Collaborative Research: Self-organization and transitions in anisotropic turbulence

旋转和热驱动对恒星和行星体的影响在远场光学观测中清晰可见。这种观测揭示了存在着差异旋转的流体大气，其嵌入式特征表现为大规模涡流和喷流，对天体的气候产生了重大影响。在地球上，高纬度急流对天气的影响以及气候变化造成的飓风的破坏性影响是显而易见的。在木星大气层内，朱诺号使命最近发现的极涡说明了涡旋结构的寿命。理论、实验和数值模拟强烈表明，大规模喷流和漩涡的产生在地球大气层等薄层内的流体湍流和木星等快速旋转的天体上很常见。该项目专注于这些范例，致力于阐明小尺度湍流波动形成这种大尺度结构的基本机制，以及通过产生孤立的，弱相互作用的中尺度屏蔽涡来破坏这种结构，并将这种理解扩展到更现实的模型，这些模型引入更高层次的物理学，如水蒸气和通过潜热释放的内部加热的影响。这种理解将为更详细的研究提供信息，例如基于现实的全球海洋和大气环流模型的研究，并为理解有利于形成大规模结构和较小规模屏蔽涡旋的条件提供希望。所采取的建模策略提供了一个基础，在此基础上可以建立更大的学科特定的复杂性。该项目将支持和培训一名研究生和一名博士后研究员，以物理理解地球物理相关系统中尺度之间的能量转移，渐近和其他建模技术，以及快速旋转流体层的直接数值模拟，适用于地球上和地球内部的行星尺度现象。该项目的目的是对不同的不稳定状态进行分类-驱动湍流在两个维度（2D）作为能量输入和耗散参数的函数，并探讨这些国家如何演变时，三维（3D）波动变得越来越重要的湍流层的高度增加。特别强调的是最近发现的屏蔽中尺度涡的产生可能会破坏逆能量级联熟悉的二维湍流随机搅拌制度。所得手性中尺度涡旋气体的性质将作为层高度的函数进行研究，因为将在2D中发生在高涡旋密度的涡旋晶体的过渡。雷诺数将系统地变化，以弥合这些现象与低雷诺数下细菌悬浮液中的相关状态之间的差距。在快速旋转的三维湍流中类似状态的可能性将使用新的Navier-Stokes流体方程的重新表述进行详细研究，将直接数值模拟扩展到较小的Rossby数，并对大尺度结构和小尺度结构之间的幅相关系进行了理论分析，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 clearly visible in far-field optical observations. Such observations reveal the presence of differentially rotating fluid atmospheres with embedded features in the form of large-scale eddies and jets that greatly influence the climate on the celestial body. On Earth the impact of the high latitude jet stream on weather and the destructive impact of hurricanes due to climate change is evident. Within the Jovian atmosphere, the recent discovery by the Juno mission of polar vortices illuminates the longevity of vortical structures. Theory, experimentation, and numerical simulations strongly suggest that the generation of large-scale jets and vortices is common in fluid turbulence within thin layers like the Earth’s atmosphere and on rapidly rotating celestial bodies such as Jupiter. Focusing on these paradigms, this project is dedicated to elucidating the basic mechanism behind the formation of such large-scale structures from small-scale turbulent fluctuations and its disruption via the generation of isolated, weakly-interacting, mesoscale shielded vortices, and to extending this understanding to more realistic models that introduce higher level physics such as the effects of water vapor and internal heating via latent heat release. This understanding will inform more detailed studies such as those based on realistic Global Ocean and Atmospheric Circulation Models and offers hope for understanding the conditions favoring the formation of both large-scale structures and of the smaller-scale shielded vortices. The modeling strategy taken provides a foundation upon which greater discipline-specific complexity can be built. The project will support and train one graduate student and one postdoctoral researcher in the physical understanding of energy transfer between scales in systems of geophysical relevance, asymptotic and other modeling techniques, as well as direct numerical simulations of rapidly rotating fluid layers, appropriate for planetary-scale phenomena on and within the Earth.The aim of this project is to classify different regimes of instability-driven turbulence in two dimensions (2D) as a function of the energy input and dissipation parameters, and to explore how these states evolve when three-dimensional (3D) fluctuations become increasingly important as the height of the turbulent layer increases. Particular emphasis will be placed on the recently discovered regime of shielded mesoscale vortices whose generation may disrupt the inverse energy cascade familiar from 2D turbulence with random stirring. Properties of the resulting chiral mesoscale vortex gas will be studied as a function of the layer height, as will the transition to a vortex crystal that takes place at high vortex density in 2D. The Reynolds number will be varied systematically to bridge the gap between these phenomena and related states in bacterial suspensions at low Reynolds numbers. The possibility of an analogous state in rapidly rotating 3D turbulence will be investigated in detail using a new reformulation of the Navier-Stokes fluid equations, extending direct numerical simulations to smaller Rossby numbers, together with a theoretical analysis dissecting the amplitude-phase relationships between large-scale structures and small-scale turbulence.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.