Numerical Analysis of the Optimality of Vortex Rings

Sphagnum moss disperses its spores by launching a vortex ring from a pressurized capsule, which carries the spores to heights above the turbulent boundary layer where they can be held aloft indefinitely. Here we use numerical simulations of peat moss explosions to assess the optimality of the vortex rings produced by Sphagnum capsules. Explosions are simulated using Ansys FLUENT for an axisymmetric geometry. Simulated flows are analyzed with Matlab to determine the fraction of circulation contained in the leading vortex ring. We find that for pressures above 1.5 atm in the capsule that significant circulation from the explosion does not make it into the leading vortex ring. This indicates that the optimal vortex ring, which is the strongest vortex ring that can contain all the circulation of the explosion, occurs at 1.5 atm. A comparison of the simulated trajectories at different pressures to video data of peat moss explosions indicates that Sphagnum capsules are pressurized to approximately 1.5 atm and are thus creating optimal vortex rings. Optimal vortex ring formation has been observed in a number of animals including squid, jellyfish, and cuttlefish, but this is the first observation of optimal vortex rings formed by plants.