Many nonlinear systems present transitions that are affected by the
presence of noise or fluctuations. Of particular interest are
bifurcations that occur when the system is forced by a fluctuating
field. Magnetohydrodynamic examples are the dynamo and mag-
netorotational instabilities observed in liquid metals, where the
velocity field is highly turbulent at the instability onset. In the
field of fluid mechanics, the existence of finite-wavelength
instabilities in turbulent flows is puzzling. Prigent et al. (2002)
report experiments on both plane Couette and Taylor-Couette flow that
show finite-wavelength modulations of their basic turbulent flows. In a
recent paper Ravelet et al. (2004) present experiments on a highly
turbulent von Kármán flow that show a hysteretic bifurcation for Re ~
105. The exchange of stability is realized between mean flows of
different average symmetry, which are actually never realized at any
given time. These results are striking because although bifurcations
and symmetry breaking occur on the route to turbulence, in the limit Re
? ° the flow is expected to recover the system basic symmetries.
This project concerns the experimental study of a transition observed
in a free-surface Taylor-Couette flow at Re ~ 106. A highly turbulent
base state, for which the mean flow is axisymmetric and thus respects
in average the symmetries of the driving apparatus, bifurcates to a
turbulent gravity-wave state that has an azimuthal wavenumber m = 1.
References
- "Hysteretic gravity-wave bifurcation in a highly turbulent swirling
flow ", N. Mujica and D.P. Lathrop, J. Fluid Mech. vol. 551, pp. 49-62.
(2006).
- "Large-scale finite-wavelength modulation within turbulent shear
flows", A. Prigent, G. Grégoire, H. Chaté, O. Dauchot, & W. van
Saarloos, Phys. Rev. Lett. Vol. 89, 164501, (2002).
- "Multistability and memory effect in a highly turbulent flow:
evidence for a global bifurcation", F. Ravelet, L. Marié, A.
Chiffaudel, & F. Daviaud, Phys. Rev. Lett. Vol. 93, 164501, (2004).
People involved:
Cristobal Arratia (Universidad de Chile)
Daniel P. Lathrop (University of Maryland)
Nicolás Mujica (Universidad de Chile)
