Anisotropic distribution of scalar in stably stratified turbulence

Abstract

We derive the anisotropic mean-square scalar (or temperature variance) spectrum and the buoyancy (or heat) flux for a stably stratified turbulent fluid by assuming the buoyancy terms in the governing dynamical equations as perturbations of the otherwise isotropic dynamics. This allows us to investigate their anisotropic distribution across scales larger and smaller than the Ozmidov scale. The ensuing 1D vertical wavenumber temperature spectrum at large scales is found to be in good agreement with stratospheric observations. The polar plot of the angle-dependent expression for temperature variance signifies the enhanced anisotropy with decreasing Froude number. It also indicates that with increasing stratification, the anisotropy persists down to smaller and smaller scales. In addition, we also display various polar plots for the components of buoyancy current, showing their anisotropic distribution.