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.
