Lagrangian dispersion in sheared flow

Two-dimensional Lagrangian trajectories are studied near an idealized ocean front with shear and convergence plus an uncorrelated random walk. Applications include fixed-depth drifters and plankton patches with perfect depth regulation. In the drifter case, observed trajectories need to be interpreted in terms of the ensemble of possibilities. In the plankton case, surveys of abundance and distribution need to be interpreted similarly if vital rates are to be deduced, often involving an individual-based model incorporating both biotic rates and motion. In both cases, forecasting requires such an ensemble description; and both model skill assessment and data assimilation requires knowledge of the ensemble statistical properties. Closed-form expressions are presented for mean and covariance of positions, and for the important case of model-data misfit. The analysis is extended to include plankton parcels – mass and position – for parcels moving within a spatially variable growth rate, originating for example in a temperature gradient. The solutions support the interpretation of Lagrangian displacement data in the presence of shear; evaluating Lagrangian misfit with simulation results; and the use of individual-based models in spatially explicit applications.