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Abstract
The development of mixed layer models in so-called density coordinates is discussed. Density coordinates, or isopycnal coordinates as they are sometimes called, are becoming increasingly popular for use in ocean models due to their highly desirable adiabatic properties. In contrast, almost all existing mixed layer models assume a continuous density variable and are therefore somewhat inconsistent with the density coordinate philosophy. Many existing isopycnal models attempt to join standard surface mixed layer models to density coordinate interior models, and it is known that problems can arise in the physical behavior of the resulting system. The problem of mixed layer model development is approached here by adopting a density coordinate framework at the outset, thereby generating a surface layer model whose construction is entirely consistent with that of existing interior density coordinate models. Examples of quantitative and qualitative behavior are presented and argued to be encouraging.
Abstract
The development of mixed layer models in so-called density coordinates is discussed. Density coordinates, or isopycnal coordinates as they are sometimes called, are becoming increasingly popular for use in ocean models due to their highly desirable adiabatic properties. In contrast, almost all existing mixed layer models assume a continuous density variable and are therefore somewhat inconsistent with the density coordinate philosophy. Many existing isopycnal models attempt to join standard surface mixed layer models to density coordinate interior models, and it is known that problems can arise in the physical behavior of the resulting system. The problem of mixed layer model development is approached here by adopting a density coordinate framework at the outset, thereby generating a surface layer model whose construction is entirely consistent with that of existing interior density coordinate models. Examples of quantitative and qualitative behavior are presented and argued to be encouraging.
Abstract
Several recent models of midlatitude climate have speculated on the role of the North Atlantic Ocean in modulating the North Atlantic oscillation (NAO). Here this role is examined by means of numerical experimentation with a quasigeostrophic ocean model underneath a highly idealized atmosphere. It is argued that the dominant midlatitude oceanic influence is due to the so-called inertial recirculations, rather than linear baroclinic waves, as have previously been studied.
In these experiments, the forced response of the inertial recirculations dominates the leading-order ocean spatial mode, but that mode is energized by oceanic intrinsic variability. The oceanic signals are amplified relative to those predicted by wave models. The primary oceanic role of the coupling is to damp sea surface temperature (SST) at longer timescales, and the interdecadal atmospheric variability is placed under the control of the ocean. The SST damping reflects competition between intrinsically driven intergyre heat flux and an opposing feedback-driven advective heat flux. Spectral SST extrema can result near the transition point where the feedback heat flux approaches equilibrium, although these are secondary phenomena.
The picture of midlatitude climate variability painted here has qualitative similarities to that obtained from the linear waves models, but differs fundamentally from them both dynamically and philosophically. Most important, ocean variability is a dominant, rather than passive, partner in all aspects of the coupled system.
Abstract
Several recent models of midlatitude climate have speculated on the role of the North Atlantic Ocean in modulating the North Atlantic oscillation (NAO). Here this role is examined by means of numerical experimentation with a quasigeostrophic ocean model underneath a highly idealized atmosphere. It is argued that the dominant midlatitude oceanic influence is due to the so-called inertial recirculations, rather than linear baroclinic waves, as have previously been studied.
In these experiments, the forced response of the inertial recirculations dominates the leading-order ocean spatial mode, but that mode is energized by oceanic intrinsic variability. The oceanic signals are amplified relative to those predicted by wave models. The primary oceanic role of the coupling is to damp sea surface temperature (SST) at longer timescales, and the interdecadal atmospheric variability is placed under the control of the ocean. The SST damping reflects competition between intrinsically driven intergyre heat flux and an opposing feedback-driven advective heat flux. Spectral SST extrema can result near the transition point where the feedback heat flux approaches equilibrium, although these are secondary phenomena.
The picture of midlatitude climate variability painted here has qualitative similarities to that obtained from the linear waves models, but differs fundamentally from them both dynamically and philosophically. Most important, ocean variability is a dominant, rather than passive, partner in all aspects of the coupled system.
