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Unstable turbulent channel flow response to spanwise-heterogeneous heat fluxes: Prandtl's secondary flow of the third kind

Journal Article · · Journal of Fluid Mechanics
DOI:https://doi.org/10.1017/jfm.2022.15· OSTI ID:1975422
 [1];  [2];  [3]
  1. University of Oklahoma, Norman, OK (United States)
  2. University of Utah, Salt Lake City, UT (United States)
  3. University of Texas at Dallas, Richardson, TX (United States)
+ Show Author Affiliations
Turbulent secondary flows are defined as Prandtl's secondary flow of the first or second kind, the former produced by stretching and/or tilting of vorticity, the latter produced via spatial heterogeneity of Reynolds stresses. Both mechanisms are instantaneously active within inertia-dominated wall turbulence; Reynolds stress spatial heterogeneity is required for Reynolds-averaged secondary flows. Spanwise-variable surface roughness can induce turbulent stress spatial heterogeneity in the spanwise–wall-normal plane and provide sustenance for streamwise-aligned mean secondary flows. Herein, we demonstrate that turbulent secondary flows can also be sustained by spanwise variability in the surface heat flux in unstably stratified turbulent channels, defined hereafter as Prandtl's secondary flow of the third kind. Support for this mechanism is established with scaling arguments, while large-eddy simulation is used to model inertia-dominated channel turbulence responding to a lower boundary with uniform aerodynamic/hydrodynamic roughness but spanwise-variable surface heat flux. Transport equations for streamwise vorticity and turbulent kinetic energy, k, outline the conditions needed for third-kind production: shear and buoyancy production over the elevated heat flux regions necessitates lateral entrainment of low- k fluid, inducing mean counter-rotating secondary cells aligned such that upwelling and downwelling occur over the high and low heat flux regions, respectively. Buoyancy-driven production of k alters aggregate flow response and thus is a distinctly different mechanism responsible for sustenance of secondary flows.
Research Organization:
University of Oklahoma, Norman, OK (United States)
Sponsoring Organization:
Alexander von Humboldt Stiftung/Foundation; National Science Foundation (NSF); USDOE Office of Science (SC); USDOE Office of Science (SC), Biological and Environmental Research (BER)
Grant/Contract Number:
SC0022124
Other Award/Contract Number:
AGS-1500224
PDM-1649067
PDM-1712538
OSTI ID:
1975422
Alternate ID(s):
OSTI ID: 1977730
Journal Information:
Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 934; ISSN 0022-1120
Publisher:
Cambridge University PressCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
turbulent boundary layers
turbulent convection