TY - JOUR

T1 - Linear stability of buffer layer streaks in turbulent channels with variable density and viscosity

AU - Rinaldi, Enrico

AU - Patel, Ashish

AU - Schlatter, Philipp

AU - Pecnik, Rene

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Boundary layers

KW - Flow instability

KW - Viscosity

KW - Fluid Dynamics

UR - http://www.scopus.com/inward/record.url?scp=85038438213&partnerID=8YFLogxK

UR - http://resolver.tudelft.nl/uuid:47f39f52-0b0f-4133-8bba-13b828f8af3a

U2 - 10.1103/PhysRevFluids.2.113903

DO - 10.1103/PhysRevFluids.2.113903

M3 - Article

AN - SCOPUS:85038438213

SN - 2469-990X

VL - 2

JO - Physical Review Fluids

JF - Physical Review Fluids

IS - 11

M1 - 113903

ER -