Temperature spectra in shear flow and thermal convection

Abstract

We show that the $P_u(\om) \propto \om^{-7/3}$ shear velocity power spectrum gives rise to a $P_\Theta (\om ) \propto \om^{-4/3}$ power spectrum for a passively advected scalar, as measured in experiment [K. Sreenivasan, Proc. R. Soc. London A {\bf 434}, 165 (1991)]. Applying our argument to high Rayleigh number Rayleigh Benard flow, we can account for the measured scaling exponents equally well as the Bolgiano Obukhov theory (BO59). Yet, of the two explanations, only the shear approach might be able to explain why no classical scaling range is seen in between the shear (or BO59) range and the viscous subrange of the experimental temperature spectrum [I. Procaccia {\it et al.}, Phys. Rev. A {\bf 44}, 8091 (1991)].