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Sideband Instability of Modulated Traveling Wave Convection

  • M. de la Torre Juárez
  • W. Zimmermann
  • I. Rehberg
Part of the NATO ASI Series book series (NSSB, volume 225)

Abstract

It has been shown theoretically (Riecke et al. 1988, Walgraef 1988), that in a system exhibiting a supercritical Hopf bifurcation a temporal modulation of the driving force with a modulation frequency ωm of about double of the Hopf frequency can stabilize standing waves (SW). An experimental verification was presented (Rehberg et al. 1988) for the electro-hydrodynamic convection of liquid crystals, where the driving ac voltage is modulated as V(t)=Vc·cos(ω·t)·[1+ε+b·cos(ωm·t)], with b being the modulation and e the reduced driving amplitude. The theoretical model is very similar to the one describing parametrically excited waves which are known to exhibit Benjamin-Feir turbulence that is characterized by a transfer of energy from the fundamental Fourier mode to the side bands (Craik 1985). When increasing e for a constant modulation amplitude b the simplified theoretical model predicts a supercritical bifurcation from SW to modulated traveling waves (TW). In the experiment SW become unstable via a different mechanism which we clarify here. The scenario includes the appearance of the sideband instability, defects and stable undulated rolls of a very short wavelength.

Keywords

Hopf Bifurcation Standing Wave Travel Wave Oscillatory Convection Supercritical Bifurcation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • M. de la Torre Juárez
    • 1
  • W. Zimmermann
    • 1
  • I. Rehberg
    • 1
  1. 1.Physikalisches InstitutUniversität BayreuthGermany

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