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 Author or Editor: J. Pedlosky x
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Abstract
An a priori estimate is given of the effect of ventilation on the process of potential vorticity homogenization. Since the homogenization process depends on the presence of weak mixing, it is shown that only a small exposure to a zone of ventilation is required to lead to an arrest of the homogenization.
Abstract
An a priori estimate is given of the effect of ventilation on the process of potential vorticity homogenization. Since the homogenization process depends on the presence of weak mixing, it is shown that only a small exposure to a zone of ventilation is required to lead to an arrest of the homogenization.
Abstract
The steady baroclinic flow in a basin containing a meridional barrier representing a midocean ridge is studied in the linear, quasigeostrophic limit of a twolayer model. Thermal damping and a simple friction provide dissipation of thickness (heat) and momentum. The ridge is pierced by two gaps in the upper layer but only a single gap in the lower layer. The flow in the model is forced by specified upwelling at the upper surface and by a specified crossisopycnal velocity at the interface in addition to the autogenerated crossisopycnal velocity associated with the thermal damping. The forcing may be either broad in longitude or narrowly confined.
The nature of the geometry of the model ridge mixes the baroclinic and barotropic response to the forcing, and this has profound consequences for the resulting circulation. In particular, when the baroclinic interaction of the two layers is strong, the recirculation region to the east of the ridge, previously discovered in earlier barotropic models of the circulation, grows in meridional extent so that the flow along the ridge segment may be unidirectional along the ridge. It is suggested that the theory may explain observations of such flow in the Angola Basin, which appeared previously to violate an application of Kelvin's theorem.
The theory also predicts zonal jets west of the gaps in the ridge, spreading meridionally with distance from the ridge. The jets are strongly barotropic whether the external forcing is baroclinic or barotropic.
Abstract
The steady baroclinic flow in a basin containing a meridional barrier representing a midocean ridge is studied in the linear, quasigeostrophic limit of a twolayer model. Thermal damping and a simple friction provide dissipation of thickness (heat) and momentum. The ridge is pierced by two gaps in the upper layer but only a single gap in the lower layer. The flow in the model is forced by specified upwelling at the upper surface and by a specified crossisopycnal velocity at the interface in addition to the autogenerated crossisopycnal velocity associated with the thermal damping. The forcing may be either broad in longitude or narrowly confined.
The nature of the geometry of the model ridge mixes the baroclinic and barotropic response to the forcing, and this has profound consequences for the resulting circulation. In particular, when the baroclinic interaction of the two layers is strong, the recirculation region to the east of the ridge, previously discovered in earlier barotropic models of the circulation, grows in meridional extent so that the flow along the ridge segment may be unidirectional along the ridge. It is suggested that the theory may explain observations of such flow in the Angola Basin, which appeared previously to violate an application of Kelvin's theorem.
The theory also predicts zonal jets west of the gaps in the ridge, spreading meridionally with distance from the ridge. The jets are strongly barotropic whether the external forcing is baroclinic or barotropic.
Abstract
The relationship between coastal upwelling and coastal longshort currents is studied in a simple model of a continuously stratified fluid in a closed basin on the fplane. It is shown that the coastal longshore current at any point on the basin's perimeter is determined primarily by the components of the longshore stress with the largest longshore scales, in particular from the perimeter average of the longshore stress. In addition, the depth structure of the upwelling itself is shown to be dependent on the longshore scale.
It is concluded that the relationship between upwelling and longshore currents is nonlocal, that mass balance is not achieved locally in planes normal to the coast, and that the relationship between onshore flows and longshore currents is scaledependent. An intrinsic longshore length scale is found separating two regimes of flow with distinctly different relations between the wind stress, onshore, and longshore flows. Since both regimes are present simultaneously for a wind stress containing a variety of longshore scales, the determination of the longshors structure of the wind stress is essential to an understanding of the local oceanic upwelling and longshore current structure.
Abstract
The relationship between coastal upwelling and coastal longshort currents is studied in a simple model of a continuously stratified fluid in a closed basin on the fplane. It is shown that the coastal longshore current at any point on the basin's perimeter is determined primarily by the components of the longshore stress with the largest longshore scales, in particular from the perimeter average of the longshore stress. In addition, the depth structure of the upwelling itself is shown to be dependent on the longshore scale.
It is concluded that the relationship between upwelling and longshore currents is nonlocal, that mass balance is not achieved locally in planes normal to the coast, and that the relationship between onshore flows and longshore currents is scaledependent. An intrinsic longshore length scale is found separating two regimes of flow with distinctly different relations between the wind stress, onshore, and longshore flows. Since both regimes are present simultaneously for a wind stress containing a variety of longshore scales, the determination of the longshors structure of the wind stress is essential to an understanding of the local oceanic upwelling and longshore current structure.
