Date of Award

Spring 1-1-2014

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Mathematics

First Advisor

Annick Pouquet

Second Advisor

Keith Julien

Third Advisor

Pablo D. Mininni

Fourth Advisor

Thomas Manteuffel

Fifth Advisor

Bengt Fornberg

Abstract

In this thesis, we investigate several properties of rotating turbulent flows. First, we ran several computer simulations of rotating turbulent flows and performed statistical analysis of the data produced by an established computational model using Large Eddy Simulations (LES). This enabled us to develop deeper phenomenological understanding of such flows, e.g. the effect of anisotropic injection in the power laws of energy and helicity spectral densities, development of shear in specific rotating flows and evidence of wave-vortex coupling. This served as a motivation for detailed theoretical investigations. Next, we undertook a theoretical study of nonlinear resonant wave interactions to deduce new understanding of rotating flow dynamics. The latter analysis pertained to the highly anisotropic regime of rotating flows. To the best of our knowledge, the application of wave-turbulence theory to asymptotically reduced equations in the limit of rapidly rotating hydrodynamic flows is presented here for the first time and aims to further our understanding of highly anisotropic turbulent flows. A coupled set of equations, known as the wave kinetic equations, for energy and helicity is derived using a novel symmetry argument in the canonical description of the wave field sustained by the flow. A modified wave turbulence schematic is proposed and includes scaling law solutions of the flow invariants that span a hierarchy of slow manifold regions where slow inertial waves are in geostrophic balance with non-linear advection processes. A brief summary of the key findings of this thesis is presented in Table 1.

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