Saturation of Shear-Flow Driven Instability and Turbulence

该奖项将使流体力学，地球大气层，天体物理系统和聚变装置中常见的集体波动类型的研究，重点是不断增长的不稳定性饱和的新机制。饱和是一个非线性过程，它通过创造一个湍流状态并改变导致不稳定性初始增长的环境来阻止波动的指数增长。 该项目研究了以前假设快速衰减的大尺度波动饱和的作用，并研究它们如何影响湍流的发展。剪切流不稳定性和湍流传输粒子和动量，导致例如奶油与咖啡的混合，云的形成以及化学物质在整个星系中的扩散。这项研究将提供新的理解这些过程如何工作，更好地预测它们产生的速率和性质的运输。稳定模式的非线性激发在饱和过程中将通过确定解析和数值的线性本征频率和本征函数的解析易处理的分段连续剪切流与均匀流对齐的磁场进行调查。 以前开发的映射技术将被用来确定非线性能量传递特性之间的不稳定和稳定的模式，从分析，稳定模式的饱和度估计将被导出。 波动的流动剖面，动量和化学物质的传输速率，以及饱和状态下二次较小尺度运动的生成速率都将使用计算的饱和度来确定。 稳定的本征模水平，传输速率，和二级结构产生的磁场和它的对齐程度的依赖性将量化的稳定模式的湍流级联和松弛的驱动配置文件的效果。 饱和状态的数值解将获得使用Dedalus代码，和相关的漂移波型剪切流不稳定性磁化等离子体将研究gyrokinetically使用基因代码。

This award will enable a study of a type of collective fluctuation common in hydrodynamics, the Earth's atmosphere, astrophysical systems, and fusion devices, focusing on novel mechanisms for saturation of a growing instability. Saturation is the nonlinear process that stops the exponential growth of fluctuations by creating a turbulent state and changing the circumstances that led to the initial growth of the instability. This project investigates the role in saturation of large-scale fluctuations previously assumed to rapidly decay, and studies how they impact the development of turbulence. Shear-flow instabilities and turbulence transport particles and momentum, resulting, for example, in the mixing of cream into coffee, formation of clouds, and dispersal of chemical species throughout the galaxy. The research supported by this grant will provide new understanding on how these processes work and better predictions of the rates and nature of the transport they produce.The nonlinear excitation of stable modes in the saturation process will be investigated by determining analytically and numerically the linear eigenfrequencies and eigenfunctions for an analytically tractable piecewise continuous shear flow with a uniform flow-aligned magnetic field. A previously developed mapping technique will be used to determine the nonlinear energy transfer properties between the unstable and stable mode, from which an analytical, stable-mode saturation-level estimate will be derived. The fluctuating flow profiles, the rates of transport of momentum and chemical species, and the rates of generation of secondary smaller scales motions in saturation will all be determined using the calculated saturation level. The dependence of stable eigenmode level, transport rates, and secondary structure generation on the magnetic field and its degree of alignment will quantify the effect of stable modes on the turbulent cascade and on the relaxation of the driving profile. Numerical solutions of the saturated state will be obtained using the Dedalus code, and related drift-wave-type shear flow instability in magnetized plasmas will be investigated gyrokinetically using the Gene code.