In fluid dynamics, we like to classify flows as laminar–smooth and orderly–or turbulent–chaotic and seemingly random–but rarely is any given flow one or the other. Many flows start out laminar and then transition to turbulence. Often this is due to the introduction of a tiny perturbation which grows due to the flow’s instability and ultimately provokes transition. An instability can typically take more than one form in a given flow, based on the characteristic lengths, velocities, etc. of the flow, and we classify these as instability modes. In the case of the vertical rotating viscous liquid jet shown above, the rotation rate separates one mode (n) from another. As the mode and rotation rate increase, the shape assumed by the rotating liquid becomes more complicated. Within each of these columns, though, we can also observe the transition process. Key features are labeled in the still photograph of the n=4 mode shown below. Initially, the column is smooth and uniform, then small vertical striations appear, developing into sheets that wrap around the jet. But this shape is also unstable and a secondary instability forms on the liquid rim, which causes the formation of droplets that stretch outward on ligaments. Ultimately, these droplets will overcome the surface tension holding them to the jet and the flow will atomize. (Video and photo credits: J. P. Kubitschek and P. D. Weidman)
