The Route to Chaos and Turbulence in Annular Electroconvection
The Route to Chaos and Turbulence
in Annular Electroconvection
Ph.D. thesis, Unpublished, Sept. 2007.
Department of Physics,
University of Toronto,
60 St. George St., Toronto, Ontario, Canada M5S 1A7.
Convection is essential and ubiquitous in Nature. For a century, classical thermal convection,
or Rayleigh-Bénard convection, has been a central paradigm for laboratory
studies. This thesis concerns an electrical analogue of Rayleigh-Bénard convection -
electroconvection in a thin fluid film. This complementary system was studied with
a combination of experiment, theory, and numerical simulation. The fluid film is
driven to convect by a critical applied electric potential interacting with a charge
inversion, in direct analogy with the buoyancy inversion that drives thermal convection.
As the imposed voltage is increased, electroconvection proceeds from steady,
laminar patterns through time-dependent flows and eventually into chaotic and turbulent
regimes. The experimental procedure consisted of precise measurements of
current-voltage (IV) characteristics when a DC voltage was applied to an annular
film between two concentric electrodes. The onset of convection was found by a
change in the slope of the IV curve; unsteady flow was indicated by a large increase
in current fluctuations. From the IV measurements, the corresponding dimensionless
charge transport, or Nusselt number Nu, was determined as a function of the electric
forcing, characterized by the dimensionless Rayleigh number R. A power-law relationship Nu ~ R^gamma
was observed in the turbulent convection regime when R > 10^4.
The influence of the annular geometry, characterized by aspect ratio Gamma, on this scaling
was investigated. A scaling theory was developed which explains the power law and its dependence on Gamma. The corresponding theory for thermal convection does not account
for this Gamma dependence. In addition, a direct numerical simulation was constructed
using a pseudo-spectral method, based on realistic governing equations. The simulation
affords deep insights into the flow dynamics, charge distribution and electric
potential of the electroconvection instability and its route to turbulence, including
for the case of an externally applied shear.
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