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117
Dynamics of the Upper Oceanic Layers in Terms of Surface Quasigeostrophy Theory
, 2006
"... In this study, the relation between the interior and the surface dynamics for nonlinear baroclinically unstable flows is examined using the concepts of potential vorticity. First, it is demonstrated that baroclinic unstable flows present the property that the potential vorticity mesoscale and subm ..."
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Cited by 59 (10 self)
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In this study, the relation between the interior and the surface dynamics for nonlinear baroclinically unstable flows is examined using the concepts of potential vorticity. First, it is demonstrated that baroclinic unstable flows present the property that the potential vorticity mesoscale and submesoscale anomalies in the ocean interior are strongly correlated to the surface density anomalies. Then, using the invertibility of potential vorticity, the dynamics are decomposed in terms of a solution forced by the threedimensional (3D) potential vorticity and a solution forced by the surface boundary condition in density. It is found that, in the upper oceanic layers, the balanced flow induced only by potential vorticity is strongly anticorrelated with that induced only by the surface density with a dominance of the latter. The major consequence is that the 3D balanced motions can be determined from only the surface density and the characteristics of the basinscale stratification by solving an elliptic equation. These properties allow for the possibility to reconstruct the 3D balanced velocity field of the upper layers from just the knowledge of the surface density by using a simpler model, that is, an "effective" surface quasigeostrophic model. All these results are validated through the examination of a primitive equation simulation reproducing the dynamics of the Antarctic Circumpolar Current.
Turbulent diffusion in the geostrophic inverse cascade
, 2002
"... Motivated in part by the problem of largescale lateral turbulent heat transport in the Earth’s atmosphere and oceans, and in part by the problem of turbulent transport itself, we seek to better understand the transport of a passive tracer advected by various types of fully developed twodimensional ..."
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Cited by 51 (7 self)
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Motivated in part by the problem of largescale lateral turbulent heat transport in the Earth’s atmosphere and oceans, and in part by the problem of turbulent transport itself, we seek to better understand the transport of a passive tracer advected by various types of fully developed twodimensional turbulence. The types of turbulence considered correspond to various relationships between the streamfunction and the advected field. Each type of turbulence considered possesses two quadratic invariants and each can develop an inverse cascade. These cascades can be modified or halted, for example, by friction, a background vorticity gradient or a mean temperature gradient. We focus on three physically realizable cases: classical twodimensional turbulence, surface quasigeostrophic turbulence, and shallowwater quasigeostrophic turbulence at scales large compared to the radius of deformation. In each model we assume that tracer variance is maintained by a largescale mean tracer gradient while turbulent energy is produced at small scales via random forcing, and dissipated by linear drag. We predict the spectral shapes, eddy scales and equilibrated energies resulting from the inverse cascades, and use the expected velocity and length scales to predict integrated tracer fluxes. When linear drag halts the cascade, the resulting diffusivities are decreasing functions of the drag coefficient, but with different dependences for each case. When β is significant, we find a clear distinction between the tracer mixing scale, which depends on β but is nearly independent of drag, and the energycontaining (or jet) scale, set by a combination of the drag coefficient and β. Our predictions are tested via highresolution spectral simulations. We find in all cases that the passive scalar is diffused downgradient with a diffusion coefficient that is wellpredicted from estimates of mixing length and velocity scale obtained from turbulence phenomenology.
Regularity of hölder continuous solutions of the supercritical quasigeostrophic equation
 In Annales de l’Institut Henri Poincare (C) Non Linear Analysis
, 2008
"... Abstract We present a regularity result for weak solutions of the 2D quasigeostrophic equation with supercritical (α < 1/2) dissipation (− ) α : If a LerayHopf weak solution is Hölder continuous θ ∈ C δ (R 2 ) with δ > 1 − 2α on the time interval [t 0 , t], then it is actually a classical s ..."
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Cited by 50 (10 self)
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Abstract We present a regularity result for weak solutions of the 2D quasigeostrophic equation with supercritical (α < 1/2) dissipation (− ) α : If a LerayHopf weak solution is Hölder continuous θ ∈ C δ (R 2 ) with δ > 1 − 2α on the time interval [t 0 , t], then it is actually a classical solution on (t 0 , t].
Global solutions of the 2D dissipative quasigeostrophic equation in Besov spaces
 SIAM J. Math. Anal
"... Abstract. The twodimensional (2D) quasigeostrophic (QG) equation is a 2D model of the 3D incompressible Euler equations, and its dissipative version includes an extra term bearing the operator (−∆) α with α ∈ [0, 1]. Existing research appears to indicate the criticality of α = 1 2 in the sense tha ..."
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Cited by 40 (9 self)
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Abstract. The twodimensional (2D) quasigeostrophic (QG) equation is a 2D model of the 3D incompressible Euler equations, and its dissipative version includes an extra term bearing the operator (−∆) α with α ∈ [0, 1]. Existing research appears to indicate the criticality of α = 1 2 in the sense that the issue of global existence for the 2D dissipative QG equation becomes extremely difficult when α ≤ 1 1. It is shown here that for any α ≤ the 2D dissipative QG equation with 2 2 an initial datum in the Besov space Br 2, ∞ or Br p, ∞ (p>2) possesses a unique global solution if the norm of the datum in these spaces is comparable to κ, the diffusion coefficient. Since the Sobolev space Hr is embedded in Br 2, ∞ , a special consequence is the global existence of small data solutions in Hr for any r>2 − 2α.
