ON THE GLOBAL ATTRACTOR OF 2D INCOMPRESSIBLE TURBULENCE WITH RANDOM FORCING Open Access
- Other title
- Type of item
- Degree grantor
University of Alberta
- Author or creator
- Supervisor and department
John C. Bowman (Mathematical and Statistical Science)
- Examining committee member and department
Morris Flynn (Mechanical Engineering)
Brendan Pass (Mathematical and Statistical Science)
Xinwei Yu (Mathematical and Statistical Science)
Department of Mathematical and Statistical Sciences
- Date accepted
- Graduation date
Master of Science
- Degree level
The importance of simulating fluid flow is indisputable. From weather forecasting to aviation to the blood flow inside our arteries, fluid flow significantly influences our everyday life. Among all possible fluid regimes, one is dominant in many physical applications. Turbulence, sometimes characterized as the “last great unsolved problem of classical mechanics,” is complicated enough that it still does not have a unified and thoroughly validated theory. Understanding the nature of turbulence even in the simplest and most ideal homogeneous isotropic incompressible case has been underway since the beginning of the twentieth century. Although there have been brilliant breakthroughs, we are far from a complete understanding of this important physical phenomenon. Among many approaches available for studying turbulence, a recent method exploits modern mathematical tools to analyze turbulence on a solid foundation. This functional analysis approach is based on the Navier–Stokes equation, the most widely adopted deterministic governing equation for Newtonian fluid flow. This study revisits bounds on the projection of the global attractor in the energy–enstrophy plane obtained by Dascaliuc, Foias, and Jolly [2005, 2010]. In addition to providing more elegant proofs of some of the required nonlinear identities, the treatment is extended from the case of constant forcing to the more realistic case of white-noise forcing typically used in numerical simulations of turbulence. Finally, these analytical bounds, which have not previously been demonstrated numerically in the literature, even for the case of constant forcing, are illustrated numerically in this work for the case of white-noise forcing.
- This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
- Citation for previous publication
R. Dascaliuc, M. Jolly, et al., Journal of Dynamics and Differential Equations, 17:643, 2005.R. Dascaliuc, C. Foias, & M. Jolly, Journal of differential Equations, 248:792, 2010.J. M. McDonough, Introductory lectures on turbulence, Unpublished lecture notes, 2007.
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