# Thesis

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Dissipative Closures for Statistical
Moments, Fluid Moments, and Subgrid Scales in Plasma Turbulence

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Stephen A. Smith (1997)

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Thesis Advisor: Dr. Gregory W. Hammett

Closures are necessary in the study
physical systems with large numbers of degrees of freedom
when it is only possible to compute a small number of
modes.
The modes that are to be computed, the resolved modes,
are coupled to unresolved modes that must be
estimated.
This thesis focuses on
dissipative closures models for two problems that
arises in the study of plasma turbulence: the fluid moment closure
problem and the subgrid scale closure problem.
The fluid moment closures of Hammett and Perkins (1990)
were originally
applied to a one-dimensional kinetic equation, the Vlasov equation.
These closures are generalized in this thesis and applied to
the stochastic oscillator problem, a standard paradigm problem
for statistical closures.
The linear theory of the Hammett--Perkins closures is
shown to converge with increasing numbers of moments.

A novel parameterized hyperviscosity is proposed for
two-dimensional drift-wave turbulence.
The magnitude and exponent of the hyperviscosity are expressed
as functions of the large scale advection velocity.
Traditionally hyperviscosities are applied to simulations
with a fixed exponent that must be arbitrarily chosen.
Expressing the exponent as a function of the simulation parameters
eliminates this ambiguity.
These functions are parameterized by comparing the hyperviscous
dissipation to the subgrid dissipation calculated from direct
numerical simulations.
Tests of the parameterization demonstrate that it performs better
than using no additional damping term or than using a standard
hyperviscosity.

Heuristic arguments are presented to extend this hyperviscosity model
to three-dimensional (3D) drift-wave turbulence where eddies are highly
elongated along the field line.
Preliminary results indicate
that this generalized 3D hyperviscosity is capable of reducing the
resolution requirements for 3D gyrofluid turbulence simulations.