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...
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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 |
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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 |