Oscillations and defect turbulence in a shallow fluidized bed
  We report an experimental study of the dynamics of an air-fluidized thin granular layer. Near-onset behavior of this shallow fluidized bed was described in the earlier paper (Tsimring et al, 1999). Above the threshold of fluidization the system exhibits a Hopf bifurcation as the layer starts to oscillate at a certain frequency due to a feedback between the layer dilation and the airflow drag force. After application of temporal band-pass filtering of this frequency we discovered the spatio-temporal dynamics in the form of defect turbulence. This type of dynamics is natural for spatio-temporal systems close to the threshold of a Hopf bifurcation. At high flow rates, low-frequency short-wavelength structures appear in addition to the long-wavelength excitations. A simple model describing the instability and occurrence of oscillations in a shallow fluidized bed, is proposed. 
D.K.Clark, L.S. Tsimring, and I.S.Aranson