• Author / Creator
    Emami, Pedram
  • 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.

  • Subjects / Keywords
  • Graduation date
    2017-06:Spring 2017
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. 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.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • John C. Bowman (Mathematical and Statistical Science)
  • Examining committee members and their departments
    • Brendan Pass (Mathematical and Statistical Science)
    • Morris Flynn (Mechanical Engineering)
    • Xinwei Yu (Mathematical and Statistical Science)