Time evolution of the height of the two-layer interface and the amplitude of the instability. (a) Growth of the interfacial heights with time for the same experiment shown in Figure
3. Here, a vertical section whose location is indicated in the left photo is cut from each image. The images are aligned horizontally at an interval of 0.033 s as a function of time. Yellow and pink lines trace the upper surface of the granular layer and the two-layer interface, respectively. I, II, and III indicate the three stages which are defined according to the relative amplitude δ z′ (see text for the details). Stars correspond to the same timing as shown in Figure
3a. (b) Growth of the amplitude (δ z) with time for the same experiment shown in (a). The three stages are defined according to the relative amplitude (δ z′) values of 0.1 and 0.6 mm. Diameters of the red and white particles which comprise the lower and upper layers, respectively, are indicated for comparison. The amplitude initially increases exponentially with time. At t ∼ 4.3 s, the upper tip of the flame structure detaches and the amplitude slightly decreases. A red arrow indicates the peak amplitude. This amplitude remains after the shaking stops at 5 s.