Published: Nov. 7, 2013

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

Michael Calkins

Applied MathematicsUniversity of Colorado Boulder

Date and time: 

Thursday, November 7, 2013 - 12:15pm


ECCR 257


Fluid turbulence is ubiquitous in the universe.  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.  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.  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.  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.  Often times, mathematically rigorous reduced equations can be derived by employing multiple scale asymptotics.  Aided with computationally fast numerical algorithms, these new models 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.  The development of accurate forward models 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.