Coherent structures in incompressible fluid flows

Fluids;Transition to turbulence;Dynamical systems

Short, Kimberly Yovel ; Ballantyne, David Physics Laguna, Pablo Fedele, Francesco Wiesenfeld, Kurt Schatz, Michael ; Ballantyne, David

University:Georgia Institute of Technology

Department:Physics

关键词: Fluids;    Transition to turbulence;    Dynamical systems;   

Others  :  https://smartech.gatech.edu/bitstream/1853/62348/1/SHORT-DISSERTATION-2019.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

The work is broadly related to thetransition to turbulence in pipe at intermediate Reynolds numbers andincludes a discussion of two classes of structures observed during the transition to turbulence: numerically-extracted solutions of the Navier-Stokes equations (the ``exact'') and localized/patterned turbulent spots that are not themselves solutions of the Navier-Stokes equation but are nonetheless pervasive during the transition (the ``inexact''). High-dimensional descriptions of turbulence is predicted by periodic orbit theory (POT) which expects to describe turbulence exactly, as opposed to approximately. The search for relative periodic orbits and traveling waves in pipe---the constituents solutions to periodic orbit theory---are discussed. The successful search for relative periodic orbits at transitional Reynolds numbers gave a catalogue of invariantsolutions; many of these solutions were continued in parameter space tofind that solutions coexist with the transitional regime. In addition to collecting solutions to eventually test periodic orbit theory, an investigation into the Barkley's pipe model---a system that successfully models the transition to turbulence in pipe---was undertaken.