Lagrangian description of the unsteady flow induced by a single pulse of a jellyfish

Lagrangian statistics and pair dispersion induced by an isolated pulse of a small jellyfish, Aurelia aurita, were quantified and characterized using 3D particle tracking velocimetry (3D-PTV). Probability density functions (PDF) of the Lagrangian velocity components indicated more intense mixing in the radial direction and revealed three stages dominated by flow acceleration, mixing, and dissipation. Time evolution of the Lagrangian acceleration variance further illustrates each phase. During the mixing phase, the flow shares characteristics of homogeneous isotropic turbulence. In addition, we show that a single pulse may induce rich wake dynamics characterized by pair dispersion with a super-diffusive t(3) regime due to large-scale flow inhomogeneity, followed by a coherent t(2)-Batchelor scaling and then t(1)-Brownian motions. The first trend occurred in the accelerated flow, whereas the second dynamic was observed in the mixed wake and depended on the initial separation. The Brownian motion was present in the late stage dominated by flow dissipation. Kolmogorov microscales during the fully mixed phase were obtained with three distinct approaches, namely, Heisenberg-Yaglom relation of the Lagrangian acceleration variance, the fluctuating rate of the strain tensor in the Eulerian frame of reference as well as the Batchelor scaling in pair dispersion, which showed good agreement.