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## Abstract

The thermodynamic processes attendant on the transfer of fluid between a surface mixed layer and a stratified thermocline beneath are discussed. For a parcel of fluid in the mixed layer to pass into the stratified thermocline—to subduct—it must be stratified by buoyancy input; this buoyancy can be supplied by local air–sea exchange and/or by lateral advective processes.

A series of experiments is described in which a mixed layer, coupled to an ideal-fluid thermocline, undergoes differing seasonal cycles: in one limit the mixed layer is held fixed in a steady, winter configuration; in the other the mixed layer is, more realistically, shallow over most of the year and deepens briefly in late winter. It is shown that the annual subduction rate *S*
_{ann} depends, to first order, only on late winter mixed layer properties. However the annual-mean air–sea buoyancy exchange is *sensitive* to the details of the seasonal cycle and becomes vanishingly small as the effective subduction period shortens. In this limit the buoyancy is provided through advective processes in the Ekman layer.

The authors conclude that in ocean models that do not explicitly represent a seasonal cycle it is necessary to parameterize the process through a prescription of the winter mixed layer density and depth. The buoyancy forcing diagnosed from such models must be interpreted as the combined contribution of the annual air–sea exchange and lateral advectivc processes in the summer Ekman layer.

## Abstract

The thermodynamic processes attendant on the transfer of fluid between a surface mixed layer and a stratified thermocline beneath are discussed. For a parcel of fluid in the mixed layer to pass into the stratified thermocline—to subduct—it must be stratified by buoyancy input; this buoyancy can be supplied by local air–sea exchange and/or by lateral advective processes.

A series of experiments is described in which a mixed layer, coupled to an ideal-fluid thermocline, undergoes differing seasonal cycles: in one limit the mixed layer is held fixed in a steady, winter configuration; in the other the mixed layer is, more realistically, shallow over most of the year and deepens briefly in late winter. It is shown that the annual subduction rate *S*
_{ann} depends, to first order, only on late winter mixed layer properties. However the annual-mean air–sea buoyancy exchange is *sensitive* to the details of the seasonal cycle and becomes vanishingly small as the effective subduction period shortens. In this limit the buoyancy is provided through advective processes in the Ekman layer.

The authors conclude that in ocean models that do not explicitly represent a seasonal cycle it is necessary to parameterize the process through a prescription of the winter mixed layer density and depth. The buoyancy forcing diagnosed from such models must be interpreted as the combined contribution of the annual air–sea exchange and lateral advectivc processes in the summer Ekman layer.

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## Abstract

It is shown that subtle changes in the velocity profile across the seaward extension of midlatitude jets, such as the Gulf Stream, can lead to dramatic changes in the zonal-penetration scale. In particular, if α = *dq*/*d*ψ > 0, where *q* is the absolute vorticity and ψ is a streamfunction for the geostrophic flow, then the jet tends to penetrate across to the eastern boundary; conversely if α < 0, the jet turns back on itself creating a tight recirculation on the scale of order |α|^{−frac12;}. This behavior is demonstrated in a quasigeostrophic ocean model in which a jet profile is prescribed as an inflow condition at the western margin of a half-basin, and radiation conditions along the remainder of the western boundary allow the injected fluid to escape. Jet inflows with both vertical and horizontal structure are considered in one and one-half-, two-, and three-layer models.

Finally, the implications of our study for numerical simulations of ocean gyres, which frequently show sensitivity of jet penetration to horizontal and vertical resolution and to choice of boundary conditions, are discussed. In particular, it is demonstrated that poor resolution of the horizontal jet structure may lead to a dramatic reduction in penetration.

## Abstract

It is shown that subtle changes in the velocity profile across the seaward extension of midlatitude jets, such as the Gulf Stream, can lead to dramatic changes in the zonal-penetration scale. In particular, if α = *dq*/*d*ψ > 0, where *q* is the absolute vorticity and ψ is a streamfunction for the geostrophic flow, then the jet tends to penetrate across to the eastern boundary; conversely if α < 0, the jet turns back on itself creating a tight recirculation on the scale of order |α|^{−frac12;}. This behavior is demonstrated in a quasigeostrophic ocean model in which a jet profile is prescribed as an inflow condition at the western margin of a half-basin, and radiation conditions along the remainder of the western boundary allow the injected fluid to escape. Jet inflows with both vertical and horizontal structure are considered in one and one-half-, two-, and three-layer models.

Finally, the implications of our study for numerical simulations of ocean gyres, which frequently show sensitivity of jet penetration to horizontal and vertical resolution and to choice of boundary conditions, are discussed. In particular, it is demonstrated that poor resolution of the horizontal jet structure may lead to a dramatic reduction in penetration.

