Search

Taking advantage of alternative expressions for potential vorticity (PV) in divergence forms, we derive balances between volume integral of PV and boundary conditions, that are then applied to practical computations of PV: • We propose a new method for diagnosing the Ertel potential vorticity from model output, that preserves the balances; • We show how the expression of PV can be derived in general coordinate systems. This is here emphasised with isopycnic coordinates by generalising the PV expression to the general Navier-Stokes equations; • We propose a generalised derivation for the Haynes-McIntyre impermeability theorem, which highlights the role of the bottom boundary condition choice (e.g. no-slip vs free-slip) and mixing near the bottom boundary for the volume integral of PV. The implications of balances between volume integral of PV and boundary conditions are then analysed for specific processes at various scales: • At large scale, we show how an integral involving surface observations (derived from satellite observations) is linked to the integral of PV within a layer (between two isopycnals). This surface integral can be calculated for models and observations and can be used for validation; • At mesoscale or sub-mesoscale, we analyse the relationship between net PV anomalies and net surface density anomalies for idealised vortices and 2D fronts. This can help determining vortex or jet structures for idealised studies or empirical methodologies; • We also confirm and integrate previous results on the modification of PV within a bottom boundary layer into a single diagnostic taking into account the effect of density and velocity modifications by diabatic processes along the topography and diapycnal mixing within the boundary layer. • Ertel potential vorticity (PV) expressions in divergence form improve PV diagnostics in models. • Balances are derived between volume integral of PV and boundary conditions. • Practical numerical computations of PV, preserving balances, are proposed. • The implications of balances are examined for selected processes. [ABSTRACT FROM AUTHOR]

We investigate the stability of a composite cyclone representative of Arabian Sea eddies using a high resolution primitive equation model. We observe that the eddy is unstable with respect to a mixed barotropic/baroclinic instability, leading to the growth of an azimuthal mode 2 perturbation. The latter deforms the eddy, which eventually evolves into a tripole after about 4 months of simulation. The presence of a critical level for the most unstable mode generates sharp fronts in the surface mixed layer where the Rossby number is large. These fronts then become unstable, and this generates submesoscale cyclones and filaments. Near these fronts, diapycnal mixing occurs, causing the potential vorticity to change sign locally, and symmetric instability to develop in the core of the cyclonic eddy. Despite the instabilities, the eddy is not destroyed and remains a large-scale coherent structure for the last 6 months of the simulation. Looking at Sea Surface Height only, the composite eddy evolves little, and fairly represents the eddy observed in the altimetry which can live for several months. The study of this simulation thus illustrates the numerous kinds of instabilities which may occur in large cyclonic eddies but cannot be captured directly by altimetric data. • A composite cyclone representative of the Arabian Sea eddies is unstable. • Submesoscale features are generated at the surface via hydrodynamical instabilities. • Currently available data cannot capture the instability occurring in the eddy. [ABSTRACT FROM AUTHOR]