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

• Main Authors: Chung, D. (Author), Illingworth, S.J (Author), Madhusudanan, A. (Author), Marusic, I. (Author)
• Format: Article
• Language: English
• Published: American Physical Society 2022
• Subjects: Bulk Richardson number; Channel flow; Constant flow; Direct-numerical-simulation; Eddy Diffusivities; Eddy viscosity; Flow structure; Impulse response; Large-scale flow structure; Linear modeling; Linear operators; Linearization; Mathematical operators; Navier Stokes; Navier Stokes equations; Turbulent channel flows; Viscous flow
• Online Access: View Fulltext in Publisher

 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 Rib=0.001 to Rib=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 Rib in direct numerical simulations (DNSs) [e.g., Pirozzoli et al., J. Fluid Mech. 821, 482 (2017)JFLSA70022-112010.1017/jfm.2017.216]. The linearized Navier-Stokes equations augmented with eddy-viscosity and eddy-diffusivity capture the emergence of the quasistreamwise rolls well. With increasing Rib, 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. © 2022 American Physical Society.