On the effects of differential diffusion and equation of state in stably stratified turbulent channel flow*

Stably stratified turbulent flows observed in underwater naval applications have density stratification dependent upon two scalar fields, namely, temperature and salinity through an equation of state (EoS). The differences in the molecular diffusivity of these scalar fields, which are characterized in terms of Lewis number (Le = Sc/Pr) lead to the occurrence of the differential diffusion phenomenon. Here, Sc and Pr denote the Schmidt and Prandtl numbers, respectively. In this study, direct numerical simulations of turbulent channel flow at a frictional Reynolds number of 395 and at two values of the frictional Richardson number 0 (neutral) and 60 (stratified) are performed to examine the role of EoS, differential diffusion, and density stratification on the flow field. The effects of EoS are characterized in terms of the use of a linear and a nonlinear EoS and the effects of differential diffusion are analyzed for Le = 1, and 4 by considering flow under neutral and stably stratified conditions. The results are analyzed in terms of the behavior of the instantaneous flow field, turbulence statistics, and other quantities of interest such as the buoyancy frequency, gradient Richardson number, length scales, etc., which are relevant to the broader class of stratified flows.