Lagrangian stochastic modelling of oceanic transport: A comparative study

A key goal in applied scientific systems involving turbulent fluids is the practical ability to predict the transport properties for substances and objects immersed in the Ocean over moderate to long periods of time.; The Lagrangian Stochastic Model (LSM) framework is a promising approach under active development. The basic idea is to model a representative (Lagrangian) particle of the immersed substance by a low-dimensional system of equations, with the influence of the turbulent environment represented in terms of parameterized coefficients and random noise.; In this thesis LSM are analyzed by examining systematically the predictions these approximations produce for a passive scalar advection model consisting of a shear flow with a fluctuating cross sweep. This model has a general geometric structure of a jet flow with transverse disturbances, which occur in a number of contexts, and it encompasses a wide variety of possible spatio-temporal statistical structures for the velocity field, including strong long-range correlations. Our comparative study illustrates the strength and weaknesses of the Lagrangian Stochastic reduction.