Abstract
The theory of the evolution of rings under a Cooling atmosphere is extended in two ways. First effects of stratification are studied analytically through the use of a “two and one-half” layer model. Second, model predictions are compared with observations. Qualitative support of the analytical model is also provided by a brief comparison of the analytical predictions with a numerical model.
Ring evolution is computed using the conservation of angular momentum. Idealizations in the analytical model include zero potential vorticity in the upper layer and an infinitely deep and resting third layer. The results from the analytical model witch is based on a crude representation of fluid thermodynamics and a continuously stratified numerical model with an active mixed layer agree qualitatively. Further, both models yield predictions of main thermocline deepening under warm rings which are consistent with field observations. This agreement supports the idea that the response of warm rings to cooling is governed by Rossby adjustmentlike mechanics.
Abstract
The theory of the evolution of rings under a Cooling atmosphere is extended in two ways. First effects of stratification are studied analytically through the use of a “two and one-half” layer model. Second, model predictions are compared with observations. Qualitative support of the analytical model is also provided by a brief comparison of the analytical predictions with a numerical model.
Ring evolution is computed using the conservation of angular momentum. Idealizations in the analytical model include zero potential vorticity in the upper layer and an infinitely deep and resting third layer. The results from the analytical model witch is based on a crude representation of fluid thermodynamics and a continuously stratified numerical model with an active mixed layer agree qualitatively. Further, both models yield predictions of main thermocline deepening under warm rings which are consistent with field observations. This agreement supports the idea that the response of warm rings to cooling is governed by Rossby adjustmentlike mechanics.
Abstract
A two-layer model of the general circulation including wind and thermal forcing is discussed. The flow in each layer is geostrophic, hydrostatic and obeys linear potential vorticity constraints. The equations are developed in spherical coordinates and reduce to a surprisingly simple, coupled, nonlinear set. Analytic solutions of this system are obtained in the quasi-geostrophic limit. The novel feature in this model is a weakly ventilated and weakly dissipative lower layer.
The quasi-geostrophic model predicts homogenized potential vorticity is regions of the lower layer which are not directly ventilated. These are also regions of locally minimum value in potential vorticity. The net balance determining the potential vorticity structure is between the diabatic forcing of the lower layer and eddy-drive mixing. As such, the structure of the solution depends on the sign of the eddy diffusion of potential vorticity (positive) and the sign of the diabatic potential vorticity source (negative). It is therefore argued that these features and not dependent on quasi-geostrophy.
A comparison of model results with data is encouraging. The 26.5 sigma-theta isopycnal is argued to be a density surface to which this theory applies. The potential vorticity structure on this surface obtains a bowl-like shape and agrees well with the model. The subtropical mode water of the North Atlantic (18°C water) is centered on this isopycnal and is identified in the model as the homogenized local potential vorticity minimum. The stability of 18°C water characteristics, documented elsewhere, is explained in terms of a gyre-scale response to variability.
Abstract
A two-layer model of the general circulation including wind and thermal forcing is discussed. The flow in each layer is geostrophic, hydrostatic and obeys linear potential vorticity constraints. The equations are developed in spherical coordinates and reduce to a surprisingly simple, coupled, nonlinear set. Analytic solutions of this system are obtained in the quasi-geostrophic limit. The novel feature in this model is a weakly ventilated and weakly dissipative lower layer.
The quasi-geostrophic model predicts homogenized potential vorticity is regions of the lower layer which are not directly ventilated. These are also regions of locally minimum value in potential vorticity. The net balance determining the potential vorticity structure is between the diabatic forcing of the lower layer and eddy-drive mixing. As such, the structure of the solution depends on the sign of the eddy diffusion of potential vorticity (positive) and the sign of the diabatic potential vorticity source (negative). It is therefore argued that these features and not dependent on quasi-geostrophy.
A comparison of model results with data is encouraging. The 26.5 sigma-theta isopycnal is argued to be a density surface to which this theory applies. The potential vorticity structure on this surface obtains a bowl-like shape and agrees well with the model. The subtropical mode water of the North Atlantic (18°C water) is centered on this isopycnal and is identified in the model as the homogenized local potential vorticity minimum. The stability of 18°C water characteristics, documented elsewhere, is explained in terms of a gyre-scale response to variability.
