Multifractal nature of plume structure in high Rayleigh number convection

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The geometrically different plan forms of near wall plume structure in turbulent natural convection, visualised by driving the convection using concentration differences across a membrane, are shown to have a common multifractal spectrum of singularities for Rayleigh numbers in the range 10¹⁰- 10¹¹ at Schmidt number of 602. The scaling is seen for a length scale range of 2⁵ and is independent of the Rayleigh number, the flux, the strength and nature of the large scale flow, and the aspect ratio. Similar scaling is observed for the plume structures obtained in the presence of a weak flow across the membrane. This common non trivial spatial scaling is proposed to be due to the same underlying generating process of the near wall plume structures.