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...utcome is that the 3D dynamics of the upper troposphere can be well described from only the potential temperature anomalies on the tropopause (Juckes 1994) using surface quasigeostrophy (SQG) theory (=-=Held et al. 1995-=-). In this study we follow a similar approach within an oceanographic context and examine the role of the surface boundary condition in the dynamics of the upper oceanic layers. The backbone of our ap...

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... and 2 references therein) while the inviscid QG equation ((1.1) with κ = 0) was derived to model frontogenesis in meteorology, a formation of sharp fronts between masses of hot and cold air (see [7],=-=[10]-=-,[15]). The problem at the center of the mathematical theory concerning the 2-D QG equation is whether or not it has a global in time smooth solution for any prescribed smooth initial data. In the sub...

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...usion coefficient and α ∈ [0,1] is a parameter, θ = θ(x, t) is a scalar representing the temperature, u is the velocity field, and ψ is the usual stream function. Besides its geophysical applications =-=[11]-=-, [12], the 2D dissipative QG equation serves as a 2D model of the 3D Navier–Stokes equations and has recently been extensively investigated (see [1], [2], [3], [5], [6], [7], [8], [9], [10], [13], [1...

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...pears when the horizontal resolution used is high. Indeed, surface density within a filament is conserved in SQG theory but the vorticity magnitude increases as the filament is stretched and thinned (=-=Held et al. 1995-=-). This means that, when the resolution is high enough, small-scale values of the relative vorticity may approach f leading to Rossby numbers of the order one in these sub-mesoscales. Surface flows wi...

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...D) quasi-sgeostrophic (QG) model with the 2D incompressiblesEuler equations, to which it is linked by a formalsresemblance. Interesting elements of such compari-sson have been studied by Held, et al. =-=[8]-=-. Here, wesconcentrate on the similarities and differences in thesprocess of front formation. It has been shown in [6]sthat front formation in the 2D QG model is analogoussin a deep sense to vortex st...

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...tegral operator. The fractional Laplace operator (−∆) α is defined through the Fourier transform ̂ (−∆) α f(ξ) = |ξ| 2α ̂ f(ξ), ξ ∈ R n . (1.1) generalizes the 2D dissipative QG equation (see [6],[8],=-=[12]-=-,[16] and the references therein). The main mathematical question concerning the 2-D dissipative QG equation is whether or not it has a global in time smooth solution for any prescribed smooth initial...

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...arallels the dynamics of the barotropic vorticity equation: the three dimensional flow is modeled entirely by horizontal advection of potential temperature on the interface (Blumen 1978; Juckes 1994; =-=Held et al. 1995-=-). Following Held et al. (1995), we shall refer to this approximation as ‘‘surface quasigeostrophy’’. An interesting attribute of surface quasigeostrophy is the absence of depth-independent (barotropi...

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... is the three dimensional Euler equation and temperature equation in Boussinesq approximation set in a strongly rotating half-space. Under certain assumptions, a simpler system can be used as a model =-=[24]-=-: ∆ψ = 0, θ = ψz, θt = (u · ∇)θ, u = ∇ ⊥ ψ. (2) Here z is the vertical axis of rotation, ψ is the streamfunction, θ is the potential temperature, and all equations hold in R 3 +. Now on the boundary o...