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Linear stability of buffer layer streaks in turbulent channels with variable density and viscosity
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-3655-7439
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0001-9627-5903
2017 (English)In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 2, no 11, article id 113903Article in journal (Refereed) Published
Abstract [en]

We investigate the stability of streaks in the buffer layer of turbulent channel flows with temperature-dependent density and viscosity by means of linear theory. The adopted framework consists of an extended set of the Orr-Sommerfeld-Squire equations that accounts for density and viscosity nonuniformity in the direction normal to the walls. The base flow profiles for density, viscosity, and velocity are averaged from direct numerical simulations (DNSs) of fully developed turbulent channel flows. We find that the inner scaling based on semilocal quantities provides an effective parametrization of the effect of variable properties on the linearized flow. The spanwise spacing of optimal buffer layer streaks scales to λz,opt≈90 for all cases considered and the maximum energy amplification decreases, compared to the one for a flow with constant properties, if the semilocal Reynolds number Reτ increases away from the walls, consistently with less energetic streaks observed in DNSs of turbulent channels. A secondary stability analysis of the two-dimensional velocity profile formed by the mean turbulent velocity and the nonlinearly saturated optimal streaks predicts a streamwise instability mode with wavelength λx,cr≈230 in semilocal units, regardless of the fluid property distribution across the channel. The threshold for the onset of the secondary instability is reduced, compared to a constant property flow, if Reτ increases away from the walls, which explains the more intense ejection events reported in DNSs. The opposite behavior is predicted by the linear theory for decreasing Reτ, in accord with DNS observations. We finally show that the phase velocity of the critical mode of secondary instability agrees well with the convection velocity calculated by DNSs in the near-wall region for both constant and variable viscosity flows.

Place, publisher, year, edition, pages
American Physical Society , 2017. Vol. 2, no 11, article id 113903
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-227072DOI: 10.1103/PhysRevFluids.2.113903ISI: 000415175400003Scopus ID: 2-s2.0-85038438213OAI: oai:DiVA.org:kth-227072DiVA, id: diva2:1206639
Note

QC 20180517

Available from: 2018-05-17 Created: 2018-05-17 Last updated: 2019-10-18Bibliographically approved

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Rinaldi, EnricoSchlatter, Philipp

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