Abstract
The effect of shelflike bottom topography on a steady, linear, stratified, threedimensional model of coastal upwelling is examined. It is shown that the presence of the bottom slope 1) reduces the role of the lower Ekman layer in the upwelling mass balance, and 2) introduces a barotropic boundary layer which can, depending on a balance of driving mechanisms, give rise to a deep poleward undercurrent. The structure, amplitude and cause of the undercurrent are distinct from those of the surface equatorward flow.
Abstract
The effect of shelflike bottom topography on a steady, linear, stratified, threedimensional model of coastal upwelling is examined. It is shown that the presence of the bottom slope 1) reduces the role of the lower Ekman layer in the upwelling mass balance, and 2) introduces a barotropic boundary layer which can, depending on a balance of driving mechanisms, give rise to a deep poleward undercurrent. The structure, amplitude and cause of the undercurrent are distinct from those of the surface equatorward flow.
Abstract
The evolution of longshore currents produced by upwelling on an fplane over shelflike bottom topography for times long compared to a barotropic spinup time, but short compared to a diffusion time, reveals in a linear, timedependent, threedimensional model that:

The topographic constraints yield a steady topographic boundary layer on these short time scales similar in structure to the layer found in an earlier steadystate model.

Within a Rossby radius of deformation of the coast a swift equatorward longshore current with a poleward countercurrent is formed.

Windstress forcing with large northsouth scales are the most efficient in driving longshore currents, but do not effectively produce internal Kelvin waves, as do the shorter longshore scales of forcing.
Abstract
The evolution of longshore currents produced by upwelling on an fplane over shelflike bottom topography for times long compared to a barotropic spinup time, but short compared to a diffusion time, reveals in a linear, timedependent, threedimensional model that:

The topographic constraints yield a steady topographic boundary layer on these short time scales similar in structure to the layer found in an earlier steadystate model.

Within a Rossby radius of deformation of the coast a swift equatorward longshore current with a poleward countercurrent is formed.

Windstress forcing with large northsouth scales are the most efficient in driving longshore currents, but do not effectively produce internal Kelvin waves, as do the shorter longshore scales of forcing.
Abstract
The transmission of westward propagating baroclinic Rossby waves incident on a gappy meridional barrier is studied in the context of the twolayer, quasigeostrophic model. The meridional barrier models the presence of very steep topography such as the midocean ridge system or extensive island arcs.
The nature of the transmission depends strongly on the nature of the gaps in the meridional barrier. If the gaps extend throughout the depth of the fluid, the Rossby waves propagate through the barrier, as a consequence of Kelvin’s theorem, with no change in vertical structure. On the other hand, if the gaps in the barrier are partial and extend only over a single layer, there is a significant transformation of the vertical structure of the wave field as it traverses the barrier. In particular, waves of baroclinic vertical structure in the model are transformed on the western side of the barrier into barotropic waves that radiate from the segment of the barrier between two such gaps. Such segments act as antennae radiating barotropic energy into the western subbasin. It is suggested that recent observations of signal enhancement of Rossby waves at the midocean ridge system in the Pacific may be related to such transformation of wave structure.
The problems of free waves and forced waves in open regions and normal modes in closed basins are described.
Abstract
The transmission of westward propagating baroclinic Rossby waves incident on a gappy meridional barrier is studied in the context of the twolayer, quasigeostrophic model. The meridional barrier models the presence of very steep topography such as the midocean ridge system or extensive island arcs.
The nature of the transmission depends strongly on the nature of the gaps in the meridional barrier. If the gaps extend throughout the depth of the fluid, the Rossby waves propagate through the barrier, as a consequence of Kelvin’s theorem, with no change in vertical structure. On the other hand, if the gaps in the barrier are partial and extend only over a single layer, there is a significant transformation of the vertical structure of the wave field as it traverses the barrier. In particular, waves of baroclinic vertical structure in the model are transformed on the western side of the barrier into barotropic waves that radiate from the segment of the barrier between two such gaps. Such segments act as antennae radiating barotropic energy into the western subbasin. It is suggested that recent observations of signal enhancement of Rossby waves at the midocean ridge system in the Pacific may be related to such transformation of wave structure.
The problems of free waves and forced waves in open regions and normal modes in closed basins are described.
Abstract
A twolayer thermocline model is modified by adding an essentially passive mixed layer above it. The surface temperature variation is simulated by a moving outcrop line. It is found that, in contrast to a surface wind stress, a surface temperature variation causes strong variability in the ventilated zone through subducted water, while it affects the shadow zone little.
