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

原行星盘（Protoplanetary disk，PPD）是围绕年轻恒星的几何薄的旋转气体和尘埃片，被认为是像我们这样的行星的诞生地。流体的不稳定性和盘内气体的湍流被认为是聚集固体颗粒和启动行星建造过程的主要机制，但目前还不知道是哪种不稳定性或两者的组合。计算约束限制PPD的数值模拟的分辨率是无法解决所有的时间和空间尺度的动态相关性。PI正在通过开发多尺度数学模型来克服这些局限性，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个新的计算和建模框架，将有可能允许最高分辨率的模拟PPD动态。特别强调的是被放置在理解的非线性特性，通过使用高分辨率的数值模拟，新的赤道涡不稳定性（EVI），已确定的PI。通过采用严格的渐近方法，一个分层的方程组，能够同时模拟小规模和全球规模的动态和两个尺度之间的耦合正在开发中的第一次。研究结果将有助于更全面地了解（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通过小颗粒的分离和聚集在促进微行星形成中的作用。原行星盘（PPD）是围绕着年轻恒星的旋转的气体和尘埃层，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聚集固体物质和启动行星建造过程的主要机制，但目前还不知道这种运动是如何产生的。 计算机模拟已被证明是有价值的工具，为推进我们对PPD动力学的理解。 然而，由于现代技术的限制，目前不可能在项目执行文件中涵盖所有时间和空间尺度的动态相关性。PI正在通过开发第一个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，将允许最高分辨率的PPD动态模拟。

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.