The propagation of a compression wave for and The black arrows designate the positions of wave front and the graph beside figure (c) shows velocities of particles at the center of bed .
The propagation of types 1 and 2 expansion wave for the case of and shown in snapshots taken at , 0.876, and 1.002 with : the Type 1 expansion wave propagates downward from the free surface and its wavefront is seen in the velocity plot as the place where the slope of particle velocities increases. The Type 2 expansion wave propagates upward from the bottom wall. The wave front of Type 2 expansion wave is distinguished from the velocity plot since particles behind the Type 2 expansion wave are moving downward. (The velocity graphs are for the particles on the center line.)
Average velocity profiles: (a) and (b) . For all, .
(a) History of the stress at the bottom wall and position of the bottom wall. (b) Snapshots showing the history of wave propagation before, during, and after convection for : convection is observed in the bed at to 1.374 in this figure. [Marked points i–xii in (a).] Here: , , and .
(a) The stress history at the bottom wall and the bottom wall position showing the convection period. (b) History of velocity and wave propagation before, during, and after convection for convection is observed in the bed at . [Marked as points i–xii in (a).] Here , , and .
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