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Permanent link (DOI): https://doi.org/10.7939/R3W70B

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Multispectral Reduction of Two-Dimensional Turbulence Open Access

Descriptions

Other title
Subject/Keyword
FFT
pseudospectral
convolution
subgrid model
turbulence
shell models
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Roberts, Malcolm Ian WIlliam
Supervisor and department
Bowman, John C. (Mathematical and Statistical Sciences)
Examining committee member and department
Swaters, Gordon (Mathematical and Statistical Sciences)
Flynn, Morris (Mechanical Engineering)
Yu, Xinwei (Mathematical and Statistical Sciences)
Heimpel, Moritz (Physics)
Kaneda, Yukio (Nagoya University)
Department
Department of Mathematical and Statistical Sciences
Specialization

Date accepted
2011-10-03T21:22:24Z
Graduation date
2011-11
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
Turbulence is a chaotic motion of fluid that can be described by the Navier--Stokes equations or even highly simplified shell models. Under the continuum limit, standard shell models of turbulence are shown to reduce to a common evolution equation that reproduces many predictions of the classical Kolmogorov theory. In the spectral domain, the quadratic advective nonlinearity of the Navier--Stokes equations appears as a convolution, which is often calculated using pseudospectral collocation. An implicit dealiasing method, which removes spurious contributions from wave beating in these convolutions more efficiently than conventional dealiasing techniques, is investigated. Even with efficient dealiasing, the simulation of highly turbulent flow is still a formidable task. Decimation schemes such as spectral reduction replace the many degrees of freedom in a turbulent flow by a limited set of representative quantities. A new method called multispectral reduction is proposed to overcome a significant drawback of spectral reduction: the requirement that all scales be decimated uniformly. Multispectral reduction, which exploits a hierarchy of synchronized spectrally reduced grids, is applied to both shell models and two-dimensional incompressible turbulence.
Language
English
DOI
doi:10.7939/R3W70B
Rights
License granted by Malcolm Roberts (malcolmr@ualberta.ca) on 2011-10-02T16:48:16Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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File title: Multispectral Reduction of Two-Dimensional Turbulence
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