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- Author or Editor: Eric P. Chassignet x
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Abstract
In an exploration of the dynamics of current separation and vorticity dissipation in a two-layer model, the following is found. 1) Results obtained in a barotropic context remain valid; namely, two major dissipation regimes can be found: either a “loop current” or a recirculating gyre. 2) A transition from one regime to the other can be achieved if one increases the strength of the front associated with the outcrop, regardless of the specified boundary conditions. 3) Separation will depend upon the choice of lateral boundary conditions if the upper-layer flow is not highly inertial.
Abstract
In an exploration of the dynamics of current separation and vorticity dissipation in a two-layer model, the following is found. 1) Results obtained in a barotropic context remain valid; namely, two major dissipation regimes can be found: either a “loop current” or a recirculating gyre. 2) A transition from one regime to the other can be achieved if one increases the strength of the front associated with the outcrop, regardless of the specified boundary conditions. 3) Separation will depend upon the choice of lateral boundary conditions if the upper-layer flow is not highly inertial.
Abstract
The Agulhas retroflection region of the wind-driven idealized South Atlantic–Indian Ocean model described by DeRuijter and Boudra is analyzed in detail. Here, in Part I, the physical mechanisms of the model retroflection are elucidated through illustration of Agulhas' vorticity balance among various experiments. In Part II, the ring formation process is described in terms of its vertical structure and the associated energy conversions.
A one-layer model demonstration shows that both inertia and internal friction may account for a partial retroflection where a linear, weakly viscous system has none. In the nonlinear, weakly viscous one-layer model, the retroflection is accomplished through a free inertial boundary layer, as suggested originally by De Ruijter. When stratification is introduced and baroclinicity increased, using the Bleck and Boudra quasi-isopycnic coordinate model with 2 or 3 layers, the stretching term exerts an increasing influence. With 40-km resolution, terms included so that the numerical model conserves potential vorticity become important as well. Both encourage retroflection of the fluid separating from Africa's trip. When grid spacing is halved, the importance of the extra conserving terms diminishes and the stretching term exerts an even greater influence. The importance of a substantial viscous stress curl along the coast of Africa, as provided by the no-slip condition, is illustrated through comparison with a slippery Africa experiment.
Finally, an experiment with a more realistic South Africa coastal geometry, giving a more realistic order of importance to βv in the separating Agulhas, is described. It is shown that the retroflection is still strong but that the associated recirculation is less intense. An interesting new aspect of the retroflection is the separation of the mean current core from the coast a few hundred kilometers upstream from the tip. The planetary vorticity advection term plays a smaller role along the coast. Viscous effects on the coastal side of the current are still strong, however, and are balanced primarily by stretching and relative vorticity advection. As the mean current passes Africa's tip, the sink of positive vorticity produced in the stretching and planetary vorticity advection terms is left behind, and the Agulhas turns eastward. These results support the notion, advanced by De Ruijter and Boudra, that the change in the vorticity balance at separation leads to the model retroflection, and they point to the increasing importance of the divergent component of flow in the vorticity balance as more realism is introduced.
Abstract
The Agulhas retroflection region of the wind-driven idealized South Atlantic–Indian Ocean model described by DeRuijter and Boudra is analyzed in detail. Here, in Part I, the physical mechanisms of the model retroflection are elucidated through illustration of Agulhas' vorticity balance among various experiments. In Part II, the ring formation process is described in terms of its vertical structure and the associated energy conversions.
A one-layer model demonstration shows that both inertia and internal friction may account for a partial retroflection where a linear, weakly viscous system has none. In the nonlinear, weakly viscous one-layer model, the retroflection is accomplished through a free inertial boundary layer, as suggested originally by De Ruijter. When stratification is introduced and baroclinicity increased, using the Bleck and Boudra quasi-isopycnic coordinate model with 2 or 3 layers, the stretching term exerts an increasing influence. With 40-km resolution, terms included so that the numerical model conserves potential vorticity become important as well. Both encourage retroflection of the fluid separating from Africa's trip. When grid spacing is halved, the importance of the extra conserving terms diminishes and the stretching term exerts an even greater influence. The importance of a substantial viscous stress curl along the coast of Africa, as provided by the no-slip condition, is illustrated through comparison with a slippery Africa experiment.
