1. Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)

2. What about for intermediate Reynolds numbers?
Plane Poiseuille flow ?
What about for intermediate Reynolds numbers?

3. First simulations

4. Prism: spectral-element/Fourier
Our simulations x
(|| to bands)
Lx=10
simulation of
Tsukahara et al. z
(⊥ to bands)
streamwise
102
Lz=40
our tilted domain
Lx=10
θ=24º 45
spanwise
Prism: spectral-element/Fourier

5. Mean flow: u(x,y,z,t) = U(y,z) streamwise velocity
integrate over time t and over direction x parallel to bands
streamwise velocity
Tsukahara et al. y z
Tsukahara et al.
cross-channel velocity y
Tsukahara et al.
turbulent kinetic energy y
spanwise velocity y

6. Time-averaged turbulent-laminar pattern
streamwise vorticity
on top plate
streamwise
direction z z y x y x
spanwise velocity
in cross-channel planes

7. Time-averaged velocity
streamwise x
y=0.9 z x
y=0.5 z y
between plates z x
y=-0.5 z x
y=-0.9 z

8. Time-averaged streamwise vorticityx
top plate z y
between plates z
bottom plate x z

9. Instantaneous streamwise vorticity
normal to streamwise direction y z
on upper plate
streamwise x z

10. Reynolds number survey
parabolic
plug
amplitude
phase
time
Reynolds
streamwise velocity profiles
mid-channel
spanwise velocity
z-Fourier transform of
mid-channel spanwise velocity

11. Thresholds via probability distributions of z-Fourier transforms

12. close to umean and Re-dependent
Velocity of bands:
close to umean and Re-dependent
×103
units of
time