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Abstract
An eigenvalue problem for the dispersion relation for planetary waves in the presence of mean flow and bottom topographic gradients is derived, under the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) assumption, for frequencies that are low when compared with the inertial frequency. Examples are given for the World Ocean that show a rich variety of behavior, including no frequency (or latitudinal) cutoff, solutions trapped at certain depths, coalescence of waves, and a lack of dispersion for most short waves.
Abstract
An eigenvalue problem for the dispersion relation for planetary waves in the presence of mean flow and bottom topographic gradients is derived, under the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) assumption, for frequencies that are low when compared with the inertial frequency. Examples are given for the World Ocean that show a rich variety of behavior, including no frequency (or latitudinal) cutoff, solutions trapped at certain depths, coalescence of waves, and a lack of dispersion for most short waves.
Abstract
Mechanisms are considered which may induct the large (over 105 km2) area of open water, or polynya, which frequently occurs within the Weddell Sea winter sea-ice. We propose that when surface cooling and ice formation decrease the temperature and increase the salinity of the surface water (the latter by salt rejection during ice formation) in a preconditioned area, static instability with intense vertical mixing can occur. The upwelled warm, salty deep water can then supply enough heat to melt the ice, or prohibit its formation, even in the middle of winter.
A simple two-level model is derived to test this theory and is found to agree well with observations. The process is found to be irregular due to different times of ice onset from one year to the next, and to a lesser extent from variations in surface heating and cooling. Further, it is shown that unless the freshwater input exactly balances the increased salinity from the overturn each year, the system will either gain or lose salt yearly and eventually stabilize permanently (i.e., attain a steady-state condition).
The model is insensitive to short term stochastic variations in surface heat flux or freshwater input rates, but is somewhat sensitive to longer scale variations in the net freshwater input and also to the depth of the pycnocline (i.e., preconditioning). It is suggested that upwelling may raise the pycnocline until convection can occur and the polynya form. The preconditioned area then advects westward with the mean flow. Permanent stability finally is attained but the preconditioned area is advected into the western boundary current of the Weddell subpolar gyre and destroyed. Prior to destruction, topographical features may quantitatively affect both the movement and occurrence of the polynya.
Regardless of the preconditioning mechanism, if overturning is responsible for the polynya, this would contribute a minimum of 106 m3 s−1 to the total deep water formation, and constitute the largest area of deep open-ocean convection yet discovered.
Abstract
Mechanisms are considered which may induct the large (over 105 km2) area of open water, or polynya, which frequently occurs within the Weddell Sea winter sea-ice. We propose that when surface cooling and ice formation decrease the temperature and increase the salinity of the surface water (the latter by salt rejection during ice formation) in a preconditioned area, static instability with intense vertical mixing can occur. The upwelled warm, salty deep water can then supply enough heat to melt the ice, or prohibit its formation, even in the middle of winter.
A simple two-level model is derived to test this theory and is found to agree well with observations. The process is found to be irregular due to different times of ice onset from one year to the next, and to a lesser extent from variations in surface heating and cooling. Further, it is shown that unless the freshwater input exactly balances the increased salinity from the overturn each year, the system will either gain or lose salt yearly and eventually stabilize permanently (i.e., attain a steady-state condition).
The model is insensitive to short term stochastic variations in surface heat flux or freshwater input rates, but is somewhat sensitive to longer scale variations in the net freshwater input and also to the depth of the pycnocline (i.e., preconditioning). It is suggested that upwelling may raise the pycnocline until convection can occur and the polynya form. The preconditioned area then advects westward with the mean flow. Permanent stability finally is attained but the preconditioned area is advected into the western boundary current of the Weddell subpolar gyre and destroyed. Prior to destruction, topographical features may quantitatively affect both the movement and occurrence of the polynya.
Regardless of the preconditioning mechanism, if overturning is responsible for the polynya, this would contribute a minimum of 106 m3 s−1 to the total deep water formation, and constitute the largest area of deep open-ocean convection yet discovered.
Abstract
The classic Stommel–Arons problem is revisited in the context of a basin with a general bottom topography containing an equator. Topography is taken to be smoothly varying and, as such, there are no vertical side walls in the problem. The perimeter of the abyssal basin is thus defined as the curve along which the layer depth vanishes. Because of this, it is not required that the component of horizontal velocity perpendicular to the boundary curve vanish on the boundary. Planetary geostrophic dynamics leads to a characteristic equation for the interface height field in which characteristics typically originate from a single point located on the eastern edge of the basin at the equator. For a simple choice of topography it is possible to solve the problem analytically. In the linear limit of weak forcing, the solution exhibits an intensified flow on the western edge of the basin. This flow is pan of the interior solution and is thus not a traditional, dissipative western boundary current.