Finally, an experiment with a more realistic South Africa coastal geometry, giving a more realistic order of importance to βv in the separating Agulhas, is described. It is shown that the retroflection is still strong but that the associated recirculation is less intense. An interesting new aspect of the retroflection is the separation of the mean current core from the coast a few hundred kilometers upstream from the tip. The planetary vorticity advection term plays a smaller role along the coast. Viscous effects on the coastal side of the current are still strong, however, and are balanced primarily by stretching and relative vorticity advection. As the mean current passes Africa's tip, the sink of positive vorticity produced in the stretching and planetary vorticity advection terms is left behind, and the Agulhas turns eastward. These results support the notion, advanced by De Ruijter and Boudra, that the change in the vorticity balance at separation leads to the model retroflection, and they point to the increasing importance of the divergent component of flow in the vorticity balance as more realism is introduced.
Abstract
An energetics analysis of several numerical experiments on an idealized South Atlantic-Indian Ocean basin is presented. The model used in the experiments is the quasi-isopycnic coordinate model of Bleck and Boundra forced by wind and configured with two or three layers. The region of focus is the most dynamically active one, the Agulhas Current retroflection south of Africa, and the dynamical mechanisms associated with formation of Agulhas rings are given special attention.
Whether rings form in the model and their frequency depend on two primary factors: the shape of Africa and southward inertia/baroclinicity in the overshooting Agulhas. The boundary condition on Africa (no-slip/free-slip) and horizontal resolution are also important. Experiments in which rings form exhibit considerably larger values of K M to K E transfer than those in which no rings form. In three of the experiments, ring formation is studied in detail with the help of instantaneous top and bottom layer flow patterns and time series energetics. In a low Rossby number experiment with a rectangular Africa, rings are formed almost continuously, and basin mode resonance plays a significant role in ring formation. Whether a form of instability (barotropic or baroclinic) play an important role as well is unclear. In two high Rossby number experiments, one with rectangular and the other with triangular African geometry, basin mode resonance is not a factor, and, it is suggested that ring formation is associated with release of mixed barotropic-baroclinic instability.
Abstract
An energetics analysis of several numerical experiments on an idealized South Atlantic-Indian Ocean basin is presented. The model used in the experiments is the quasi-isopycnic coordinate model of Bleck and Boundra forced by wind and configured with two or three layers. The region of focus is the most dynamically active one, the Agulhas Current retroflection south of Africa, and the dynamical mechanisms associated with formation of Agulhas rings are given special attention.
Whether rings form in the model and their frequency depend on two primary factors: the shape of Africa and southward inertia/baroclinicity in the overshooting Agulhas. The boundary condition on Africa (no-slip/free-slip) and horizontal resolution are also important. Experiments in which rings form exhibit considerably larger values of K M to K E transfer than those in which no rings form. In three of the experiments, ring formation is studied in detail with the help of instantaneous top and bottom layer flow patterns and time series energetics. In a low Rossby number experiment with a rectangular Africa, rings are formed almost continuously, and basin mode resonance plays a significant role in ring formation. Whether a form of instability (barotropic or baroclinic) play an important role as well is unclear. In two high Rossby number experiments, one with rectangular and the other with triangular African geometry, basin mode resonance is not a factor, and, it is suggested that ring formation is associated with release of mixed barotropic-baroclinic instability.
Abstract
The one-layer, reduced-gravity, also called equivalent-barotropic, model has been widely used in countless applications. Although its validity is based on the assumption that a second, lower layer is sufficiently deep to be dynamically inactive, the question of how deep that second layer ought to be has not yet received thorough examination. When one considers the importance of the two processes excluded from the reduced-gravity model, namely barotropic motion and baroclinic instability, the conventional choice of a second layer much deeper than the first might be too simplistic.
A scaling analysis aimed at covering all two-layer regimes, geostrophic as well as ageostrophic, leads to a double criterion, requiring that the total depth of fluid be much larger than either of two values. These values, resulting from f-plane and β-plane dynamics, apply to the shorter and longer scales, respectively. A number of numerical experiments on the propagation of eddies on the β-plane with various eddy radii and lower-layer depths verify the applicability of the criterion. A final set of experiments with dipoles on the f-plane and β-plane also clearly illustrates the two sides of the criterion.
