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

原行星盘（PPD）是几何形状薄的、旋转的气体和尘埃片，围绕着年轻的恒星，被认为是像我们这样的行星的诞生地。圆盘气体内的流体不稳定性和湍流被认为是集中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性或其组合造成的。计算约束将 PPD 数值模拟的分辨率限制为无法解析动态相关性的所有时间和空间尺度。 PI 正在通过开发多尺度数学模型来克服这些限制，以识别和模拟 PPD 中的流体不稳定性和湍流。在这方面，所提出的工作可以被视为一种新的计算和建模框架，该框架将有可能实现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来了解 PI 确定的新赤道涡不稳定性 (EVI) 的非线性特性。通过采用严格的渐近方法，首次开发了一组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耦合的分层方程组。拟议的研究结果将提供对（1）各种不稳定机制之间的效率和相互作用的更全面的理解，（2）全局和局部不稳定性之间的相互作用，以及（3）更好地理解湍流涡旋在通过小颗粒的分离和聚集来增强星子形成中的作用。原行星盘（PPD）是围绕年轻恒星的旋转的气体和尘埃片，被认为是诞生地像我们自己这样的行星。 圆盘气体内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起源的。 事实证明，计算机模拟是增进我们对 PPD 动力学理解的宝贵工具。 然而，鉴于现代技术的限制，目前不可能捕获 PPD 中动态相关性的所有时间和空间尺度。 PI 正在克服这些限制，开发了第一个多尺度数学模型，用于识别和模拟 PPD 中的流体运动。在这方面，所提出的工作可以被视为一个新的计算和建模框架，它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.