Spectral calculations in stably stratified turbulence

Abstract

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.

Spectral calculations for pressure–velocity and pressure–strain correlations in homogeneous shear turbulence

“…For the case of homogeneous shear turbulence [39], it yields encouraging results for the universal numbers associated with the anisotropic part of the velocity correlation tensor. For the case of stably stratified turbulence [40], it has not only allowed us to calculate the prefactors associated with the velocity-velocity, temperature-temperature, and velocity-temperature correlations, but also correctly captured the trend of observed layered structure. These provide renewed hope for the applicability of Leslie's perturbation method in capturing the turbulent statistics for more general anisotropic turbulence.…”

“…Despite the abovementioned constraints, it may be noted that our derived results are direct analytical consequences of the underlying equation of the homogeneous shear turbulence. Owing to its relative simplicity, although the capability of Leslie's perturbation scheme in capturing the experimental results for pressure related spectra is not satisfactory, it has correctly captured the eect of anisotropy in the inertial range of homogeneous shear [39] and stably stratified turbulence [40]. For the case of homogeneous shear turbulence [39], it yields encouraging results for the universal numbers associated with the anisotropic part of the velocity correlation tensor.…”

Effect of parameters of refractive index fluctuation spectra with non-Kolmogorov power law on the characteristics of optical radiation propagated through a high-speed turbulent flow: analytical estimates and simulation results

“…Investigations of atmospheric turbulence 1,2 and experimental studies on propagation of optical radiation through a supersonic flows 3 show that the spectra of refractive index fluctuations   n   can be described by a power-law model, but the value of the index in the inertial interval can differ markedly from 11/3 (model of developed turbulence). To describe the spectrum, we will use the power-law model…”