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.

The interaction between two oppositely travelling, horizontally offset, antisymmetric quasi-geostrophic hetons

We investigate numerically the nonlinear interactions between hetons. Hetons are baroclinic structures consisting of two vortices of opposite sign lying at different depths. Hetons are long-lived. They most often translate (they can sometimes rotate) and therefore they can noticeably contribute to the transport of scalar properties in the oceans. Heton interactions can interrupt this translation and thus this transport, by inducing a reconfiguration of interacting hetons into more complex baroclinic multipoles. More specifically, we study here the general case of two hetons, which collide with an offset between their translation axes. For this purpose, we use the point vortex theory, the ellipsoidal vortex model and direct simulations in the three-dimensional quasi-geostrophic contour surgery model. More specifically, this paper shows that there are in general three regimes for the interaction. For small horizontal offsets between the hetons, their vortices recombine as same-depth dipoles which escape at an angle. The angle depends in particular on the horizontal offset. It is a right angle for no offset, and the angle is shallower for small but finite offsets. The second limiting regime is for large horizontal offsets where the two hetons remain the same hetonic structures but are deflected by the weaker mutual interaction. Finally, the intermediate regime is for moderate offsets. This is the regime where the formation of a metastable quadrupole is possible. The formation of this quadrupole greatly restrains transport. Indeed, it constrains the vortices to reside in a closed area. It is shown that the formation of such structures is enhanced by the quasi-periodic deformation of the vortices. Indeed, these structures are nearly unobtainable for singular vortices (point vortices) but may be obtained using deformable, finite-core vortices.

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.