The Imprint of Beta on Individual Lagrangian Trajectories

We use a novel statistical method to show that large scale anisotropies in fluid motion imprint themselves onto the observable second-order velocity statistics of individual Lagrangian trajectories. Using trajectories from forced-dissipative quasigeostrophic turbulence on a beta-plane, we demonstrate that a Rhine’s scale modified for Lagrangian trajectories can be determined from individual trajectories. To estimate this parameter we construct a stochastic model that treats the complex valued velocity of each trajectory as a Matern process, but additionally supposes the existence of a time scale above which the rotary coherence linearly approaches unity and therefore becomes fully anisotropic. Fitting this model to trajectories from both anisotropic (beta-plane) and isotropic (f-plane) experiments shows that, indeed, the model can be used to determine the existence of such a time scale and beta can be recovered almost exactly.