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。这样的观测揭示了不同旋转的流体大气的存在，其中嵌入了大规模漩涡和喷流的特征，这些特征极大地影响了天体的气候。了解这些特征的形成、演化、全球动量和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，即从下方加热的旋转流体层，代表了提高我们知识的典型范例，也是本项目的主题。该项目的最终目标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旋（LSVs）是由于流动接近浅的、大约二维的湍流，还是由于LSVs能够形成驱动其形成的小尺度三维波动之间的相关性。这一结论似乎是理解浅层地球物理和天体物理流产生LSVs和射流的倾向的基础，并将为研究这些自然流开辟新的方向。该项目的更广泛影响包括研究生和博士后学者参与研究。包括涡旋和喷流在内的大规模结构在地球物理流中无处不在，在小行星、气态巨星和恒星的内部和大气中的能量传输中起着重要作用。该项目致力于为小尺度湍流波动自发形成大尺度结构背后的基本机制提供详细的了解。该项目的最终目标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旋（LSVs）是由于气流接近二维湍流，还是由于LSVs能够形成驱动其形成的小尺度波动之间的相关性。这一结论似乎是理解浅层地球物理和天体物理流产生LSVs和射流的倾向的基础，并将为研究这些自然流开辟新的方向。因此，对这些流动特征的分裂（正向和逆向）能量级联进行了全面的检查。这是通过利用(i)新的简化渐近模型来推断极端参数设置，（ii）新的Navier-Stokes流体方程的重新表述，扩展了直接数值模拟的计算能力，以及（iii）解析远连大尺度结构和小尺度湍流之间的幅相关系的理论分析来实现的。流体方程的新渐近建模和重新缩放方法提供了一种独特的能力，可以在大尺度和小尺度流体运动之间实现物理上真实的尺度分离。重要的是，导致大规模旋涡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各个学科。该奖项反映了美国国家科学基金会的法定使命，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.