A two‐dimensional model of mesoscale frontogenesis in the ocean

Abstract

A two-dimensional primitive equation model conserving potential vorticity is used to simulate the effect of a horizontal barotropic deformation field on a pre-existing isopycnic potential vorticity gradient. The novel feature of the prognostic model is that it accurately describes the development of the density and velocity distributions up to local Rossby number 0.5 and beyond. The model coordinates are based in the vertical on quasi-isopycnic vertical coordinates and in the horizontal on geostrophic coordinates. The model is integrated forward in time for three days creating a density front and a jet of 0.4 m s-] in the surface layers. Cross-jet velocities are one order of magnitude smaller. Conservation of potential vorticity leads to a modulation of spacing between isopycnals as both the cyclonic and anticyclonic vorticity associated with the horizontal shear of the accelerating jet increase. Vortex stretching and compression sustain a strong vertical circulation. The paper shows how the jet kinetic energy is limited by the amount of available potential energy in a catchment area defined by the extent of the region of confluence. The jet becomes shallower as frontogenesis approaches this limit.The model is also applicable to the development of permanent streams in the large-scale circulation of the upper ocean, by slow (order one month) frontogenesis due to gyre-scale deformation acting on an isopycnic potential vorticity gradient in the seasonal thermocline.The vigorous upwelling on the anticyclonic side of the jet raises nutrients through the euphotic zone, increasing primary productivity. This explains observed meoscale modulations of biomass.

Biological and chemical signs of upward motions in permanent geostrophic fronts of the western Mediterranean

“…Moreover, in such simulations, the timescale needed to achieve a steady state is probably overestimated, owing to the crude biological model [Zakardjian and P•ieur, 1994 Second, it is unlikely that the stratification of the water column will remain constant under conditions of upward advection, which is supposed to shift the isopycnals toward the surface. Vertical motions in front, and more generally secondary circulations, are related to frontogenesis [Mooers, 1977;Hoskins, 1982], because of large-scale geostrophic forcings [e.g., Woods, 1988;Bleck et al, 1988;Pollard and Regier, 1992] or wave-like instabilities of the geostrophic jet [e.g., Onken, 1992;Wang, 1993;Barth, 1994]. All these processes imply rapid time evolution of the density, velocity, and vorticity of the front.…”

On the relevance of diapycnal mixing for the stability of frontal meanders

“…. The deformation constant is chosen as characteristic of oceanic deformation fields (Bleck et al, 1988), while the simulation period corresponds to the time required by different phases of Gulf Stream meanders to pass through a fixed position in the northern Blake Plateau (Rodríguez-Santana et al, 1999).…”

Modeling a Limited Region of the Ocean

“…The higher resolution model runs exhibit a greater length of frontal zone across which properties change rapidly. Since much of the vertical motion in the ocean occurs at fronts [19,1], resolving the frontal structure and eddies has considerable implications in modeling the vertical exchange of properties between the surface and deep ocean. Increased resolution enhances, for example, the vertical transport of nutrients for phytoplankton production [7], heat and salt fluxes, and the exchange of oxygen, carbon dioxide, and other atmospheric gases.…”