Abstract
Observations suggest that heat loss to the atmosphere causes an important modification of the density structure of warm core rings. In this study, f-plane models of rings under a cooling atmosphere are examined in order to provide a dynamic framework for the interpretation of ring observations and to assess ring effects on their environment.
Two-layer models with finite upper-layer volumes are examined The idealizations in these models include zero potential vorticity in the ring and an initially motionless lower layer. In the simplest problem, the atmosphere is assumed to completely remove the heat anomaly of the ring through cooling. The results of this calculation place limits on the restructuring of warm rings that can be forced by heat exchange. The time-dependent ventilation problem is also examined by considering the effects of partial heat withdrawals and cold air outbreaks. Estimates of energy release by rings during adjustment are large, suggesting the flux of significant energy into the internal wave bands by a single cooling event.
Abstract
Observations suggest that heat loss to the atmosphere causes an important modification of the density structure of warm core rings. In this study, f-plane models of rings under a cooling atmosphere are examined in order to provide a dynamic framework for the interpretation of ring observations and to assess ring effects on their environment.
Two-layer models with finite upper-layer volumes are examined The idealizations in these models include zero potential vorticity in the ring and an initially motionless lower layer. In the simplest problem, the atmosphere is assumed to completely remove the heat anomaly of the ring through cooling. The results of this calculation place limits on the restructuring of warm rings that can be forced by heat exchange. The time-dependent ventilation problem is also examined by considering the effects of partial heat withdrawals and cold air outbreaks. Estimates of energy release by rings during adjustment are large, suggesting the flux of significant energy into the internal wave bands by a single cooling event.
Abstract
A number of general circulation models have recently been proposed that compute the steady-state structure of the general circulation. Observation of 18°C water formation, on the other hand, suggest the need for a study of the time-dependent large-scale structure of the oceans. In this paper, the planetary geostrophic equations are used to compute the evolution of large thermal anomalies with a view toward understanding the variability in the general circulation caused by water mass formation events.
The evolution of a thermal anomaly is considered in the absence of wind forcing. In this case, the planetary geostrophic equations can be reduced to a first-order equations, the Planetary Geostrophic Wave Equation (PGWE). Arbitrary initial conditions governed by the PGWE tend to steepen and, under an assumed diffusive closure, from shock waves. The evolution of an initially columnar eddy is obtained, and four different phases of shock propagation are identified. The implications for heat transport, potential vorticity transport and thermocline ventilation are discussed.
Abstract
A number of general circulation models have recently been proposed that compute the steady-state structure of the general circulation. Observation of 18°C water formation, on the other hand, suggest the need for a study of the time-dependent large-scale structure of the oceans. In this paper, the planetary geostrophic equations are used to compute the evolution of large thermal anomalies with a view toward understanding the variability in the general circulation caused by water mass formation events.
The evolution of a thermal anomaly is considered in the absence of wind forcing. In this case, the planetary geostrophic equations can be reduced to a first-order equations, the Planetary Geostrophic Wave Equation (PGWE). Arbitrary initial conditions governed by the PGWE tend to steepen and, under an assumed diffusive closure, from shock waves. The evolution of an initially columnar eddy is obtained, and four different phases of shock propagation are identified. The implications for heat transport, potential vorticity transport and thermocline ventilation are discussed.
Abstract
Simple analytical and numerical models of gratified circulation are discussed. The models are driven by buoyancy and mechanical forcing, and buoyancy diffusion is parameterized in term of diapycnal mass fluxes. The interior responds in typical Sverdrup fashion, and the requirements of balanced heat and energy budgets are invoked to calculate the eastern boundary stratification parameters.
This effort differs from past attempts to calculate stratification in that buoyancy flux boundary conditions or explicitly considered in the calculation of diapycnal fluxes. A major feature of the solutions is the interplay of planetary dynamics and buoyancy diffusion. This results in the most important components of the thermocline structure, namely density outcrops and interior “pinchoffs.” These are, in turn, essential to the production of thermodynamically balanced states. Some aspects of the present model resemble features found in previous numerical models.
