Collaborative Research: Inverse Cascade Pathways in Turbulent Convection - The Impact of Spatial Anisotropy

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The impact of rotation and thermal driving on stellar and planetary bodies is readily visible in far-field optical observations. Such observations reveal the presence of differentially rotating fluid atmospheres embedded with features in the form of large-scale eddies and jets that greatly influence the climate of the celestial body. Understanding the formation, evolution and global momentum and energy balances of these features remains a challenging problem. Rotating Rayleigh-Benard convection, i.e., a rotating layer of fluid heated from below, represents a canonical paradigm for advancing our knowledge and is the subject of this project. The ultimate aim of the project is to determine unambiguously whether the large scale vortices (LSVs) observed in rapidly rotating Rayleigh-Benard convection are a consequence of the proximity of the flow to shallow, approximately two-dimensional turbulence or due to the ability of the LSVs to shape the correlations among the small scale three-dimensional fluctuations that appear to drive its formation. This determination appears to be fundamental to understanding the propensity for shallow layer geophysical and astrophysical flows to produce LSVs and jets and will open new directions for studying these natural flows. Broader impacts of the project include the involvement of graduate students and post-doctoral scholars in the research. Large scale structures, including vortices and jets, are ubiquitous in geophysical flows and play a fundamental role in energy transport in the interiors and the atmospheres of minor planets, gas giants and stars. This project is dedicated to providing a detailed understanding of the basic mechanisms behind the spontaneous formation of large-scale structures from small scale turbulent fluctuations. The ultimate aim of the project is to determine unambiguously whether the large scale vortices (LSVs) observed in rapidly rotating Rayleigh-Benard convection are a consequence of the proximity of the flow to 2D turbulence or due to the ability of the LSVs to shape the correlations among the small scale fluctuations that appear to drive its formation. This determination appears to be fundamental to understanding the propensity for shallow layer geophysical and astrophysical flows to produce LSVs and jets and will open new directions for studying these natural flows. A comprehensive examination of the split (forward and inverse) energy cascade that appears characteristic of these flows is thus undertaken. This is accomplished by utilizing (i) novel reduced asymptotic models that extrapolate to extreme parameter settings, (ii) new reformulations of the Navier-Stokes fluid equations that extend the computational capabilities of direct numerical simulations, and (iii) theoretical analysis that dissects the amplitude-phase relationships between the teleconnected large-scale structures and small-scale turbulence. The new asymptotic modeling and rescaling approaches to the fluid equations provide a unique capability of achieving physically realistic scale separation between large- and small-scale fluid motions. Importantly, the fundamental mechanisms of energy transport leading to the spontaneous formation of large-scale vortices and jets constitutes a complex problem that reaches across disciplines in the mathematical and physical sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.