Abstract
Dynamical equations governing the energy, temperature and heat-flux spectra in homogeneous axisymmetric Boussinesq turbulence are formulated by applying the modified zero-fourth-cumulant approximation. For nearly-isotropic turbulence with a weak buoyancy force, it is shown that they are reduced to the equations of turbulent field convecting a passive scalar. For this case, numerical calculations are performed to determine the spectra at the Reynolds number 32, Rayleigh number 100 and Plandtl number unity. The results show that the approach to isotropy seems rather slow. The temperature and heat-flux spectra indicate that there are several subranges of the wavenumbers governed by different similarity laws. Also the heat-flux spectrum is found to have a sharp peak which shifts toward the low-wavenumber range.
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