Berkeley Fluids Seminar

Wednesday, October 19, 2016

3110 Etcheverry Hall, 12:00-13:00

Dr. Jeffrey Parker (Livermore)

Study of zonal flow through statistical dynamics

Abstract: Zonal flows appear in a diverse array of physical systems, including magnetically confined plasmas and planetary atmospheres. Recent numerical simulations also point to the possibility of zonal flows occurring in astrophysical disks. These zonal flows, which arise from turbulence, are a spectacular example of self-organization and order out of chaos. A major tool in the study of fluidlike and turbulent systems is direct numerical simulation (DNS), in which one typically studies the statistical properties of the resulting solution. The emphasis of this talk is an alternative viewpoint, where one considers dynamics of statistical quantities themselves, such as correlation functions. Although a range of statistical dynamics approaches with various simplifications are possible, a relatively simple method known as the second-order cumulant expansion (CE2) has recently garnered significant attention from multiple groups. One of the major reasons CE2 has been useful because it is simple enough to perform some analytic calculations and gain qualitative insight into the dynamics of zonal flows, leading to an understanding of zonostrophic instability. This instability is a generalized version of the modulational or secondary instability of a primary Rossby or drift wave. Moreover, near marginal stability, symmetry constrains the dynamics. Various approximations to CE2 in terms of geometrical optics or wave kinetic equations will be discussed. Another reason CE2 is interesting is because its numerical solutions in many situations often exhibit zonal flow that is reasonably close to what is observed in full DNS. These statistical methods, not intended to replace DNS, enhance our qualitative understanding and may provide the foundation for future subgrid models.

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Acknowledgments

Prof. Graham Fleming (Vice Chancellor for Research, UC Berkeley)

Prof. Eliot Quataert on behalf of The Theoretical Astrophysics Center and the Astronomy Department (UC Berkeley)

Prof. Philip S. Marcus on behalf of the Mechanical Engineering Department (UC Berkeley)

Prof. Michael Manga (Earth and Planetary Science, UC Berkeley)

Prof. Evan Variano (Civil and Environmental Engineering, UC Berkeley)