The rule for the validity of the reduced-gravity model can be summarized as follows. For characteristic horizontal length scales of motion (e.g., eddy radius, wavelength, …) up to the deformation radius, it is sufficient that the lower layer be much deeper (e.g., by a factor ten or so) than the upper layer. For length scales increasing beyond the deformation radius, on both the f- and β-planes, the reduced-gravity model rapidly loses its validity. The model recovers its validity toward larger scales on the β-plane.
Abstract
The one-layer, reduced-gravity, also called equivalent-barotropic, model has been widely used in countless applications. Although its validity is based on the assumption that a second, lower layer is sufficiently deep to be dynamically inactive, the question of how deep that second layer ought to be has not yet received thorough examination. When one considers the importance of the two processes excluded from the reduced-gravity model, namely barotropic motion and baroclinic instability, the conventional choice of a second layer much deeper than the first might be too simplistic.
A scaling analysis aimed at covering all two-layer regimes, geostrophic as well as ageostrophic, leads to a double criterion, requiring that the total depth of fluid be much larger than either of two values. These values, resulting from f-plane and β-plane dynamics, apply to the shorter and longer scales, respectively. A number of numerical experiments on the propagation of eddies on the β-plane with various eddy radii and lower-layer depths verify the applicability of the criterion. A final set of experiments with dipoles on the f-plane and β-plane also clearly illustrates the two sides of the criterion.
The rule for the validity of the reduced-gravity model can be summarized as follows. For characteristic horizontal length scales of motion (e.g., eddy radius, wavelength, …) up to the deformation radius, it is sufficient that the lower layer be much deeper (e.g., by a factor ten or so) than the upper layer. For length scales increasing beyond the deformation radius, on both the f- and β-planes, the reduced-gravity model rapidly loses its validity. The model recovers its validity toward larger scales on the β-plane.
Abstract
The separation Point of a midlatitude jet from the western boundary in ocean numerical models depends upon both the governing equations and the vertical coordinate used. Systematic differences in the point of separation between level and layer models are shown. In level models, the separation usually occurs poleward of the zero wind-stress curl line, whereas, in layer models, it usually occurs equatorward. These differences are caused by two aspects of the numerical implementation. First, the wind forcing is usually assumed to act as a body force over the upper layer or level in the models, and this corresponds to a different physical assumption. Second, the free-slip boundary condition is imposed as zero vorticity in both models. This is an inconsistency because vorticity is not the same quantity when the governing equations are formulated in physical (level model) and isopycnal (layer model) coordinates. The effects on separation of these numerical implementation differences are illustrated using analytical solutions of linear models and numerical solutions of several nonlinear models.
Abstract
The separation Point of a midlatitude jet from the western boundary in ocean numerical models depends upon both the governing equations and the vertical coordinate used. Systematic differences in the point of separation between level and layer models are shown. In level models, the separation usually occurs poleward of the zero wind-stress curl line, whereas, in layer models, it usually occurs equatorward. These differences are caused by two aspects of the numerical implementation. First, the wind forcing is usually assumed to act as a body force over the upper layer or level in the models, and this corresponds to a different physical assumption. Second, the free-slip boundary condition is imposed as zero vorticity in both models. This is an inconsistency because vorticity is not the same quantity when the governing equations are formulated in physical (level model) and isopycnal (layer model) coordinates. The effects on separation of these numerical implementation differences are illustrated using analytical solutions of linear models and numerical solutions of several nonlinear models.
Abstract
The influence of outcropping isopycnal layers on the separation of western boundary currents is investigated in a series of wind-driven eddy-resolving multilayer primitive equation numerical experiments. The outcropping mechanism of Parsons allows the midlatitude jet to separate south of the zero wind-stress curl line (ZWCL), an important property when one considers that most realistic numerical experiments to date exhibit an over-shooting subtropical western boundary current.
