Abstract
Temperature and vertical velocity fluctuations are measured in turbulent Rayleigh-B\'enard convection for Rayleigh numbers $2\ifmmode\times\else\texttimes\fi{}{10}^{8}lRl4\ifmmode\times\else\texttimes\fi{}{10}^{9}$ in cells with cylindrical and square geometries with approximately unit-aspect ratios. The geometries are constructed such that they have the same height and cross sectional area. We find, very unexpectedly, that both the magnitudes and scalings of fluctuations as a function of $R$ depend strongly on the geometry. This latter result implies a possible nonuniversality in internal fluctuations and poses significant difficulties for existing model descriptions of turbulent convection.
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