Ph.D. Dissertation Defense: Amrik Sen
A Tale of Waves and Eddies in a Sea of Rotating Turbulence
Amrik Sen
Applied Mathematics,Ìý
Date and time:Ìý
Monday, December 16, 2013 - 2:00pm
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Engineering Center, ECOT 831
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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 pertains 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 spans a hierarchy of slow manifold regions
where slow inertial waves are in geostrophic balance with non-linear advection
processes.