On Lagrangian stochastic modelling of material transport in oceanic gyres

The introduction of ‘spin’ into second-order Lagrangian stochastic models (LSM) for stationary turbulence with broken reflectional symmetry is shown to result in the prediction of super-diffusive transport at intermediate times and the occurrence of anomalously large normal diffusion at later times. These characteristic features of material transport in oceanic gyres cannot be reproduced by two-dimensional first-order LSM. A correspondence is established between high-dimensional, low-order LSM and lower-dimensional, higher-order LSM. It is found that time-dependent spin statistics allow for the coexistence of rotating particle trajectories and non-oscillatory Lagrangian velocity autocorrelation functions.