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## Abstract

A strategy for diagnosing and interpreting flow regimes that is firmly rooted in dynamical theory is presented and applied to the study of observed and modeled planetary-scale regimes of the wintertime circulation in the Northern Hemisphere. The method assumes a nonlinear dynamical model of the atmospheric motion, and determines a subspace of the phase space of the model in which multiple quasi-stationary solutions of the equations of motion are likely to be located. The axes that generate this subspace are the vectors that possess the smallest amplitude of the time derivative computed from a linearized version of the model, using the time-mean state of the system as a basic state. These vectors are called here “neutral vectors,” and are shown to be eigenvectors of a self-adjoint operator derived from the linearized model.

As a prototype of a dynamical system with quadratic nonlinearity relevant to atmospheric dynamics, the three-variable convection model that generates the well-known Lorenz attractor is first investigated. It is shown that the presence of two unstable stationary solutions, which determine the shape of the attractor, generates a strong bimodality in the projection of the state vector of the system onto the most neutral vector, once a proper time filter is used on the data.

To apply this method to the analysis of atmospheric low-frequency variability, a three-level quasigeostrophic model in spherical geometry is adopted as the dynamical model. Neutral vectors are computed using the observed mean atmospheric state in winter as a basic state; alternative basic states, in which the eddies in the time-mean state are partially or fully removed, are also used in sensitivity experiments. The spatial patterns of the leading neutral vectors are relative insensitive to variations in some model parameters, but are strongly controlled by the form of the basic state; such dependence can be understood in terms of linear planetary-wave theory. The neutral vectors of the wintertime climatology are then used to analyse a 32-winter sample of observed atmospheric fields. It is found that the time series of the projection of these fields onto one particular neutral vector has a significantly bimodal probability density function, suggesting the existence of (at least) two separate flow regimes associated with anomalies of opposite sign. The two regimes are hemispheric in extent, and are close to some of the clusters found in previous studies that made use of empirical orthogonal functions.

Finally, it is shown that, if an appropriate forcing function is employed, the quasigeostrophic model is able to generate a very realistic climatology in a long nonlinear integration and, furthermore, two regimes similar to the observed ones. Again, these regimes can be identified by the presence of bimodality in the probability density function of the projections of model fields onto neutral vectors. Modeled and observed regimes have not only similar spatial patterns but also an almost identical distribution of the residence time.

## Abstract

A strategy for diagnosing and interpreting flow regimes that is firmly rooted in dynamical theory is presented and applied to the study of observed and modeled planetary-scale regimes of the wintertime circulation in the Northern Hemisphere. The method assumes a nonlinear dynamical model of the atmospheric motion, and determines a subspace of the phase space of the model in which multiple quasi-stationary solutions of the equations of motion are likely to be located. The axes that generate this subspace are the vectors that possess the smallest amplitude of the time derivative computed from a linearized version of the model, using the time-mean state of the system as a basic state. These vectors are called here “neutral vectors,” and are shown to be eigenvectors of a self-adjoint operator derived from the linearized model.

As a prototype of a dynamical system with quadratic nonlinearity relevant to atmospheric dynamics, the three-variable convection model that generates the well-known Lorenz attractor is first investigated. It is shown that the presence of two unstable stationary solutions, which determine the shape of the attractor, generates a strong bimodality in the projection of the state vector of the system onto the most neutral vector, once a proper time filter is used on the data.

To apply this method to the analysis of atmospheric low-frequency variability, a three-level quasigeostrophic model in spherical geometry is adopted as the dynamical model. Neutral vectors are computed using the observed mean atmospheric state in winter as a basic state; alternative basic states, in which the eddies in the time-mean state are partially or fully removed, are also used in sensitivity experiments. The spatial patterns of the leading neutral vectors are relative insensitive to variations in some model parameters, but are strongly controlled by the form of the basic state; such dependence can be understood in terms of linear planetary-wave theory. The neutral vectors of the wintertime climatology are then used to analyse a 32-winter sample of observed atmospheric fields. It is found that the time series of the projection of these fields onto one particular neutral vector has a significantly bimodal probability density function, suggesting the existence of (at least) two separate flow regimes associated with anomalies of opposite sign. The two regimes are hemispheric in extent, and are close to some of the clusters found in previous studies that made use of empirical orthogonal functions.

Finally, it is shown that, if an appropriate forcing function is employed, the quasigeostrophic model is able to generate a very realistic climatology in a long nonlinear integration and, furthermore, two regimes similar to the observed ones. Again, these regimes can be identified by the presence of bimodality in the probability density function of the projections of model fields onto neutral vectors. Modeled and observed regimes have not only similar spatial patterns but also an almost identical distribution of the residence time.

