Spectral calculations in stably stratified turbulence.

We perform a Leslie-type perturbative treatment on stably stratified turbulence with Boussinesq approximation, where the buoyancy terms in the corresponding dynamical equations are treated as perturbations against the isotropic background fields. Thus we calculate the anisotropic corrections to various correlation functions, namely, velocity-velocity, temperature-temperature, and velocity-temperature correlations, up to second order in this scheme. We find that the prefactors associated with the anisotropic corrections depend on the energy flux, scalar flux, Kolmogorov constant, Batchelor constant, and the eddy-damping amplitudes. The correlation functions further yield the anisotropic parts of the energy and mean-square temperature spectra as k(-3) and the anisotropic buoyancy spectrum as k(-7/3). The resulting angle-dependent energy density is found to be concentrated predominantly around the vertical wave vector signifying layered structures in the physical space.