Rotating Split-Cylinder Flows

abstract: The three-dimensional flow contained in a rapidly rotating circular split cylinder is studied numerically solving the Navier--Stokes equations. The cylinder is completely filled with fluid and is split at the midplane. Three different types of boundary conditions were imposed, leading...

Full description

Bibliographic Details
Other Authors: Gutierrez Castillo, Paloma (Author)
Format: Doctoral Thesis
Language:English
Published: 2017
Subjects:
Online Access:http://hdl.handle.net/2286/R.I.43976
id ndltd-asu.edu-item-43976
record_format oai_dc
spelling ndltd-asu.edu-item-439762018-06-22T03:08:12Z Rotating Split-Cylinder Flows abstract: The three-dimensional flow contained in a rapidly rotating circular split cylinder is studied numerically solving the Navier--Stokes equations. The cylinder is completely filled with fluid and is split at the midplane. Three different types of boundary conditions were imposed, leading to a variety of instabilities and complex flow dynamics. The first configuration has a strong background rotation and a small differential rotation between the two halves. The axisymmetric flow was first studied identifying boundary layer instabilities which produce inertial waves under some conditions. Limit cycle states and quasiperiodic states were found, including some period doubling bifurcations. Then, a three-dimensional study was conducted identifying low and high azimuthal wavenumber rotating waves due to G\"ortler and Tollmien–-Schlichting type instabilities. Over most of the parameter space considered, quasiperiodic states were found where both types of instabilities were present. In the second configuration, both cylinder halves are in exact counter-rotation, producing an O(2) symmetry in the system. The basic state flow dynamic is dominated by the shear layer created in the midplane. By changing the speed rotation and the aspect ratio of the cylinder, the flow loses symmetries in a variety of ways creating static waves, rotating waves, direction reversing waves and slow-fast pulsing waves. The bifurcations, including infinite-period bifurcations, were characterized and the flow dynamics was elucidated. Additionally, preliminary experimental results for this case are presented. In the third set up, with oscillatory boundary conditions, inertial wave beams were forced imposing a range of frequencies. These beams emanate from the corner of the cylinder and from the split at the midplane, leading to destructive/constructive interactions which produce peaks in vorticity for some specific frequencies. These frequencies are shown to be associated with the resonant Kelvin modes. Furthermore, a study of the influence of imposing a phase difference between the oscillations of the two halves of the cylinder led to the interesting result that different Kelvin modes can be excited depending on the phase difference. Dissertation/Thesis Gutierrez Castillo, Paloma (Author) Lopez, Juan M. (Advisor) Herrmann, Marcus (Committee member) Platte, Rodrigo (Committee member) Welfert, Bruno (Committee member) Tang, Wenbo (Committee member) Arizona State University (Publisher) Applied mathematics dynamical systems inertial waves rotating flows eng 168 pages Doctoral Dissertation Applied Mathematics 2017 Doctoral Dissertation http://hdl.handle.net/2286/R.I.43976 http://rightsstatements.org/vocab/InC/1.0/ All Rights Reserved 2017
collection NDLTD
language English
format Doctoral Thesis
sources NDLTD
topic Applied mathematics
dynamical systems
inertial waves
rotating flows
spellingShingle Applied mathematics
dynamical systems
inertial waves
rotating flows
Rotating Split-Cylinder Flows
description abstract: The three-dimensional flow contained in a rapidly rotating circular split cylinder is studied numerically solving the Navier--Stokes equations. The cylinder is completely filled with fluid and is split at the midplane. Three different types of boundary conditions were imposed, leading to a variety of instabilities and complex flow dynamics. The first configuration has a strong background rotation and a small differential rotation between the two halves. The axisymmetric flow was first studied identifying boundary layer instabilities which produce inertial waves under some conditions. Limit cycle states and quasiperiodic states were found, including some period doubling bifurcations. Then, a three-dimensional study was conducted identifying low and high azimuthal wavenumber rotating waves due to G\"ortler and Tollmien–-Schlichting type instabilities. Over most of the parameter space considered, quasiperiodic states were found where both types of instabilities were present. In the second configuration, both cylinder halves are in exact counter-rotation, producing an O(2) symmetry in the system. The basic state flow dynamic is dominated by the shear layer created in the midplane. By changing the speed rotation and the aspect ratio of the cylinder, the flow loses symmetries in a variety of ways creating static waves, rotating waves, direction reversing waves and slow-fast pulsing waves. The bifurcations, including infinite-period bifurcations, were characterized and the flow dynamics was elucidated. Additionally, preliminary experimental results for this case are presented. In the third set up, with oscillatory boundary conditions, inertial wave beams were forced imposing a range of frequencies. These beams emanate from the corner of the cylinder and from the split at the midplane, leading to destructive/constructive interactions which produce peaks in vorticity for some specific frequencies. These frequencies are shown to be associated with the resonant Kelvin modes. Furthermore, a study of the influence of imposing a phase difference between the oscillations of the two halves of the cylinder led to the interesting result that different Kelvin modes can be excited depending on the phase difference. === Dissertation/Thesis === Doctoral Dissertation Applied Mathematics 2017
author2 Gutierrez Castillo, Paloma (Author)
author_facet Gutierrez Castillo, Paloma (Author)
title Rotating Split-Cylinder Flows
title_short Rotating Split-Cylinder Flows
title_full Rotating Split-Cylinder Flows
title_fullStr Rotating Split-Cylinder Flows
title_full_unstemmed Rotating Split-Cylinder Flows
title_sort rotating split-cylinder flows
publishDate 2017
url http://hdl.handle.net/2286/R.I.43976
_version_ 1718701388141166592