If the inertial terms are removed from the momentum equations, the Sverdrup relation for the interior flow emerges as the dominant constraint on the placement of the upper-layer jet separation latitude. As long as the upper/lower layer ratio is small enough, a good agreement is obtained with the analytical theory, namely a separation south of the ZWCL. If the ratio is large, the resulting flow pattern changes drastically by favoring a configuration that satisfies the Sverdrup relation and maintains a jet separation at the ZWCL.
As soon as the inertial terms are included, the Sverdrup constraint becomes less dominant, allowing the upper-layer midlatitude jet separation latitude to shift southward whenever the upper layer is chosen sufficiently shallow to cause large-scale outcropping. The degree to which this southward shift depends on the amount of mass in the top layer and on the parameterization of the wind-induced stress profile in the water column is explored in detail.
Abstract
The influence of outcropping isopycnal layers on the separation of western boundary currents is investigated in a series of wind-driven eddy-resolving multilayer primitive equation numerical experiments. The outcropping mechanism of Parsons allows the midlatitude jet to separate south of the zero wind-stress curl line (ZWCL), an important property when one considers that most realistic numerical experiments to date exhibit an over-shooting subtropical western boundary current.
If the inertial terms are removed from the momentum equations, the Sverdrup relation for the interior flow emerges as the dominant constraint on the placement of the upper-layer jet separation latitude. As long as the upper/lower layer ratio is small enough, a good agreement is obtained with the analytical theory, namely a separation south of the ZWCL. If the ratio is large, the resulting flow pattern changes drastically by favoring a configuration that satisfies the Sverdrup relation and maintains a jet separation at the ZWCL.
As soon as the inertial terms are included, the Sverdrup constraint becomes less dominant, allowing the upper-layer midlatitude jet separation latitude to shift southward whenever the upper layer is chosen sufficiently shallow to cause large-scale outcropping. The degree to which this southward shift depends on the amount of mass in the top layer and on the parameterization of the wind-induced stress profile in the water column is explored in detail.
Abstract
The emergence of Fofonoff-like flows over a wide range of dissipative parameter regimes is explored in a wind-driven two-layer quasigeostrophic model. Two regimes are found in which Fofonoff-like circulations emerge as a direct consequence of the baroclinic nature of the system, since the wind forcing used in these experiments has been shown to inhibit the formation of Fofonoff flows in the barotropic case. The first regime is one in which the magnitudes of the frictional coefficients (viscosity and bottom dissipation) are extremely small. The experiments clearly illustrate the transition of the numerical solution from a conventional wind-driven circulation to an inertial Fofonoff-like regime. The latter circulation first appears in the lower layer and then spreads throughout the water column via barotropization. The second regime, surprisingly, is obtained with very high bottom friction. This result indicates that entropy can be maximized independently in each layer, depending on the distribution of forcing and dissipation. This sheds a new perspective on the common assumption that forcing and dissipation are disruptive effects that prevent the system from displaying a Fofonoff state.
Abstract
The emergence of Fofonoff-like flows over a wide range of dissipative parameter regimes is explored in a wind-driven two-layer quasigeostrophic model. Two regimes are found in which Fofonoff-like circulations emerge as a direct consequence of the baroclinic nature of the system, since the wind forcing used in these experiments has been shown to inhibit the formation of Fofonoff flows in the barotropic case. The first regime is one in which the magnitudes of the frictional coefficients (viscosity and bottom dissipation) are extremely small. The experiments clearly illustrate the transition of the numerical solution from a conventional wind-driven circulation to an inertial Fofonoff-like regime. The latter circulation first appears in the lower layer and then spreads throughout the water column via barotropization. The second regime, surprisingly, is obtained with very high bottom friction. This result indicates that entropy can be maximized independently in each layer, depending on the distribution of forcing and dissipation. This sheds a new perspective on the common assumption that forcing and dissipation are disruptive effects that prevent the system from displaying a Fofonoff state.
Abstract
The generation of interannual and near-decadal variability in the formation of mode waters in the western North Atlantic is investigated in the realistic framework of an isopycnic coordinate ocean model forced with atmospheric data from 1946 to 1988. At Bermuda, the model reproduces quite well the observed potential vorticity and isopycnal depth anomalies associated with the subtropical mode water (STMW). Heat storage and preconditioning of the convective activity are found to be the important factors for the generation of STMW variability, with persistence of cold (warm) conditions, associated with anomalous heat loss (gain) over the western subtropics, being more significant for the generation of the simulated variability than are strong anomalous events in isolated years.
