Gyrostatic low-order models in fluid dynamics
Abstract
A physically-motivated, modular approach for constructing low-order models (LOMs) of fluid flows is provided by using LOMs in the form of coupled gyrostats. Models with this structure possess conservation properties in common with the original system, thereby preventing certain unphysical behaviors (e.g., unbounded solutions). Such models are also composed of simple “building blocks” (gyrostats) that are added or modified when the order of approximation is increased and when additional physical effects are introduced. In this study, gyrostatic LOMs are used to model two-dimensional (2D) and three-dimensional (3D) Rayleigh-Bénard convection, including the effects of spontaneously generated vertical shear, externally forced vertical shear, rotation, magnetohydrodynamics, and double diffusive conditions. LOMs for 2D convection with shear, 3D convection, and 2D magnetoconvection with shear, introduced earlier by other investigators, are found to possess unphysical features (violation of energy and vorticity conservation and unbounded solutions). In this study, the aforementioned LOMs are modified according to the coupled gyrostats approach, eliminating the pathological behavior. The thus modified LOM for 3D convection is shown to have better qualitative agreement with experimental results than previous models. The first known study of the smallest nontrivial LOM for 3D convection, the 3D analog of the celebrated Lorenz model, is also presented.
Degree
Ph.D.
Advisors
Hirsch, Purdue University.
Subject Area
Fluid dynamics|Gases
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