Abstract
Simple analytical and numerical models of gratified circulation are discussed. The models are driven by buoyancy and mechanical forcing, and buoyancy diffusion is parameterized in term of diapycnal mass fluxes. The interior responds in typical Sverdrup fashion, and the requirements of balanced heat and energy budgets are invoked to calculate the eastern boundary stratification parameters.
This effort differs from past attempts to calculate stratification in that buoyancy flux boundary conditions or explicitly considered in the calculation of diapycnal fluxes. A major feature of the solutions is the interplay of planetary dynamics and buoyancy diffusion. This results in the most important components of the thermocline structure, namely density outcrops and interior “pinchoffs.” These are, in turn, essential to the production of thermodynamically balanced states. Some aspects of the present model resemble features found in previous numerical models.
Abstract
Two models of the oceanic response to cooling are discussed. Both are motivated by a desire to understand the effects of variable diabatic forcing on the general circulation. The first model considers an initial value problem in which an initially resting warm ocean is “slowly”cooled on "broad”scales. The lower layer in this model is fully active and it is further argued that the slow and broad scales are relevant to 1 8°C water formation. The purpose of this model is to illustrate the short term barotropic and baroclinic response to variability in thermal forcing.
The second problem addresses the longer-term evolution of finite amplitude thermocline anomalies (which are assumed to have been formed by diabatic effects). A “one and three-quarter”model is used. i.e., the lower layer is assumed to be deep, but not stagnant, and its evolution is computed.
Based on these models, it is argued that diabatic forcing can result in local modifications of the Sverdrup constraint and that mass transport evolves through at least three distinct phases. The first short-term ocean response to cooling is the radiation of eastward moving barotropic planetary waves, which leaves the Sverdrup transport and the planetary geostrophic wave equation (PGWE) in its wake. Local Sverdrup dynamics and the PGWE dominate the second phase of evolution. The last phase occurs as the fronts obtain deformation radius length scales, and the tendency for the system to produce coherent structures results in persistent, spreading regions of anomalous transport. Global measures of the mass transport, however, are in agreement with the classic Sverdrup constraint. Implications for the generation of barotropic and baroclinic variability are discussed.
Abstract
Two models of the oceanic response to cooling are discussed. Both are motivated by a desire to understand the effects of variable diabatic forcing on the general circulation. The first model considers an initial value problem in which an initially resting warm ocean is “slowly”cooled on "broad”scales. The lower layer in this model is fully active and it is further argued that the slow and broad scales are relevant to 1 8°C water formation. The purpose of this model is to illustrate the short term barotropic and baroclinic response to variability in thermal forcing.
The second problem addresses the longer-term evolution of finite amplitude thermocline anomalies (which are assumed to have been formed by diabatic effects). A “one and three-quarter”model is used. i.e., the lower layer is assumed to be deep, but not stagnant, and its evolution is computed.
Based on these models, it is argued that diabatic forcing can result in local modifications of the Sverdrup constraint and that mass transport evolves through at least three distinct phases. The first short-term ocean response to cooling is the radiation of eastward moving barotropic planetary waves, which leaves the Sverdrup transport and the planetary geostrophic wave equation (PGWE) in its wake. Local Sverdrup dynamics and the PGWE dominate the second phase of evolution. The last phase occurs as the fronts obtain deformation radius length scales, and the tendency for the system to produce coherent structures results in persistent, spreading regions of anomalous transport. Global measures of the mass transport, however, are in agreement with the classic Sverdrup constraint. Implications for the generation of barotropic and baroclinic variability are discussed.
