Diapositive 1F.Daviaud
B. Dubrulle, L. Marié, F. Ravelet, P. Cortet
Transition to turbulence and turbulent bifurcation in a von Karman flow
VKS team
Turbulent von Karman flow
fluid: water and glycerol-water
Mean on 60 s
Re = 90
Stationary axisymmetric
*
Time spectra as a function of Re
Re = 330
Re = 380
Re = 440
Time spectra as a function of Re
Re = 1000
Re = 4000
*
Rec= 330
Ret = 3300
Developed turbulence
Globally supercritical transition via a Kelvin-Helmholtz type instability of the shear layer and secondary bifurcations
Transition to turbulence:
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Multiplicity of solutions
Turbulent Bifurcation of the mean flow
Bifurcated flow (b) : no more shear layer broken symmetry
two cells
one state
one cell
two states
Symmetry broken:
Re = 3.105
Turbulent Bifurcation
Re = 3.105
Kp = Torque/ρRc5 (2π f)2 ΔKp= Kp1- Kp2
θ = (f2-f1) / (f2+f1)
Stability of the symmetric state
Statistics on
P(tbif>t)=A exp(-(t-t0)/τ)
Stability of the symmetric state
symmetric state
marginally stable
Mutistability = f(Re)
Forbidden zone with velocity regulation
θ = (F1-F2)/(F1+F2)
g = (Kp1-Kp2)/(Kp1+Kp2)
1 cell (velocity)
2 cells (velocity)
*
Intermittent states (i)
θ = (F1-F2)/(F1+F2)
g = (Kp1-Kp2)/(Kp1+Kp2)
intermittent states (i)
*
q , f
Kp1 ~ Kp2,
*
Meridional annulus
Small curvature,
diameter 3/4
Position of the shear layer = f(θ)
SPIV measurements
θc = 0.09
θc = 0.175
without annulus
with annulus
stagnation point
r = 0.7
Transition 1 cell - 2 cells  at θc= ± 0.175
θ = (F1-F2)/(F1+F2)
<Kp>
Transition at θc= ± 0.175
Mean ΔKp is continuous
Measurements : 2 – 200 min
Transition at θc= ± 0.175
θc = 0.174
θ = (F1-F2)/(F1+F2)
*
Origin of erratic field reversals
observed in VKS experiment?
Bifurcations in turbulent flows: theory?
von Karman : turbulent bifurcation
Prigent, Dauchot et al.