Saturation of Shear-Flow Driven Instability and Turbulence

该奖项将支持对流体动力学、地球大气、天体物理系统和聚变装置中常见的一种集体波动的研究，重点关注日益增长的不稳定性饱和的新机制。饱和是一种非线性过程，它通过创造湍流状态和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。本项目研究了以前假设的快速衰减的大尺度波动在饱和中的作用，并研究了它们如何影响湍流的发展。剪切流的不稳定性和湍流传输粒子和动量，例如，导致奶油混合到咖啡中，形成云，以及整个星系中化学物质的扩散。这项拨款支持的研究将提供对这些过程如何工作的新认识，并更好地预测它们产生的运输速率和性质。本文将通过确定具有均匀流向磁场的解析可处理分段连续剪切流的线性特征频率和特征函数，研究饱和过程中稳定模态的非线性激励。先前开发的映射技术将用于确定不稳定模式和稳定模式之间的非线性能量传递特性，从中将推导出解析的稳定模式饱和水平估计。脉动流剖面、动量和化学物质的输运率以及在饱和状态下次级小尺度运动的产生率都将使用计算的饱和水平来确定。稳定本征模水平、输运率和二次结构产生对磁场及其对准程度的依赖将量化稳定模对湍流级联和驱动剖面松弛的影响。利用Dedalus代码获得饱和状态的数值解，并利用Gene代码对磁化等离子体中相关的漂波型剪切流不稳定性进行回旋动力学研究。

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.