Abstract
Midocean fronts have by now been well documented in the World Ocean. In view of this, a general circulation theory that admits interior fronts is considered in this paper and a new class of frontal solutions is discussed. The present solutions are distinguished by having fronts that originate at locations within the interior of the circulation. The locations of the front origins do not depend upon local effects; rather, they are set by conditions far from the front. Such fronts are thus referred to as “spontaneous shocks.” They occur in adiabatic wind-driven models, and participate in the ventilated thermocline. Indeed, calculating basin conditions that result in spontaneous shocks is a central objective of this paper. Aspects of some observed fronts also have counterparts in the theory, and it is suggested that spontaneous shocks in the ventilated thermocline resemble certain North Pacific observations.
Abstract
Midocean fronts have by now been well documented in the World Ocean. In view of this, a general circulation theory that admits interior fronts is considered in this paper and a new class of frontal solutions is discussed. The present solutions are distinguished by having fronts that originate at locations within the interior of the circulation. The locations of the front origins do not depend upon local effects; rather, they are set by conditions far from the front. Such fronts are thus referred to as “spontaneous shocks.” They occur in adiabatic wind-driven models, and participate in the ventilated thermocline. Indeed, calculating basin conditions that result in spontaneous shocks is a central objective of this paper. Aspects of some observed fronts also have counterparts in the theory, and it is suggested that spontaneous shocks in the ventilated thermocline resemble certain North Pacific observations.
Abstract
Convection in the world's oceans often occurs in small, semienclosed basins where bottom slopes and nearby continental shelf breaks are commonplace. The evolution of convectively generated heat anomalies in such settings is studied using quasigeostrophic finite-difference and point vortex models. The displayed behaviors divide essentially into two categories: whole fluid column convection, in which bottom-slope effects are felt immediately, and partial fluid column convection, in which the topographic effects can be delayed. In both cases, topography significantly modifies the evolution of convective patches from that occurring over flat bottoms. Vertical walls induce strong self-propagation mechanisms that accelerate alongslope heat transport, while the continental shelf slope is repulsive and rejects lower-layer anticyclones. These anomalies are then “stranded,” being too far offshore to interact with the shelf break and having lost their heton partner in the interaction. Weaker deep ocean topographic slopes disrupt heton formation and disperse convective patches by topographic mechanisms. Partial fluid column convection, with stratification under the mixed layer, proceeds through a cascade from small to large length scales. In oceanically relevant regimes, smaller scales are shielded from bottom slopes and can disperse as small hetons. Larger-scale structures are prevented by the topography from forming into hetons and instead evolve as if in a sloping-bottom two-layer system. The small hetons, when encountering shelf breaks, can experience topographic repulsion and stranding. Comparisons with the Mediterranean Sea suggest alternative interpretations for some observations, and several observed Labrador Sea mesoscale convective characteristics can be ascribed to topographic effects.
Abstract
Convection in the world's oceans often occurs in small, semienclosed basins where bottom slopes and nearby continental shelf breaks are commonplace. The evolution of convectively generated heat anomalies in such settings is studied using quasigeostrophic finite-difference and point vortex models. The displayed behaviors divide essentially into two categories: whole fluid column convection, in which bottom-slope effects are felt immediately, and partial fluid column convection, in which the topographic effects can be delayed. In both cases, topography significantly modifies the evolution of convective patches from that occurring over flat bottoms. Vertical walls induce strong self-propagation mechanisms that accelerate alongslope heat transport, while the continental shelf slope is repulsive and rejects lower-layer anticyclones. These anomalies are then “stranded,” being too far offshore to interact with the shelf break and having lost their heton partner in the interaction. Weaker deep ocean topographic slopes disrupt heton formation and disperse convective patches by topographic mechanisms. Partial fluid column convection, with stratification under the mixed layer, proceeds through a cascade from small to large length scales. In oceanically relevant regimes, smaller scales are shielded from bottom slopes and can disperse as small hetons. Larger-scale structures are prevented by the topography from forming into hetons and instead evolve as if in a sloping-bottom two-layer system. The small hetons, when encountering shelf breaks, can experience topographic repulsion and stranding. Comparisons with the Mediterranean Sea suggest alternative interpretations for some observations, and several observed Labrador Sea mesoscale convective characteristics can be ascribed to topographic effects.