Two types of buoyancyforced solution are found. When the outcrop line moves slowly, the solutions are nonentrainment solutions. For these solutions, the surface beat flux is mainly balanced by the horizontal advection in the permanent thermocline. The mixed layer never entrains. The timemean thermocline is close to the steady thermocline with the timemean outcrop line.
When the outcrop line moves southward rapidly during the cooling season, the solutions become entrainment solutions. Now, deep vertical convection must occur because the horizontal advection in the permanent thermocline is no longer strong enough to balance the surface cooling. The timemean thermocline resembles the steady thermocline with the early spring mixed layer, as suggested by Stommel. The local variability in the permanent thermocline is most efficiently produced by decadal forcings.
Abstract
A twolayer thermocline model is modified by adding an essentially passive mixed layer above it. The surface temperature variation is simulated by a moving outcrop line. It is found that, in contrast to a surface wind stress, a surface temperature variation causes strong variability in the ventilated zone through subducted water, while it affects the shadow zone little.
Two types of buoyancyforced solution are found. When the outcrop line moves slowly, the solutions are nonentrainment solutions. For these solutions, the surface beat flux is mainly balanced by the horizontal advection in the permanent thermocline. The mixed layer never entrains. The timemean thermocline is close to the steady thermocline with the timemean outcrop line.
When the outcrop line moves southward rapidly during the cooling season, the solutions become entrainment solutions. Now, deep vertical convection must occur because the horizontal advection in the permanent thermocline is no longer strong enough to balance the surface cooling. The timemean thermocline resembles the steady thermocline with the early spring mixed layer, as suggested by Stommel. The local variability in the permanent thermocline is most efficiently produced by decadal forcings.
Abstract
A theory that describes the ventilated part of the ocean thermocline in the presence of a continuous density distribution is developed. The theory is based on the Sverdrup relation, on the conservation of the potential vorticity, and it assumes that the thermocline is fully ventilated in order to have a simplified dynamics. A finite density step is allowed between the bottom of the thermocline and the underlying quiescent abyss. If the outcrop lines have constant latitude, the potential vorticity and Montgomery function are proved to be inversely proportional. Their product is a function of the fluid density only, and it can be determined numerically from an arbitrary density distribution at the sea surface. The dependence of the coefficient of proportionality on the sea surface density distribution and on the parameter that controls both the nonlinearity and the baroclinicity of the solution is investigated and an analytical expression is proposed. The theory results in an integral–differential equation, which allows the derivation of the vertical stratification in the thermocline from the sea surface density distribution. The equation is solved numerically for a typical midlatitude ocean gyre. The solution shows the presence of a region of low vorticity fluid at the bottom of the thermocline as a consequence of a fully inviscid model physics. This theory is the generalization of the Lionello and Pedlosky manylayer model to an infinite number of layers of infinitesimal thickness. It is therefore shown that the layer model of the thermocline can be considered the discrete approximation of the continuous system.
Abstract
A theory that describes the ventilated part of the ocean thermocline in the presence of a continuous density distribution is developed. The theory is based on the Sverdrup relation, on the conservation of the potential vorticity, and it assumes that the thermocline is fully ventilated in order to have a simplified dynamics. A finite density step is allowed between the bottom of the thermocline and the underlying quiescent abyss. If the outcrop lines have constant latitude, the potential vorticity and Montgomery function are proved to be inversely proportional. Their product is a function of the fluid density only, and it can be determined numerically from an arbitrary density distribution at the sea surface. The dependence of the coefficient of proportionality on the sea surface density distribution and on the parameter that controls both the nonlinearity and the baroclinicity of the solution is investigated and an analytical expression is proposed. The theory results in an integral–differential equation, which allows the derivation of the vertical stratification in the thermocline from the sea surface density distribution. The equation is solved numerically for a typical midlatitude ocean gyre. The solution shows the presence of a region of low vorticity fluid at the bottom of the thermocline as a consequence of a fully inviscid model physics. This theory is the generalization of the Lionello and Pedlosky manylayer model to an infinite number of layers of infinitesimal thickness. It is therefore shown that the layer model of the thermocline can be considered the discrete approximation of the continuous system.
Abstract
The ocean thermocline is resolved in a very large number of layers by means of a recursive relation that extends the LPS model of the ventilated flow from a small to an arbitrary number of layers. In order to have simplified dynamics, the basin is semiinfinite in the zonal direction, the thermocline is fully ventilated, and its thickness vanishes at the northern boundary. In this model, the potential vorticity of each layer is shown to be inversely proportional to the Bernoulli function. The high vertical resolution adopted for the thermocline allows the study of the dependence of its motion on the ratio between the density contrast at the sea surface and the density step separating the thermocline bottom from the underlying quiescent abyss. This ratio controls both the nonlinearity and the baroclinicity of the solution. The behavior of the solution as this ratio varies from zero (linear and barotropic case) to infinity (“fully nonlinear” and baroclinic case) is described. The singularity that is found in the fully nonlinear case is discussed.
