Abstract
In this paper we solve the direct-interaction approximation (DIA) equations numerically for homogeneous shear turbulence and homogeneous, anisotropic turbulence in a rotating fluid. The numerical method uses Fourier transform techniques to evaluate efficiently wave-number convolutions in three dimensions that are characteristic of analytical theories of turbulence including the DIA. Solutions for special cases of isotropic and axisymmetric turbulence compare favorably with previously published results that were obtained using different methods. Our results do not show any significant influence of rotation on initially isotropic turbulence. For the shear case we find buildup of anisotropy that cannot be explained by Rotta-like hypotheses. Neglecting completely triple correlations in our calculations still yields qualitatively correct energetics of the system, although two-time quantities are very different. Our results show that it is now feasible to consider numerical solutions of the equations of analytical theories of turbulence, but much work remains to be done before these methods will be of direct engineering utility.
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Domaradzki, J.A., Orszag, S.A. Numerical solutions of the direct interaction approximation equations for anisotropic turbulence. J Sci Comput 2, 227–248 (1987). https://doi.org/10.1007/BF01061111
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DOI: https://doi.org/10.1007/BF01061111