When the fully nonlinear continuity equation is considered, the characteristics form a caustic on the western side of the basin. Characteristics cannot be integrated through the caustic so that a boundary layer involving higher-order dynamics is required. Approaching the caustic from the cast, velocities predicted by the interior solution become infinite. Because of this and because of global man budget considerations, the boundary layer is shown to lie east of the caustic. The position of the boundary layer is, however, not unique. Away from the equator, it is straightforward to append a Stommel boundary layer to the interior solution.
Next, localized mass sources are considered. Their dynamics (planetary geostrophy is assumed, except where boundary currents are required) include caustics and boundary layers in a manner similar to the sink-driven problem described above. For topography such that characteristics have a positive westward component, a caustic lies on the poleward side of the source and extends to the equator. Again, to balance the mass budget, a dissipative boundary layer is required inside the caustic. This, together with all the characteristics leaving the source region, intersects the equator at a finite angle. There, velocities become infinite, while the layer depth goes to zero. Although the details of the implied boundary layer are left unresolved, it is argued that the boundary current crosses the equator at a small angle to the eastward direction.
Abstract
The classic Stommel–Arons problem is revisited in the context of a basin with a general bottom topography containing an equator. Topography is taken to be smoothly varying and, as such, there are no vertical side walls in the problem. The perimeter of the abyssal basin is thus defined as the curve along which the layer depth vanishes. Because of this, it is not required that the component of horizontal velocity perpendicular to the boundary curve vanish on the boundary. Planetary geostrophic dynamics leads to a characteristic equation for the interface height field in which characteristics typically originate from a single point located on the eastern edge of the basin at the equator. For a simple choice of topography it is possible to solve the problem analytically. In the linear limit of weak forcing, the solution exhibits an intensified flow on the western edge of the basin. This flow is pan of the interior solution and is thus not a traditional, dissipative western boundary current.
When the fully nonlinear continuity equation is considered, the characteristics form a caustic on the western side of the basin. Characteristics cannot be integrated through the caustic so that a boundary layer involving higher-order dynamics is required. Approaching the caustic from the cast, velocities predicted by the interior solution become infinite. Because of this and because of global man budget considerations, the boundary layer is shown to lie east of the caustic. The position of the boundary layer is, however, not unique. Away from the equator, it is straightforward to append a Stommel boundary layer to the interior solution.
Next, localized mass sources are considered. Their dynamics (planetary geostrophy is assumed, except where boundary currents are required) include caustics and boundary layers in a manner similar to the sink-driven problem described above. For topography such that characteristics have a positive westward component, a caustic lies on the poleward side of the source and extends to the equator. Again, to balance the mass budget, a dissipative boundary layer is required inside the caustic. This, together with all the characteristics leaving the source region, intersects the equator at a finite angle. There, velocities become infinite, while the layer depth goes to zero. Although the details of the implied boundary layer are left unresolved, it is argued that the boundary current crosses the equator at a small angle to the eastward direction.
Abstract
No Abstract Available.
Abstract
No Abstract Available.
Abstract
The linear stability of two-layer primitive equation ocean rings is considered in the case when the rings are wide compared with a deformation radius, as is usually observed. Asymptotic theory is developed to show the existence of solutions for arbitrarily wide rings, and these solutions can be followed as the rings are made successively narrower. An exponential cubic radial dependence is used for the mean flow, rather than the more usual Gaussian structure. There are two reasons: a Gaussian shape was fully discussed in a previous paper, and a Gaussian has exceptional properties, unlike other power laws. The specific cases of warm and cold Gulf Stream rings are considered in detail. The theory provides an accurate prediction of phase velocity and growth rate for cold rings and a reasonable prediction for warm rings. Solutions in the asymptotic regime have a larger growth rate than other (nonasymptotic) solutions for cold rings, but not for warm rings. Attention is given to the role of the mean barotropic circulation, which had been found in earlier work to have a strong effect on ring stability. There is still evidence for stabilization when the mean flow in the lower layer vanishes, but other features are also involved. In particular, the linear stability of a ring appears to be as sensitive to subtle shape details as it is to the sense of the deep flow. The authors generally find warm co-rotating rings with a cubic exponential form to be unstable, although somewhat less so than counterrotating rings.
