Saturation of Shear-Flow Driven Instability and Turbulence

这一奖项将使人们能够研究流体动力学、地球大气、天体物理系统和聚变设备中常见的一种集体波动，重点是日益不稳定的饱和的新机制。饱和是一个非线性过程，它通过创建湍流状态和改变导致不稳定最初增长的环境来阻止波动的指数增长。这个项目调查了先前假设为快速衰减的大范围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，以及化学物质在整个银河系中的扩散。这一资助的研究将提供对这些过程如何工作的新的理解，并更好地预测它们所产生的输运的速率和性质。饱和过程中稳定模的非线性激发将通过解析和数值确定具有均匀流对齐磁场的可解析的分段连续剪切流的线性本征频率和本征函数来研究。一种先前开发的映射技术将被用来确定不稳定模式和稳定模式之间的非线性能量传递特性，由此将得到一个解析的稳定模式饱和水平估计。脉动的流动剖面、动量和化学物质的输运率以及饱和时二次小尺度运动的生成率都将使用计算的饱和度来确定。稳定本征模能级、输运率和二级结构的产生与磁场及其取向程度的依赖关系将量化稳定模对湍流级联和驱动轮廓松弛的影响。饱和状态的数值解将用Dedalus程序得到，相关的漂移波型剪切流不稳定性将用Gene码回转研究磁化等离子体中的不稳定。

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.