An "objective" definition of potential vorticity. Generalized evolution equation and application to the study of coastal upwelling instability

2023

Article référencé dans le Web of Science WOS:001110871700001

Morel Y., Morvan Guillaume, Benshila R., Renault Lionel, Gula J., Auclair F.

Ocean Modelling, 2023, 186, p. 102287 [18 p.] ISSN 1463-5003

In this paper, we propose a form for potential vorticity (PV), rescaled using the Lorenz's rearranged density profile, the novelty being that we here take into account its time evolution. We argue this rescaled PV is more representative of the dynamics, in particular to evaluate the respective impact of mixing and friction on the generation of geostrophic circulation. The impact of mixing at global scale, which only modifies the global stratification at rest, is taken into account in the evolution equation of this "objective"definition of PV, in the sense that it scales the PV changes with respect to its effect on the circulation. Numerically, we show that all terms can be calculated coherently using a single computation cell.We illustrate our purpose by studying the instability of coastal upwelling currents, using a numerical model at high resolution. The configuration is a periodic flat channel on the f-plane with vertical walls at the southern and northern boundaries. A constant wind is applied over a fluid at rest with an initial linear stratification. An upwelling current forms at the northern coast. After a few days, instabilities develop and vortices eventually emerge with surface intensified cyclones and subsurface anticyclones. We show that these instabilities and eddies are associated with (rescaled) PV anomalies, triggered by mixing and friction.We describe rescaled PV budgets in a layer bounded between the surface and an isopycnal level. Eulerian and Lagrangian diagnostics allow to analyze irreversible PV production terms, distinguishing the influence of advection, friction (associated with wind stress) and mixing. We find that friction plays the main role, generating negative PV anomalies, while mixing acts to dampen this negative PV production. The association of this negative PV anomaly with the outcropping front leads to the baroclinic destabilization of the upwelling front, creating subsurface anticyclonic vortices and surface intensified cyclonic vortices. Varying the strength of the wind forcing shows that mixing is the most sensitive process, with a net effect that is strongly reduced or even reversed with moderate to weak winds. When the dynamics is fully turbulent, with filaments and vortices of small sizes, the PV production by mixing and friction is enhanced but the Lagrangian diagnostics are more difficult to analyze, since fluctuations at grid scale become significant and numerical effects - associated with imperfections of the numerical schemes - spoil the PV budget calculation.

Sciences fondamentales / Techniques d'analyse et de recherche [020] ; Limnologie physique / Océanographie physique [032]

Fonds IRD [F B010088736]

fdi:010088736