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

Abstract

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 λ z,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 Re τ 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 λ x,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 Re τ 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 Re τ , 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.

Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls

“…The turbulent viscosity can be obtained either by fitting an analytical model to a given flow condition, or by direct calculation viaμ turb = ρu v /(dU/dy). For the first method, Cess (1958) has proposed an analytical form of μ turb as a function of Reynolds number and pressure gradient in an incompressible turbulent pipe flow, which has been later adapted by Reynolds & Tiederman (1967) and Reynolds & Hussain (1972) for incompressible channel flow (see also Del Alamo & Jimenez 2006;Pujals et al 2009;Rinaldi et al 2017;Sebastian et al 2019). The second method is more straightforward, but leads to error propagation due to the division operation.…”

Linear instability of Poiseuille flows with highly non-ideal fluids

“…Patel et al (2016) studied the influence of variable properties on fully developed turbulent channel flows and derived a velocity transformation that allows to collapse velocity profiles for heated or cooled non-ideal fluids. Moreover, Rinaldi et al (2017) provided an explanation of near wall turbulence modulation, especially the intercomponent energy transfer that has been observed by, e.g. Morinishi et al (2004), Pirozzoli et al (2008), Duan et al (2010).…”

Turbulence modulation in thermally expanding and contracting flows

“…Despite all the profiles of Π 11 showing a decrease in intensity for the heated cases, the impact of variable properties is noticed for the streamwise and spanwise pressure terms, where a local increase in magnitude near the wall is visible for case A-H 2 O. Since A-H 2 O has an increasing Re τ in the wall-normal direction, the streamwise vortices tend to destabilize (as shown in Rinaldi et al (2017)), and thus counteract the effect of acceleration. This is particularly visible for y < 15, where Π 11 /ε 11 is higher than for the reference inlet profile.…”