Abstract
The ocean thermocline is resolved in a very large number of layers by means of a recursive relation that extends the LPS model of the ventilated flow from a small to an arbitrary number of layers. In order to have simplified dynamics, the basin is semiinfinite in the zonal direction, the thermocline is fully ventilated, and its thickness vanishes at the northern boundary. In this model, the potential vorticity of each layer is shown to be inversely proportional to the Bernoulli function. The high vertical resolution adopted for the thermocline allows the study of the dependence of its motion on the ratio between the density contrast at the sea surface and the density step separating the thermocline bottom from the underlying quiescent abyss. This ratio controls both the nonlinearity and the baroclinicity of the solution. The behavior of the solution as this ratio varies from zero (linear and barotropic case) to infinity (“fully nonlinear” and baroclinic case) is described. The singularity that is found in the fully nonlinear case is discussed.
Abstract
Lowfrequency, largescale baroclinic Rossby basin modes, resistant to scaledependent dissipation, have been recently theoretically analyzed and discussed as possible efficient coupling agents with the atmosphere for interactions on decadal time scales. Such modes are also consistent with evidence of the westward phase propagation in satellite altimetry data. In both the theory and the observations, the scale of the waves is large in comparison with the Rossby radius of deformation and the orientation of fluid motion in the waves is predominantly meridional. These two facts suggest that the waves are vulnerable to baroclinic instability on the scale of the deformation radius. The key dynamical parameter is the ratio Z of the transit time of the long Rossby wave to the efolding time of the instability. When this parameter is small the wave easily crosses the basin largely undisturbed by the instability; if Z is large the wave succumbs to the instability and is largely destroyed before making a complete transit of the basin. For small Z, the instability is shown to be a triad instability; for large Z the instability is fundamentally similar to the Eady instability mechanism. For all Z, the growth rate is on the order of the vertical shear of the basic wave divided by the deformation radius. If the parametric dependence of Z on latitude is examined, the condition of unit Z separates latitudes south of which the Rossby wave may successfully cross the basin while north of which the wave will break down into smallscale eddies with a barotropic component. The boundary between the two corresponds to the domain boundary found in satellite measurements. Furthermore, the resulting barotropic wave field is shown to propagate at speeds about 2 times as large as the baroclinic speed, and this is offered as a consistent explanation of the observed discrepancy between the satellite observations of Chelton and Schlax and simple linear wave theory. Here it is suggested that Rossby basin modes, if they exist, would be limited to tropical domains and that a considerable part of the observed midlatitude eddy field north of that boundary is due to the instability of windforced, long Rossby waves.
Abstract
Lowfrequency, largescale baroclinic Rossby basin modes, resistant to scaledependent dissipation, have been recently theoretically analyzed and discussed as possible efficient coupling agents with the atmosphere for interactions on decadal time scales. Such modes are also consistent with evidence of the westward phase propagation in satellite altimetry data. In both the theory and the observations, the scale of the waves is large in comparison with the Rossby radius of deformation and the orientation of fluid motion in the waves is predominantly meridional. These two facts suggest that the waves are vulnerable to baroclinic instability on the scale of the deformation radius. The key dynamical parameter is the ratio Z of the transit time of the long Rossby wave to the efolding time of the instability. When this parameter is small the wave easily crosses the basin largely undisturbed by the instability; if Z is large the wave succumbs to the instability and is largely destroyed before making a complete transit of the basin. For small Z, the instability is shown to be a triad instability; for large Z the instability is fundamentally similar to the Eady instability mechanism. For all Z, the growth rate is on the order of the vertical shear of the basic wave divided by the deformation radius. If the parametric dependence of Z on latitude is examined, the condition of unit Z separates latitudes south of which the Rossby wave may successfully cross the basin while north of which the wave will break down into smallscale eddies with a barotropic component. The boundary between the two corresponds to the domain boundary found in satellite measurements. Furthermore, the resulting barotropic wave field is shown to propagate at speeds about 2 times as large as the baroclinic speed, and this is offered as a consistent explanation of the observed discrepancy between the satellite observations of Chelton and Schlax and simple linear wave theory. Here it is suggested that Rossby basin modes, if they exist, would be limited to tropical domains and that a considerable part of the observed midlatitude eddy field north of that boundary is due to the instability of windforced, long Rossby waves.