Convection rolls in a rotating box filled with beads

Fill a box partially with a dry mixture of beads and rotate it slowly. As it is known from granular physics segregation patterns appear. Now put in more beads so that the box is almost completely filled and the beads can't move freely. Do we expect something unusual? Basically, only the quantity of beads was changed in the experiment but the results of that modification are clearly visible. Convection rolls are now observed that possess the same phenomenology as rolls in liquids or shaken granulates. The answer of that could not be easily defined and explained as in the cases of instable liquids that have a gradient (i.e. in density or temperature) or shaken systems that are strongly agitated. Besides the simplicity of the experiment known mechanisms for granular convection could not be applied