Four Types of Chaotic Dynamics
in Cellular Flames

Experimental Observations of Ordered States

In a previous paper (Gorman, el-Hamdi and Robbins, 1993) some of the characteristics of ordered states of cells were described. Ordered states consist of one or more concentric rings of cells. These states are labeled according to the number of cells in each ring, starting from the outside moving inward. The 11/4 ordered state, with eleven outer cells surrounding four inner cells, is shown in Figure la.

The five successive frames of videotape, which run down the page, indicate a steady pattern. However, the power spectrum of the light intensity shown in Figure 2a, has a broad background extending from 0 to 25 Hz, with a shoulder about 7 Hz. Such a power spectrum is characteristic of every ordered state.

The temporal evolution of this state is difficult to depict on paper. The motion of the individual cells does not change the overall appearance of the ring pattern so successive frames of videotape look identical. An image processing technique is used to demonstrate the motion of the cells. In Figure 3 two frames of the 12/6/1 state, separated by nine frames, are digitized and then subtracted. The absolute values of the differences are displayed as bright regions and the resulting image is multiplied by fifteen. The final differential image, displayed in Figure 3, shows that the intensity differences are strongest near the cusps and folds at the boundaries of the cells. All the observed ordered states exhibit these small amplitude chaotic oscillations in which individual cells change their size and shape in a subtle, irregular manner.

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