Item Details

Turbulence, Regularity, and Geometry in Solutions to the Navier-Stokes and Magnetohydrodynamic Equations

Leitmeyer, Keith
Format
Thesis/Dissertation; Online
Author
Leitmeyer, Keith
Advisor
Grujic, Zoran
Abstract
Inertial transport in the Navier--Stokes and magnetohydrodynamic equations is shown to concentrate enstrophy towards smaller scales under physically motivated and numerically supported assumptions. This is possible with an assumption of vorticity coherence wherever the velocity has large gradients in combination with interpreting enstrophy concentration in physical space, using averaged fluxes through spherical shells. Concentration of enstrophy is consistent with the dynamically generated vortex filaments or current sheets seen in numerical simulations of turbulent fluids. Complementing this, a Besov space regularity criterion is proven by relating the analytic condition of scaling behavior of the amplitude of high frequency components with the geometric property of sparseness of a super-level set. Together these results demonstrate deep connections between geometric aspects of velocity fields, regularity of solutions of deterministic fluid equations, and turbulence.
Language
English
Date Received
20161130
Published
University of Virginia, Department of Mathematics, PHD (Doctor of Philosophy), 2016
Published Date
2016-11-30
Degree
PHD (Doctor of Philosophy)
Collection
Libra ETD Repository
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