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Published online by Cambridge University Press: 11 May 2010
Recently Pumir, Shraiman & Siggia (1991) proposed an idea that a nonlinear mean temperature is essential to produce exponentiallike tails for probability density functions (PDFs) of temperature fluctuations in convection. In this paper, results of numerical simulations of the 3D random advection equation with a mean gradient term will be shown. Some theoretical analysis is given based on a transport equation without molecular diffusion. The simplified analysis can capture the characteristic shapes of PDFs well.
INTRODUCTION
The study of passive scalar advection provides fundamental understanding of various phenomena such as convection and mixing that are ubiquitous in nature. In particular, the probability distribution of amplitude and its spatial gradients are of vital importance in relation to recent active studies of non-Gaussian probability density functions (PDFs) endemic in turbulence.
Since Castaing et al. (1989) reported exponential-like tails on the PDF of temperature fluctuations in thermal convection at very high Rayleigh numbers, there has been increasing interest in the mechanism of the non-Gaussian tails on PDFs of amplitudes. In a recent paper, Pumir, Shraiman & Siggia (1991) have suggested that the non-Gaussian tails for an advected passive temperature field may be induced by the presence of a mean-temperature profile. A simple physical mechanism for this is proposed in the present paper. The resultant non-Gaussian statistics will be shown by numerical simulations and theoretical analysis for a transport equation without molecular diffusion. In this paper, the result on PDFs is summarized; other details will be presented elsewhere (Kimura & Kraichnan 1993).
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