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

Anagha Madhusudanan1,2,*, Simon J. Illingworth1, Ivan Marusic1, and Daniel Chung1

  • 1Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
  • 2Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, California 91125, USA

  • *anaghamadhu91@gmail.com
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Phys. Rev. Fluids 7, 044601 – Published 6 April, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.044601

Abstract

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)]. 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.

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Phys. Rev. Fluids 7, 044601– Published 6 April, 2022
  • Received 10 September 2021
  • Accepted 25 February 2022
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