Applications of stochastic particle models to oceanographic problems

Three Markovian particle models are reviewed, providing a hierarchy of increasingly detailed descriptions of particle motion and dispersion. Model 1 assumes that the scales of turbulent motion are infinitesimal, and it is equivalent to the advection-diffusion equation. Model 2 introduces a finite scale T for the turbulent velocity,, and model 3 introduces an additional scale for the acceleration, T a < T. The models are compared with oceanographic data from drifting buoys, which satisfactorily approximate the motion of ideal particles in mesoscale turbulent fields. Model 2 appears to provide a satisfactory description of the second order particle statistics in the upper ocean. Model 3 appears to be applicable to deep ocean data with some questions still remaining open. Some examples of analytical calculations of dispersion using the models are shown for some simple oceanographie flows. The results indicate that the introduction of finite scales of turbulence plays an important role not only at initial times, t < T, but also for dispersion at longer times if the mean flow is strongly dependent on space and time, so that the scales of the mean flow and of the turbulence are of the same order. In these situations, which are characteristics of important current systems in the ocean, the advection-diffusion equation is not accurate, and the use of stochastic models such as 2 and 3 is especially indicated. Two different classes of applications for the models are reviewed: “direct” applications, where the models are directly integrated to compute dispersion, and “inverse” applications where the models are used to extract information about the velocity field from the Lagrangian data. A discussion is also provided on future applications of the models to study more general classes of oceanic flows including coherent structures.