physical processes at realistic flow regimes and fluid properties that remain out of reach to DNS and laboratory experiments. In this presentation, I will discuss some of the problems on which we are employing these strategies, and in ways in which they are advancing the science.Ìý The development of accurate forward 91ÃÛÌÒ¸ó for geophysical and astrophysical fluid systems is becoming increasingly important in the face of new observational constraints provided by current and future space exploration missions.