http://arxiv.org/abs/1605.04852
Approximate empirical models of thermal convection can allow us to identify the essential properties of the flow in simplified form, and to produce empirical estimates using only a few parameters. Such “low-dimensional” empirical models can be constructed systematically by writing numerical or experimental measurements as superpositions of a set of appropriate basis modes, a process known as Galerkin projection. For Boussinesq convection in a cylinder, those basis modes should be defined in cylindrical coordinates, vector-valued, divergence-free, and mutually orthogonal. Here we construct two such basis sets, one using Bessel functions in the radial direction, and one using Chebyshev polynomials. We demonstrate that each set has those desired characteristics and demonstrate the advantages and drawbacks of each set. We show their use for representing sample simulation data and point out their potential for low-dimensional convection models.
D. Kelley, E. Blackman and C. Knox
Tue, 17 May 16
56/65
Comments: submitted to Journal of Fluid Mechanics; 17 pages; 11 figures
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