Upper Ocean Turbulence from HighResolution 3D Simulations
 JOURNAL OF PHYSICAL OCEANOGRAPHY
, 2008
"... The authors examine the turbulent properties of a baroclinically unstable oceanic flow using primitive equation (PE) simulations with high resolution (in both horizontal and vertical directions). Resulting dynamics in the surface layers involve large Rossby numbers and significant vortical asymmetri ..."
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Cited by 33 (5 self)
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The authors examine the turbulent properties of a baroclinically unstable oceanic flow using primitive equation (PE) simulations with high resolution (in both horizontal and vertical directions). Resulting dynamics in the surface layers involve large Rossby numbers and significant vortical asymmetries. Furthermore, the ageostrophic divergent motions associated with smallscale surface frontogenesis are shown to significantly alter the nonlinear transfers of kinetic energy and consequently the time evolution of the surface dynamics. Such impact of the ageostrophic motions explains the emergence of the significant cyclone–anticyclone asymmetry and of a strong restratification in the upper layers, which are not allowed by the quasigeostrophic (QG) or surface quasigeostrophic (SQG) theory. However, despite this strong ageostrophic character, some of the main surface properties are surprisingly still close to the surface quasigeostrophic equilibrium. They include a noticeable shallow (�k �2) velocity spectrum as well as a conspicuous local spectral relationship between surface kinetic energy, sea surface height, and density variance over a large range of scales (from 400 to 4 km). Furthermore, surface velocities can be remarkably diagnosed from only the surface density using SQG relations. This suggests that the validity of some specific SQG relations extends to dynamical regimes with large Rossby numbers. The interior dynamics, on the
Biharmonic friction with a Smagorinsky viscosity for use in largescale eddypermitting ocean models
 MON. WEA. REV
, 2000
"... This paper discusses a numerical closure, motivated from the ideas of Smagorinsky, for use with a biharmonic operator. The result is a highly scaleselective, statedependent friction operator for use in eddypermitting geophysical fluid models. This friction should prove most useful for largescale ..."
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Cited by 30 (2 self)
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This paper discusses a numerical closure, motivated from the ideas of Smagorinsky, for use with a biharmonic operator. The result is a highly scaleselective, statedependent friction operator for use in eddypermitting geophysical fluid models. This friction should prove most useful for largescale ocean models in which there are multiple regimes of geostrophic turbulence. Examples are provided from primitive equation geopotential and isopycnalcoordinate ocean models.
A twodimensional model for quasigeostrophic flow: comparison with the twodimensional Euler flow
 Physisa D
, 1996
"... A simple twodimensional model for quasigeostrophic flow is contrasted with the twodimensional incompressible Euler equations. The model arises under the assumptions of fast rotation, uniform stratification and uniform potential vorticity. It is found that the more local feedback of the quasigeost ..."
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Cited by 28 (0 self)
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A simple twodimensional model for quasigeostrophic flow is contrasted with the twodimensional incompressible Euler equations. The model arises under the assumptions of fast rotation, uniform stratification and uniform potential vorticity. It is found that the more local feedback of the quasigeostrophic model gives rise to strongly nonlinear front formation, as opposed to twodimensional Euler, where the steepening process of mature fronts obeys a nonlocal, nearly linear mechanism.
Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations
, 2007
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A new surface model for cycloneanticyclone asymmetry
 J. Atmos. Sci
, 2002
"... Cyclonic vortices on the tropopause are characterized by compact structure and larger pressure, wind, and temperature perturbations when compared to broader and weaker anticyclones. Neither the origin of these vortices nor the reasons for the preferred asymmetries are completely understood; quasigeo ..."
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Cited by 21 (1 self)
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Cyclonic vortices on the tropopause are characterized by compact structure and larger pressure, wind, and temperature perturbations when compared to broader and weaker anticyclones. Neither the origin of these vortices nor the reasons for the preferred asymmetries are completely understood; quasigeostrophic dynamics, in particular, have cyclone–anticyclone symmetry. In order to explore these and related problems, a novel small Rossby number approximation is introduced to the primitive equations applied to a simple model of the tropopause in continuously stratified fluid. This model resolves dynamics that give rise to vortical asymmetries, while retaining both the conceptual simplicity of quasigeostrophic dynamics and the computational economy of twodimensional flows. The model contains no depthindependent (barotropic) flow, and thus may provide a useful comparison to twodimensional flows dominated by this flow component. Solutions for random initial conditions (i.e., freely decaying turbulence) exhibit vortical asymmetries typical of tropopause observations, with strong localized cyclones, and weaker diffuse anticyclones. Cyclones cluster around a distinct length scale at a given time, whereas anticyclones do not. These results differ significantly from previous studies of cyclone–anticyclone asymmetry in the shallowwater primitive equations and the periodic balance equations. An important source of asymmetry in the present solutions is divergent flow associated with frontogenesis and the forward cascade of tropopause potential temperature variance. This thermally direct flow changes the mean potential temperature of the tropopause, selectively maintains anticyclonic filaments relative to cyclonic filaments, and appears to promote the merger of anticyclones relative to cyclones. 1.
Regularity and blow up for active scalars
"... We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasigeostrophic equation, the Burgers equation, and the CordobaCordobaFontelos model. We discuss nonlocal maximum principle methods which al ..."
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Cited by 20 (1 self)
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We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasigeostrophic equation, the Burgers equation, and the CordobaCordobaFontelos model. We discuss nonlocal maximum principle methods which allow to prove existence of global regular solutions for the critical dissipation. We also recall what is known about the possibility of finite time blow up in the supercritical regime. 1