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Dissertation/Thesis Abstract

Hydrodynamic and magnetohydrodynamic turbulence: Invariants, cascades, and locality
by Aluie, Hussein, Ph.D., The Johns Hopkins University, 2009, 234; 3399106
Abstract (Summary)

This dissertation employs the coarse-graining approach, commonly used as a modeling tool in the LES community, to analyze scale interactions in turbulent flows, following [1]. The main scientific contributions of this dissertation to the fields of hydrodynamic and magnetohydrodynamic (MHD) turbulence are: (1) Establishing necessary conditions for turbulent MHD flows to sustain cascades of energy and cross-helicity to arbitrarily small scales, and proving that it is impossible for magnetic-helicity to undergo a forward cascade. These results provide rigorous constraints on any phenomenological theory of MHD turbulence. (2) Presenting both rigorous results and physical theory on the breakdown of magnetic flux conservation for plasmas by nonlinear effects, independent of any microscopic non-ideality. It shows that instantaneous violation of flux-conservation can occur if singular current sheets and vortex sheets both exist and intersect in sets of non-zero length. This result gives analytical support to and rigorous constraints on theories of fast turbulent reconnection. (3) Establishing scale-locality of the energy cascade in a turbulent flow using Fourier analysis and showing that the primary participants in the process are triplets of "eddies" comprised of adjacent logarithmic bands of Fourier modes. The analysis disproves an alternate picture of "local transfer by nonlocal triads" by showing that such triads make a vanishingly small contribution to the energy flux in the inertial range and that it is only the aggregate effect of a geometrically increasing number of local wavenumber triads which can sustain the cascade to small scales. It also shows that the SGS definition of the flux is the proper measure of the cascading energy and demonstrates the danger in the widespread notion that the elementary interactions in turbulence are those involving triads of single Fourier modes. Numerical support is presented from simulations of Navier-Stokes turbulence. (4) Extending the proofs on locality to MHD turbulence where there is a growing consensus that the cascade is "short-circuited" due to the large-scale flow transferring energy to the magnetic field at arbitrarily small scales in the inertial range (e.g. [2–5]). The obtained results rigorously refute such claims. Numerical support is presented from a record-size pseudospectral simulation of forced MHD turbulence on a grid of 1024 3 points with phase-shift dealiasing.

Indexing (document details)
Advisor: Eyink, Gregory L.
School: The Johns Hopkins University
School Location: United States -- Maryland
Source: DAI-B 71/03, Dissertation Abstracts International
Subjects: Astrophysics, Plasma physics
Keywords: Energy cascades, Magnetic reconnection, Magnetohydrodynamics, Turbulence
Publication Number: 3399106
ISBN: 978-1-109-65389-2
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