Consider a bottle of orange juice with pieces of the fruit gathered at the bottom of the bottle. You need to shake the bottle to evenly distribute the pieces in the bottle.
The first part of the process seems straight forward, just giving the bottle a few sharp shakes to create turbulence and destroy the conglomerate of fruity pieces.
However, what's the most energy-efficient strategy to create a global flow to distribute the stuff?
Since at the start of the process, the interesting parts are gathered at the bottom of the bottle, a strong axial component would be neccesary, for energy reasons a laminar flow would be interesting (assuming the dispersal has allready happened).
Edit to add: Efficient means the least energy input from me. If your mixing method involves throwing the bottle off a cliff, the energy for cyrrying it up there counts.
Where I live, juice comes in round bottles or in boxy containers.