Collaborative Research: Formation, properties and evolution of protoplanetary vortices: Multiscale Investigations of baroclinic Instability

原行星盘(PPD)是环绕在年轻恒星周围的由气体和尘埃组成的旋转薄片，被认为是像我们自己的行星的诞生地。盘状气体中的流体不稳定和湍流被认为是浓缩固体颗粒和启动行星形成过程的主要机制，但目前尚不清楚是哪种不稳定或它们的组合负责。计算限制将PPD的数值模拟限制为不能分辨所有与动力相关的时间和空间尺度的分辨率。PI正在通过开发多尺度数学模型来克服这些限制，目的是识别和模拟PPD中的流体不稳定性和湍流。在这方面，拟议的工作可以被视为一个新的计算和建模框架，它将潜在地允许迄今为止最高分辨率的PPD动力学模拟。特别强调通过使用高分辨率数值模拟，了解指数指数确定的新的赤道涡旋不稳定(EVI)的非线性特性。通过使用严格的渐近方法，首次开发了能够同时模拟小尺度和全球尺度动力学以及两个尺度之间的耦合的层次化方程组。这项拟议的研究结果将使我们更全面地了解(1)各种不稳定机制之间的效率和相互作用，(2)全球和局部不稳定之间的相互作用，以及(3)更好地理解湍流涡旋通过小粒子的分离和聚集促进小行星的形成。原行星盘(PPD)是环绕在年轻恒星周围的旋转的气体和尘埃片，被认为是像我们这样的行星的诞生地。盘状气体中的流体运动被认为是浓缩固体物质和启动行星形成过程的主要机制，但目前尚不清楚这种运动是如何产生的。计算机模拟已被证明是促进我们对PPD动力学的理解的有价值的工具。然而，由于现代技术的限制，目前还不可能捕捉到PPD中动态相关性的所有时间和空间尺度。PI正在通过开发第一个多尺度数学模型来克服这些限制，目的是识别和模拟PPD中的流体运动。在这方面，拟议的工作可以被视为一个新的计算和建模框架，将允许迄今为止最高分辨率的PPD动力学模拟。

Protoplanetary disks (PPDs) are geometrically thin, rotating sheets of gas and dust that surround young stars, and are thought to be the birthplace of planets such as our own. Fluid instabilities and turbulence within the disk gas are thought to be the primary mechanisms for concentrating solid particles and initiating the planet building process, yet it is not known currently which instability or combination thereof is responsible. Computational constraints limit numerical simulations of PPDs to resolutions that are incapable of resolving all temporal and spatial scales of dynamical relevance. The PIs are overcoming these limitations by developing a multi-scale mathematical model for the purpose of identifying and simulating fluid instabilities and turbulence in PPDs. In this respect, the proposed work can be viewed as a new computational and modeling framework that will potentially allow for the highest resolution simulations of PPD dynamics to date. Particular emphasis is being placed on understanding the nonlinear properties, through the use of high resolution numerical simulations, of the new Equatorial Vortex Instability (EVI) that has been identified by the PIs. By employing rigorous asymptotic methods, a hierarchical set of equations that is capable of simultaneously modeling small-scale and global-scale dynamics and the coupling between the two scales is under development for the first time. The results of the proposed investigation will provide a more comprehensive understanding of (1) the effi_ciency and interplay between various instability mechanisms, (2) the interaction between global and local instabilities, and (3) a better understanding of the role of turbulent vortices in enhancing the formation of planetesimals through the segregation and agglomeration of small particles.Protoplanetary disks (PPDs) are rotating sheets of gas and dust that surround young stars, and are thought to be the birthplace of planets such as our own. Fluid motions within the disk gas are thought to be the primary mechanism for concentrating solid material and initiating the planet building process, yet it is not known currently how such motions originate. Computer simulations have proven to be valuable tools for advancing our understanding of PPD dynamics. However, it is not currently possible to capture all the temporal and spatial scales of dynamical relevance in PPDs given modern-day technological constraints. The PIs are overcoming these limitations by developing the first multi-scale mathematical model for the purpose of identifying and simulating fluid motion in PPDs. In this respect, the proposed work can be viewed as a new computational and modeling framework that will allow for the highest resolution simulations of PPD dynamics to date.