Abstract
The linear stability of two-layer primitive equation ocean rings is considered in the case when the rings are wide compared with a deformation radius, as is usually observed. Asymptotic theory is developed to show the existence of solutions for arbitrarily wide rings, and these solutions can be followed as the rings are made successively narrower. An exponential cubic radial dependence is used for the mean flow, rather than the more usual Gaussian structure. There are two reasons: a Gaussian shape was fully discussed in a previous paper, and a Gaussian has exceptional properties, unlike other power laws. The specific cases of warm and cold Gulf Stream rings are considered in detail. The theory provides an accurate prediction of phase velocity and growth rate for cold rings and a reasonable prediction for warm rings. Solutions in the asymptotic regime have a larger growth rate than other (nonasymptotic) solutions for cold rings, but not for warm rings. Attention is given to the role of the mean barotropic circulation, which had been found in earlier work to have a strong effect on ring stability. There is still evidence for stabilization when the mean flow in the lower layer vanishes, but other features are also involved. In particular, the linear stability of a ring appears to be as sensitive to subtle shape details as it is to the sense of the deep flow. The authors generally find warm co-rotating rings with a cubic exponential form to be unstable, although somewhat less so than counterrotating rings.
Abstract
Planetary or Rossby waves are the predominant way in which the ocean adjusts on long (year to decade) timescales. The motion of long planetary waves is westward, at speeds ≥1 cm s−1. Until recently, very few experimental investigations of such waves were possible because of scarce data. The advent of satellite altimetry has changed the situation considerably. Curiously, the speeds of planetary waves observed by TOPEX/Poseidon are mainly faster than those given by standard linear theory. This paper examines why this should be. It is argued that the major changes to the unperturbed wave speed will be caused by the presence of baroclinic east–west mean flows, which modify the potential vorticity gradient. Long linear perturbations to such flow satisfy a simple eigenvalue problem (related directly to standard quasigeostrophic theory). Solutions are mostly real, though a few are complex. In simple situations approximate solutions can be obtained analytically. Using archive data, the global problem is treated. Phase speeds similar to those observed are found in most areas, although in the Southern Hemisphere an underestimate of speed by the theory remains. Thus, the presence of baroclinic mean flow is sufficient to account for the majority of the observed speeds. It is shown that phase speed changes are produced mainly by (vertical) mode-2 east–west velocities, with mode-1 having little or no effect. Inclusion of the mean barotropic flow from a global eddy-admitting model makes only a small modification to the fit with observations; whether the fit is improved is equivocal.
Abstract
Planetary or Rossby waves are the predominant way in which the ocean adjusts on long (year to decade) timescales. The motion of long planetary waves is westward, at speeds ≥1 cm s−1. Until recently, very few experimental investigations of such waves were possible because of scarce data. The advent of satellite altimetry has changed the situation considerably. Curiously, the speeds of planetary waves observed by TOPEX/Poseidon are mainly faster than those given by standard linear theory. This paper examines why this should be. It is argued that the major changes to the unperturbed wave speed will be caused by the presence of baroclinic east–west mean flows, which modify the potential vorticity gradient. Long linear perturbations to such flow satisfy a simple eigenvalue problem (related directly to standard quasigeostrophic theory). Solutions are mostly real, though a few are complex. In simple situations approximate solutions can be obtained analytically. Using archive data, the global problem is treated. Phase speeds similar to those observed are found in most areas, although in the Southern Hemisphere an underestimate of speed by the theory remains. Thus, the presence of baroclinic mean flow is sufficient to account for the majority of the observed speeds. It is shown that phase speed changes are produced mainly by (vertical) mode-2 east–west velocities, with mode-1 having little or no effect. Inclusion of the mean barotropic flow from a global eddy-admitting model makes only a small modification to the fit with observations; whether the fit is improved is equivocal.
Abstract
A frictional geostrophic model is used to examine how the stability of the thermohaline circulation is affected by idealized topographic variations and the presence or absence of wind stress. If the flow exhibits collapses, the authors consider how topography and wind stress affect the ensuing oscillations. Large-scale slope up toward the north or the west can significantly destabilize the circulation by modifying the barotropic flow and reducing the depth of convection. Wind stress stabilizes the circulation by deepening the thermocline in the subtropical gyre. Wind driving can also radically reduce the period of oscillations by destabilizing the northern halocline in the collapsed phase. The overall period of the oscillation is usually governed by the time taken for diffusive warming to destabilize the deep ocean.
