Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations

The modelling of diffusive terms in particle methods is a delicate matter and several models were proposed in the literature to take such terms into account. The diffusion velocity method (DVM), originally designed for the diffusion of passive scalars, turns diffusive terms into convective ones by expressing them as a divergence involving a so-called diffusion velocity. In this paper, DVM is extended to the diffusion of vectorial quantities in the three-dimensional Navier–Stokes equations, in their incompressible, velocity–vorticity formulation. The integration of a large eddy simulation (LES) turbulence model is investigated and a DVM general formulation is proposed. Either with or without LES, a novel expression of the diffusion velocity is derived, which makes it easier to approximate and which highlights the analogy with the original formulation for scalar transport. From this statement, DVM is then analysed in one dimension, both analytically and numerically on test cases to point out its good behaviour.

A four-dimensional analysis of the thermal structure in the Gulf of Lion

The Theoretical and Experimental Tomography in the Sea Experiment (THETIS 1) took place in the Gulf of Lion to observe the evolution of the temperature field and the process of deep convection during the 1991-1992 winter. The temperature measurements consist, of moored sensors, conductivity-temperature-depth and expendable bathythermograph surveys, ana acoustic tomography. Because of this diverse data set and since the field evolves rather fast, the analysis uses a unified framework, based on estimation theory and implementing a Kalman filter. The resolution and the errors associated with the model are systematically estimated. Temperature is a good tracer of water masses. The time-evolving three-dimensional view of the field resulting from the analysis shows the details of the three classical convection phases: preconditioning, vigourous convection, and relaxation. In all phases, there is strong spatial nonuniformity, with mesoscale activity, short timescales, and sporadic evidence of advective events (surface capping, intrusions of Levantine Intermediate Water (LIW)). Deep convection, reaching 1500 m, was observed in late February; by late April the field had not yet returned to its initial conditions (strong deficit of LIW). Comparison with available atmospheric flux data shows that advection acts to delay the occurence of convection and confirms the essential role of buoyancy fluxes. For this winter, the deep. mixing results in an injection of anomalously warm water (Delta T similar or equal to 0.03 degrees) to a depth of 1500 m, compatible with the deep warming previously reported.