This INSPIRE award is partially funded by the Climate and Large-scale Dynamics Program in the Division of Atmospheric and Geospace Science of the NSF Directorate for Geosciences (GEO), and the Plasma Physics Program in the Physics Division of the NSF Directorate for Mathematical and Physical Sciences (MPS).
The goal of the project is to develop a theory for the relationship between turbulence and large-scale coherent structures that can be applied very generally to a variety problems in disciplines including atmospheric circulation, plasma physics, planet formation, and the generation of planetary magnetic fields. The work is based on stochastic structural stability theory (SSST), a theoretical framework which the Principal Investigator has developed in the context of geophysical fluid dynamics. The SSST method framework is used to create equations for the mutual interaction of turbulence and coherent structures, and the equilibrium solutions of the equations identify the statistical mean states of the system. For example, when the theory is applied to the formation of jet streams due to interactions between the zonal-mean atmospheric flow and wave motions, it predicts an entire bifurcation structure from jet emergence as a linear instability to finite amplitude equilibration followed by a specific series of structural bifurcations as a function of parameters, such as turbulence intensity, as well as existence of limit cycles and chaotic mean state behavior. Applications of the theory considered here include the formation of zonal jets in planetary atmospheres, jet formation in toroidally confined plasmas, the self-sustaining magnetic fields of planets, boundary layer turbulence accompanied by streamwise rolls and streaks (of interest in meteorology and oceanography), and the maintenance of turbulent angular momentum transport in Keplerian discs required for planetary formation.
The project has broader scientific impacts in that it seeks to identify unifying principles for phenomena in several scientific disciplines that are not currently recognized as having the same underlying structures and dynamics. The unifying, cross-disciplinary nature of the work to be performed is the justification for funding the project through the INSPIRE mechanism.
