Navier-Stokes-based linear model for unstably stratified turbulent channel flows

We use the linearized Navier-Stokes equations to study the large-scale flow structures in unstably stratified turbulent channel flows. The impulse response of the linear operator at bulk Richardson numbers from Ri(b) = 0.001 to Ri(b) = 1.0 are considered, corresponding to the increasing influence of buoyancy relative to shear. We compare the streamwise-constant flow structures predicted by the linear model to the quasistreamwise rolls that emerge with increasing Ri(b) in direct numerical simulations (DNSs) [e.g., Pirozzoli et al., J. Fluid Mech. 821. 482 (2017)]. The linearized Navier-Stokes equations augmented with eddy-viscosity and eddy-diffusivity capture the emergence of the quasistreamwise rolls well. With increasing Ri(b), the temperature fluctuations of the streamwise-constant flow structures transition from having a peak in intensity at the channel centerline to having two peaks, one at each wall, consistent with DNS.

Automated summary

In this study, the linearized Navier-Stokes equations were used to investigate the large-scale flow structures in unstably stratified turbulent channel flows. By comparing the results of the linear model with direct numerical simulations, it was found that the linearized Navier-Stokes equations augmented with eddy-viscosity and eddy-diffusivity could successfully predict the emergence of quasistreamwise rolls, and the temperature fluctuations exhibited similar characteristics as observed in the simulations.