The geometry of isothermal surfaces for Rayleigh-Bénard convection at Rayleigh numbers R in the range 107 to 3 × 108 (close to the soft to hard turbulence transition) are measured. The measurements were made by imaging the color of light scattered from chiral nematic particles suspended in the fluid. Although the isotherms are multiply connected and convoluted, they do not display fractal scaling. The minimum scale for convolutions can be understood as resulting from the competition between folding and thermal diffusion. The isotherms are characterized statistically by the probability distribution of the local curvature, which may be described approximately as a stretched exponential. The distribution is essentially independent of the position and orientation of the plane of observation, and of R over the range explored. The geometry of the isotherms is compared to that of isoconcentration surfaces for dye injected into the flow; the latter do show a limited range of approximate fractal scaling because of the smaller diffusivity of the dye. The thermal measurements are supplemented by simultaneous measurements of the velocity field obtained by particle image velocimetry. Unstable waves often form on the thermal boundary layers in regions of high horizontal velocity gradient.
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