Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS...
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Transcript of Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS...
![Page 1: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/1.jpg)
Turbulent-laminar banded patterns
in plane Poiseuille flow
Laurette TuckermanPMMH-ESPCI-CNRS (France)
Dwight BarkleyUniversity of Warwick (United Kingdom)
![Page 2: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/2.jpg)
Plane Poiseuille flow
What about for intermediate Reynolds numbers?
?
![Page 3: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/3.jpg)
First simulations2004-2005
![Page 4: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/4.jpg)
our tilted domain
(⊥ to bands)z
Our simulations
simulation of Tsukahara et al.
Prism: spectral-element/Fourier
45spanwise
streamwise102 Lz=40
Lx=10
θ=24º
x(|| to bands)Lx=10
![Page 5: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/5.jpg)
streamwise velocityTsukahara et al.
Tsukahara et al.cross-channel velocity
Tsukahara et al.
turbulent kinetic energy
spanwise velocity
Mean flow:
yz
y
y
y
integrate over time t and over direction x parallel to bands
u(x,y,z,t) = U(y,z)
![Page 6: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/6.jpg)
Time-averaged turbulent-laminar pattern
spanwise velocityin cross-channel planes
streamwise vorticityon top plate streamwise
direction
x
z
x
zy
y
![Page 7: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/7.jpg)
y=0.9
y=0.5
y=-0.5
y=-0.9
Time-averaged velocity
between plates
streamwise
z
x
y
z
z
z
x
x
x
z
![Page 8: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/8.jpg)
Time-averaged streamwise vorticity
top plate
bottom plate
between plates
streamwise
x
x
y
z
z
z
![Page 9: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/9.jpg)
Instantaneous streamwise vorticity
normal to streamwise direction
on upper plate
z
x
y
streamwise
z
![Page 10: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/10.jpg)
time Reynolds
Reynolds number survey
mid-channelspanwise velocity
streamwise velocity profiles
z-Fourier transform of mid-channel spanwise
velocity
para
bol
icp
lug
amplitude phase
![Page 11: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/11.jpg)
Thresholds via probability distributions of z-Fourier
transforms
![Page 12: Turbulent-laminar banded patterns in plane Poiseuille flow Laurette Tuckerman PMMH-ESPCI-CNRS (France) Dwight Barkley University of Warwick (United Kingdom)](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649f535503460f94c7828f/html5/thumbnails/12.jpg)
Velocity of bands: close to umean and Re-dependent
units of
×103
time