In the Labrador Sea, the model captures the phase and order of magnitude of the observed near-decadal variability in the convective activity, if not its maximum amplitude. The simulated potential vorticity anomalies are, as observed, out-of-phase with those in the western subtropics and correlate well with the North Atlantic Oscillation (NAO) at near-decadal timescales, with the oceanic response lagging the NAO by ∼2–3 years. These results support the idea that the variability in water mass formation in the western North Atlantic can be attributed, to a large extent, to changes in the pattern of the large-scale atmospheric circulation, which generate sensible and latent heat flux variability by modifying the strength and position of the westerly winds and the advection of heat and moisture over the ocean. To the authors' knowledge, this is the first time that the interannual and near-decadal subsurface variability associated with STMW and Labrador Sea Water, and its relationship to the NAO, has been simulated in an ocean general circulation model.
Abstract
The generation of interannual and near-decadal variability in the formation of mode waters in the western North Atlantic is investigated in the realistic framework of an isopycnic coordinate ocean model forced with atmospheric data from 1946 to 1988. At Bermuda, the model reproduces quite well the observed potential vorticity and isopycnal depth anomalies associated with the subtropical mode water (STMW). Heat storage and preconditioning of the convective activity are found to be the important factors for the generation of STMW variability, with persistence of cold (warm) conditions, associated with anomalous heat loss (gain) over the western subtropics, being more significant for the generation of the simulated variability than are strong anomalous events in isolated years.
In the Labrador Sea, the model captures the phase and order of magnitude of the observed near-decadal variability in the convective activity, if not its maximum amplitude. The simulated potential vorticity anomalies are, as observed, out-of-phase with those in the western subtropics and correlate well with the North Atlantic Oscillation (NAO) at near-decadal timescales, with the oceanic response lagging the NAO by ∼2–3 years. These results support the idea that the variability in water mass formation in the western North Atlantic can be attributed, to a large extent, to changes in the pattern of the large-scale atmospheric circulation, which generate sensible and latent heat flux variability by modifying the strength and position of the westerly winds and the advection of heat and moisture over the ocean. To the authors' knowledge, this is the first time that the interannual and near-decadal subsurface variability associated with STMW and Labrador Sea Water, and its relationship to the NAO, has been simulated in an ocean general circulation model.
Abstract
In light of previous numerical studies demonstrating a strong sensitivity of the strength of thermohaline circulation to the representation of overflows in ocean general circulation models, the dynamics of bottom gravity currents are investigated using a two-dimensional, nonhydrostatic numerical model. The model explicitly resolves the Kelvin–Helmholtz instability, the main mechanism of mixing in nonrotating bottom gravity currents.
A series of experiments were conducted to explore the impact of density difference and slope angle on the dynamics of bottom gravity currents in a nonrotating and homogeneous environment. The features of the simulated currents; that is, a characteristic head at the leading edge and lumped vortices in the trailing fluid, agree qualitatively well with those observed in laboratory experiments. Quantitative comparisons of speed of descent indicate that laboratory results remain valid at geophysical scales.
Two distinct regimes of entrainment of ambient fluid into bottom gravity currents are identified: (i) the laminar entrainment regime is associated with the initial growth of the characteristic head due to the drag exerted by the fresh fluid in front and (ii) the turbulent entrainment is associated with the Kelvin–Helmholtz instabilities. The turbulent entrainment is found to be much stronger than the laminar entrainment, and entrainment in the turbulent regime is less sensitive to the slope angle than that in the laminar regime. The entrainment is quantified as a function of basic parameters of the system, the buoyancy flux and the slope angle, for the purpose of parameterizing the mixing induced by bottom gravity currents.
Abstract
In light of previous numerical studies demonstrating a strong sensitivity of the strength of thermohaline circulation to the representation of overflows in ocean general circulation models, the dynamics of bottom gravity currents are investigated using a two-dimensional, nonhydrostatic numerical model. The model explicitly resolves the Kelvin–Helmholtz instability, the main mechanism of mixing in nonrotating bottom gravity currents.
