Saturation of Shear-Flow Driven Instability and Turbulence

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

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.