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

旋转和热驱动对恒星和行星体的影响在远场光学观测中很容易看到。这种观测揭示了存在着差异旋转的流体大气，其中包含着大规模涡流和喷流形式的特征，这些特征极大地影响着天体的气候。 了解这些特征的形成、演化和全球动量与能量平衡仍然是一个具有挑战性的问题。旋转瑞利-贝纳德对流，即，一个旋转的流体层从下面加热，代表了一个典型的范式，为推进我们的知识，是这个项目的主题。 该项目的最终目的是明确地确定在快速旋转的瑞利-贝纳德对流中观察到的大尺度涡（LSV）是否是流接近浅的、近似二维湍流的结果，或者是由于LSV塑造小尺度三维波动之间的相关性的能力，这些波动似乎是驱动其形成的。这一决定似乎是根本的理解倾向浅层地球物理和天体物理流产生LSV和射流，并将打开新的方向，研究这些自然流动。该项目的更广泛影响包括研究生和博士后学者参与研究。 大尺度结构，包括涡旋和喷流，在地球物理流动中无处不在，在小行星、气体巨星和恒星的内部和大气中的能量传输中发挥着重要作用。这个项目致力于提供一个详细的了解背后的小尺度湍流波动自发形成大尺度结构的基本机制。该项目的最终目的是明确地确定在快速旋转的Rayleigh-Benard对流中观察到的大尺度涡（LSV）是否是流接近2D湍流的结果，或者是由于LSV塑造小尺度波动之间的相关性的能力，这些波动似乎是驱动其形成的原因。这一决定似乎是根本的理解倾向浅层地球物理和天体物理流产生LSV和射流，并将打开新的方向，研究这些自然流动。因此，进行了一个全面的检查分裂（正向和反向）的能量级联，出现这些流量的特点。这是通过利用（i）新的减少渐近模型，外推到极端的参数设置，（ii）新的重新制定的Navier-Stokes流体方程，扩展直接数值模拟的计算能力，和（iii）理论分析，解剖的幅度-相位之间的关系的遥相关的大尺度结构和小尺度湍流。 新的渐近建模和重新缩放的方法，流体方程提供了一个独特的能力，实现物理上现实的规模之间的分离大规模和小规模的流体运动。重要的是，导致大规模涡流和射流自发形成的能量传输的基本机制构成了一个复杂的问题，涉及数学和物理科学的多个学科。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.