Spectral and modal characteristics of stably stratified turbulent channel flows with differential diffusion effects

The presence of density stratification adds to the complexity of turbulence by affecting the small-scale mixing, the large-scale circulation, and the inter-scale interactions. The density in underwater naval flows depends upon temperature and salinity scalars. The differences in the molecular diffusivity of these scalars lead to the occurrence of the differential diffusion phenomenon. A key feature of such flows is the presence of internal waves, which affect the spatio-temporal dynamics in these flows. Therefore, an improved understanding of the effects of differential diffusion on the characteristics of the internal waves is required for reliable modeling of such flows. In this study, the effects of differential diffusion on the spectral and modal characteristics of internal waves in stably stratified turbulent channel flows are examined by considering direct numerical simulation datasets at a frictional Reynolds number of 395 and the frictional Richardson number of 60. The two-dimensional spectra of fluctuations in the vertical velocity, density, momentum flux, and buoyancy flux at different wall-normal planes are obtained to examine the effects of buoyancy and shear-generated turbulence. The presence of internal waves is inferred in terms of the phase relationship between the vertical velocity and density fluctuations. The spatial structure of the internal waves is examined using the dynamic mode decomposition technique to obtain the dynamically relevant flow structures.