Abstract
A frictional geostrophic model is used to examine how the stability of the thermohaline circulation is affected by idealized topographic variations and the presence or absence of wind stress. If the flow exhibits collapses, the authors consider how topography and wind stress affect the ensuing oscillations. Large-scale slope up toward the north or the west can significantly destabilize the circulation by modifying the barotropic flow and reducing the depth of convection. Wind stress stabilizes the circulation by deepening the thermocline in the subtropical gyre. Wind driving can also radically reduce the period of oscillations by destabilizing the northern halocline in the collapsed phase. The overall period of the oscillation is usually governed by the time taken for diffusive warming to destabilize the deep ocean.
Abstract
As sea ice is advected on the surface of the ocean, the ice concentration (0 ≤ A ≤ 1) and the mean ice thickness change in response to thermodynamic and mechanical forcing. In this paper the authors review the existing advection schemes and compare their properties in the absence of thermodynamic effects. In Hibler's classical scheme, the ice area fraction at a material particle changes due to the divergence of the large-scale horizontal velocity field, and a further constraint is applied in order to keep A ≤ 1. This scheme is used in almost all sea ice models, although Hibler and Shinohara have both since included a ridging sink tem In this paper the authors show that the Hibler advection scheme is a special case of Gray and Morland's ridging model and compare the ridging schemes of Hibler and Shinohara with the simple scheme of Gray and Morland. It is demonstrated that the Hibler scheme still allows ice concentrations to exceed unity in maintained convergence and that both Hibler and Shinohara schemes admit the possibility of negative ice concentrations during maintained shearing. A general framework is formulated for the functional form of the ridging sink term that guarantees 0 ≤ A ≤ 1. Finally, some elementary analytic solutions are derived, which imply that, if ridging is independent of shear effects, quantities are conserved along particle paths.
Abstract
As sea ice is advected on the surface of the ocean, the ice concentration (0 ≤ A ≤ 1) and the mean ice thickness change in response to thermodynamic and mechanical forcing. In this paper the authors review the existing advection schemes and compare their properties in the absence of thermodynamic effects. In Hibler's classical scheme, the ice area fraction at a material particle changes due to the divergence of the large-scale horizontal velocity field, and a further constraint is applied in order to keep A ≤ 1. This scheme is used in almost all sea ice models, although Hibler and Shinohara have both since included a ridging sink tem In this paper the authors show that the Hibler advection scheme is a special case of Gray and Morland's ridging model and compare the ridging schemes of Hibler and Shinohara with the simple scheme of Gray and Morland. It is demonstrated that the Hibler scheme still allows ice concentrations to exceed unity in maintained convergence and that both Hibler and Shinohara schemes admit the possibility of negative ice concentrations during maintained shearing. A general framework is formulated for the functional form of the ridging sink term that guarantees 0 ≤ A ≤ 1. Finally, some elementary analytic solutions are derived, which imply that, if ridging is independent of shear effects, quantities are conserved along particle paths.
Abstract
The response of the deep ocean to periodic and steady forcing by mass sources is considered, in the presence of fluid loss, diffusion, and topography, which may or may not have regions of closed planetary vorticity. There can be a preexisting deep layer, or the forcing may produce one. The long-time response to forcing, which varies annually, is shown to have only a small periodic component, essentially because the mass loss by diapycnic transfer is weak. This is in qualitative agreement with observations of overflows, which show little seasonal signal. Ridges do not form an effective block to the flow, which can bypass the ridges, approximately following lines of constant planetary vorticity. A brief discussion of how fluid leaks out of closed planetary vorticity regions by diffusion is included.
Abstract
The response of the deep ocean to periodic and steady forcing by mass sources is considered, in the presence of fluid loss, diffusion, and topography, which may or may not have regions of closed planetary vorticity. There can be a preexisting deep layer, or the forcing may produce one. The long-time response to forcing, which varies annually, is shown to have only a small periodic component, essentially because the mass loss by diapycnic transfer is weak. This is in qualitative agreement with observations of overflows, which show little seasonal signal. Ridges do not form an effective block to the flow, which can bypass the ridges, approximately following lines of constant planetary vorticity. A brief discussion of how fluid leaks out of closed planetary vorticity regions by diffusion is included.
