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是清晰可见的。这样的观测揭示了差异旋转流体大气的存在，其嵌入特征以大规模漩涡和喷流的形式存在，极大地影响了天体的气候。在地球上，由于气候变化，高纬度急流对天气的影响和飓风的破坏性影响是显而易见的。在木星大气层中，朱诺号最近发现的极地涡旋说明了涡旋结构的寿命。理论、实验和数值模拟都有力地表明，在像地球大气层这样的薄层流体湍流中，以及在像木星这样的快速旋转的天体上，大规模喷流和漩涡的产生是很常见的。以这些范例为重点，本项目致力于阐明小规模湍流波动及其通过产生孤立的、弱相互作用的中尺度屏蔽涡而产生的破坏背后的基本机制，并将这种理解扩展到更现实的模型中，引入更高层次的物理，如水蒸气和内部加热通过潜热释放的影响。这一认识将为更详细的研究提供信息，例如那些基于现实的全球海洋和大气环流模型的研究，并为理解有利于大尺度结构和较小尺度屏蔽涡旋形成的条件提供希望。所采用的建模策略提供了一个基础，在此基础上可以构建更大的特定于学科的复杂性。该项目将支持和培训一名研究生和一名博士后研究人员，对地球物理相关系统中尺度间能量转移的物理理解、渐近和其他建模技术，以及适用于地球上和地球内部行星尺度现象的快速旋转流体层的直接数值模拟。该项目的目的是在二维（2D）中将不稳定驱动的湍流的不同状态分类为能量输入和耗散参数的函数，并探索当三维（3D）波动随着湍流层高度的增加而变得越来越重要时，这些状态是如何演变的。特别强调的是最近发现的屏蔽中尺度涡旋，它的产生可能会破坏随机搅拌的二维湍流所熟悉的逆能量级联。由此产生的手性中尺度涡旋气体的性质将被研究为层高度的函数，以及在二维高涡旋密度下向涡旋晶体的转变。在低雷诺数的细菌悬浮液中，将系统地改变雷诺数，以弥合这些现象和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的研究，将直接数值模拟扩展到更小的罗斯比数，同时进行理论分析，解剖大尺度结构和小尺度湍流之间的幅相关系。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 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.