A computational study of Rayleigh–Bénard convection. Part 1. Rayleigh-number scaling

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Abstract
A parametric study is made of chaotic Rayleigh–Bénard convection over moderate Rayleigh numbers. As a basis for comparison over the Rayleigh number (Ra) range we consider mean quantities, r.m.s. fluctuations, Reynolds number, probability distributions and power spectra. As a further means of investigating the flow we use the Karhunen–Loéve procedure (empirical eigenfunctions, proper orthogonal decomposition). Thus, we also examine the variation in eigenfunctions with.Ra. This in turn provides an analytical basis for describing the manner in which the chaos is enriched both temporarily and spatially as Ra increases. As Ra decreases, the significant mode count decreases but, in addition, the eigenfunctions tend more nearly to the eigenfunctions of linearized theory. As part of this parametric study a variety of scaling properties are investigated. For example it is found that the empirical eigenfunctions themselves show a simple scaling in Ra.

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