Statistical Field Spectral Calculations in Some Problems of Anisotropic Turbulence

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In this research work we apply the standard perturbative methods to some anisotropic cases of fluid turbulence and obtain information about the effect of anisotropy within such frameworks. As a matter of fact, the anisotropy makes the problems much more complex than the corresponding isotropic cases, and we hope that such a study will have both academic and practical relevance. Homogeneous shear turbulence has been studied in great details in the last few decades. The cases of anisotropic turbulence have been mostly dealt with SO(3) decomposition [102]. However, we take alternative routes to the problems of anisotropic turbulence and hence we are interested in tackling directly the anisotropic terms appearing in the dynamical equations by means of standard perturbative methods. In practical applications, what one is interested in is the effect of turbulence on the mean flow and on transport, which is parametrized in terms of eddy-viscosities and eddy-diffusivities. In some cases, in order to calculate these quantities, information about the turbulent energy spectrum is necessary, and the universal Kolmogorov spectrum with scaling law E(k) = C 2/3k5/3 is usually assumed. Here k is the wavenumber, is the energy flux, and C the universal Kolmogorov constant...
Supervisor: M. K. Nandi