Zonal flows in Rayleigh-Bénard convection

Abstract eng:
Low-dimensional models of thermal convection can allow us to study the essential dynamics of the flow in simplified form, and to produce empirical estimates using only a few parameters. Low-dimensional representations of convection can be constructed systematically by writing numerical or experimental measurements as summations of a set of appropriate basis functions. For Boussinesq convection in a cylinder, those basis functions should be defined in cylindrical coordinates, vector-valued, divergence-free, and complete. Here we present such a basis set, the vector cylindrical harmonics. We demonstrate that they have the desired characteristics, show their use for representing measurements, and point out their potential for low-dimensional convection models.

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