Vibration and flow conditions needed to produce structured bubbling: Correlation coefficient versus (A) vibration frequency, (B) vibration amplitude, and (C) U/Umf. Each panel of images varies a property while keeping other properties constant: (A) Constant properties: vibration amplitude = 4.5 mm, U/Umf = 1.4. (B) Constant properties: vibration frequency = 5 Hz, U/Umf = 1.4. (C) Constant properties: vibration frequency = 5 Hz, vibration amplitude = 4.5 mm. The initial bed height is 10 cm in A–C. The right-pointing triangles in C denote experiments without system vibration.