A series of experiments were conducted to explore the impact of density difference and slope angle on the dynamics of bottom gravity currents in a nonrotating and homogeneous environment. The features of the simulated currents; that is, a characteristic head at the leading edge and lumped vortices in the trailing fluid, agree qualitatively well with those observed in laboratory experiments. Quantitative comparisons of speed of descent indicate that laboratory results remain valid at geophysical scales.
Two distinct regimes of entrainment of ambient fluid into bottom gravity currents are identified: (i) the laminar entrainment regime is associated with the initial growth of the characteristic head due to the drag exerted by the fresh fluid in front and (ii) the turbulent entrainment is associated with the Kelvin–Helmholtz instabilities. The turbulent entrainment is found to be much stronger than the laminar entrainment, and entrainment in the turbulent regime is less sensitive to the slope angle than that in the laminar regime. The entrainment is quantified as a function of basic parameters of the system, the buoyancy flux and the slope angle, for the purpose of parameterizing the mixing induced by bottom gravity currents.
Abstract
The response of an ocean general circulation model to several distinct parameterizations of the surface heat and freshwater fluxes, which differ primarily by their representation of the ocean–atmosphere feedbacks, is investigated in a realistic configuration for the North Atlantic Ocean. The impact of explicitly introducing oceanic information (climatological sea-surface temperature) into the computation of the heat flux through a Haney-type restoring boundary condition, as opposed to the case in which the flux is based on atmosphere-only climatologies and is computed with the full bulk formulation, is considered. The strong similarity between these two approaches is demonstrated, and the sources of possible differences are discussed. When restoring boundary conditions are applied to the surface salinity, however, an unphysical feedback mechanism is being introduced. The model's response to this restoring is contrasted to the response to a flux boundary condition that prescribes the freshwater flux derived from evaporation, precipitation, and river runoff climatologies (and therefore does not allow any feedback), as well as to the more realistic case in terms of the feedback parameterization, in which the dependence of evaporation on the model sea surface temperature is explicitly represented. Limited-area models introduce a further complicating factor for the thermodynamic adjustment, namely the representation of the oceanic heat and freshwater fluxes at the lateral boundaries. The degree to which the model solution is influenced by such fluxes, in combination with the different surface parameterizations, is also assessed. In all cases, the various components of the model's thermodynamic adjustment are considered, and the interdependence between the surface fluxes and the simulated sea surface temperature and surface salinity, their combined effect upon the ventilation of subsurface layers and production of different water masses, and their effect upon the simulated meridional heat and freshwater transports are analyzed.
Abstract
The response of an ocean general circulation model to several distinct parameterizations of the surface heat and freshwater fluxes, which differ primarily by their representation of the ocean–atmosphere feedbacks, is investigated in a realistic configuration for the North Atlantic Ocean. The impact of explicitly introducing oceanic information (climatological sea-surface temperature) into the computation of the heat flux through a Haney-type restoring boundary condition, as opposed to the case in which the flux is based on atmosphere-only climatologies and is computed with the full bulk formulation, is considered. The strong similarity between these two approaches is demonstrated, and the sources of possible differences are discussed. When restoring boundary conditions are applied to the surface salinity, however, an unphysical feedback mechanism is being introduced. The model's response to this restoring is contrasted to the response to a flux boundary condition that prescribes the freshwater flux derived from evaporation, precipitation, and river runoff climatologies (and therefore does not allow any feedback), as well as to the more realistic case in terms of the feedback parameterization, in which the dependence of evaporation on the model sea surface temperature is explicitly represented. Limited-area models introduce a further complicating factor for the thermodynamic adjustment, namely the representation of the oceanic heat and freshwater fluxes at the lateral boundaries. The degree to which the model solution is influenced by such fluxes, in combination with the different surface parameterizations, is also assessed. In all cases, the various components of the model's thermodynamic adjustment are considered, and the interdependence between the surface fluxes and the simulated sea surface temperature and surface salinity, their combined effect upon the ventilation of subsurface layers and production of different water masses, and their effect upon the simulated meridional heat and freshwater transports are analyzed.
