We investigate the Lagrangian properties of homogeneous, stratified turbulence at different Brunt-Väisälä frequencies.We show increasing vertical confinement of trajectories with increasing stratification strength highlighting the predominantly horizontal dynamics of these flows. We characterize the intermittent properties of the fluid motion by computing the probability distributions of the horizontal and vertical Lagrangian velocity increments and Lagrangian horizontal velocity structure functions, and find that horizontal velocity differences display intermittency at higher orders. Our results provide an understanding of the Lagrangian dynamics in stratified turbulence, and highlight the importance of buoyancy forces in shaping the Lagrangian statistics in these flows.

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