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The energy cascade in both hydrodynamic and hydromagnetic Boussinesq convection is investigated at large Rayleigh numbers, using a scalar model for turbulence. Depending on the relative importance of direct and inverse transfer, either we observe classical Kolmogorov k^-5/3 spectra or, if there is a strong inverse transfer of kinetic energy, we find a k^-7/5 spectrum for the temperature fluctuation and a k^-11/5 spectrum for the kinetic energy (Bolgiano-Obukhov scaling). We derive dissipative cutoff wave numbers that are consistent with these spectra.
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Axel Brandenburg (1992) studied this question.
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