Abstract
Oceanic and atmospheric dynamics are often interpreted through potential vorticity, as this quantity is conserved along the geostrophic flow. However, in addition to potential vorticity, surface buoyancy is a conserved quantity, and this also affects the dynamics. Buoyancy at the ocean surface or at the atmospheric tropopause plays the same role of an active tracer as potential vorticity does since the velocity field can be deduced from these quantities. The surface quasi-geostrophic model has been proposed to explain the dynamics associated with surface buoyancy conservation and seems appealing for both the ocean and the atmosphere. In this review, we present its main characteristics in terms of coherent structures, instabilities and turbulent cascades. Furthermore, this model is mathematically studied for the possible formation of singularities, as it presents some analogies with three-dimensional Euler equations. Finally, we discuss its relevance for the ocean and the atmosphere.
Highlights
A large fraction of kinetic energy of oceanic flows is concentrated in quasi-horizontal motions of horizontal scales between 10 and 500 km and covering the upper 1500 m
Some studies [6,7] pointed out the possible use of the Surface Quasi-Geostrophy (SQG) model that was introduced by Blumen [8] to interpret ocean dynamics at these scales
This review concerned surface quasi-geostrophic flows, a special class of quasi-geostrophic flows, which is based on the conservation of surface buoyancy with uniform potential vorticity within the fluid
Summary
A large fraction of kinetic energy of oceanic flows is concentrated in quasi-horizontal motions of horizontal scales between 10 and 500 km and covering the upper 1500 m (the thermocline). We will recall the general formulation of SQG, by introducing it in the quasi-geostrophic setting This model is based on the conservation of an active scalar (surface buoyancy) along the horizontal geostrophic. Setting aside lateral conditions (for instance, for a doubly-periodic domain) and imagining a semi-infinite domain in the vertical, the remaining condition is at the surface z = 0, i.e., Equation (9) Both PV in the fluid interior and surface buoyancy are needed in determining the three-dimensional streamfunction field. Observed that, in the QG approximation, buoyancy at the surface plays the same role as potential vorticity in the interior of the fluid This can be analytically established (see [7,12]), and the surface condition:. Observe in particular that the decrease is even faster when small horizontal scales are considered (large K)
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