Turbulent-laminar banded patterns

in plane Poiseuille flow

Laurette TuckermanPMMH-ESPCI-CNRS (France)

Dwight BarkleyUniversity of Warwick (United Kingdom)

Plane Poiseuille flow

What about for intermediate Reynolds numbers?

?

First simulations2004-2005

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

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)

Time-averaged turbulent-laminar pattern

spanwise velocityin cross-channel planes

streamwise vorticityon top plate streamwise

direction

x

z

x

zy

y

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

Time-averaged streamwise vorticity

top plate

bottom plate

between plates

streamwise

x

x

y

z

z

z

Instantaneous streamwise vorticity

normal to streamwise direction

on upper plate

z

x

y

streamwise

z

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

Thresholds via probability distributions of z-Fourier

transforms

Velocity of bands: close to umean and Re-dependent

units of

×103

time