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## Abstract

Observations of the poleward heat transport of the earth (*H*) suggest that the atmosphere is the primary transporting agent poleward of 30°, that oceanic (*H _{O}
*) and atmospheric (

*H*) contributions are comparable in the tropical belt, and that ocean transport dominates in the deep Tropics.

_{A}*H*/

_{A}*H*as

_{O}*A*and

*O*denoting atmosphere and ocean, respectively) is the meridional mass transport within

*θ*layers (moist potential temperature for the atmosphere, potential temperature for the ocean), and

*C*Δ

*θ*(

*C*being the specific heat) is the change in energy across the circulation defined by Ψ.

It is argued here that the observed partitioning of heat transport between the atmosphere and ocean is a robust feature of the earth's climate and reflects two limits: (i) dominance of atmospheric mass transport in mid-to-high latitudes (Ψ*
_{A}
* ≫ Ψ

*with*

_{O}*C*Δ

_{A}*θ*∼

_{A}*C*Δ

_{O}*θ*and hence

_{O}*H*/

_{A}*H*≫ 1) and (ii) dominance of oceanic energy contrast in the Tropics (

_{O}*C*Δ

_{O}*θ*≫

_{O}*C*Δ

_{A}*θ*with Ψ

_{A}*∼ Ψ*

_{A}*and hence*

_{O}*H*/

_{A}*H*≪ 1).

_{O}Motivated by simple dynamical arguments, these ideas are illustrated through diagnosis of atmospheric reanalyses, long simulations of an ocean model, and a coupled atmosphere–ocean model of intermediate complexity.

## Abstract

Observations of the poleward heat transport of the earth (*H*) suggest that the atmosphere is the primary transporting agent poleward of 30°, that oceanic (*H _{O}
*) and atmospheric (

*H*) contributions are comparable in the tropical belt, and that ocean transport dominates in the deep Tropics.

_{A}*H*/

_{A}*H*as

_{O}*A*and

*O*denoting atmosphere and ocean, respectively) is the meridional mass transport within

*θ*layers (moist potential temperature for the atmosphere, potential temperature for the ocean), and

*C*Δ

*θ*(

*C*being the specific heat) is the change in energy across the circulation defined by Ψ.

It is argued here that the observed partitioning of heat transport between the atmosphere and ocean is a robust feature of the earth's climate and reflects two limits: (i) dominance of atmospheric mass transport in mid-to-high latitudes (Ψ*
_{A}
* ≫ Ψ

*with*

_{O}*C*Δ

_{A}*θ*∼

_{A}*C*Δ

_{O}*θ*and hence

_{O}*H*/

_{A}*H*≫ 1) and (ii) dominance of oceanic energy contrast in the Tropics (

_{O}*C*Δ

_{O}*θ*≫

_{O}*C*Δ

_{A}*θ*with Ψ

_{A}*∼ Ψ*

_{A}*and hence*

_{O}*H*/

_{A}*H*≪ 1).

_{O}Motivated by simple dynamical arguments, these ideas are illustrated through diagnosis of atmospheric reanalyses, long simulations of an ocean model, and a coupled atmosphere–ocean model of intermediate complexity.

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## Abstract

An analytical model of the mutual interaction of the middle-latitude atmosphere and ocean is formulated and studied. The model is found to support coupled modes in which oceanic baroclinic Rossby waves of decadal period grow through positive coupled feedback between the thermal forcing of the atmosphere induced by SST anomalies and the resulting wind stress forcing of the ocean. Growth only occurs if the atmospheric response to thermal forcing is equivalent barotropic, with a particular phase relationship with the underlying SST anomalies. The dependence of the growth rate and structure of the modes on the nature of the assumed physics of air–sea interaction is explored, and their possible relation to observed phenomena discussed.

## Abstract

An analytical model of the mutual interaction of the middle-latitude atmosphere and ocean is formulated and studied. The model is found to support coupled modes in which oceanic baroclinic Rossby waves of decadal period grow through positive coupled feedback between the thermal forcing of the atmosphere induced by SST anomalies and the resulting wind stress forcing of the ocean. Growth only occurs if the atmospheric response to thermal forcing is equivalent barotropic, with a particular phase relationship with the underlying SST anomalies. The dependence of the growth rate and structure of the modes on the nature of the assumed physics of air–sea interaction is explored, and their possible relation to observed phenomena discussed.

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## Abstract

The degree to which total meridional heat transport is sensitive to the details of its atmospheric and oceanic components is explored. A coupled atmosphere, ocean, and sea ice model of an aquaplanet is employed to simulate very different climates—some with polar ice caps, some without—even though they are driven by the same incoming solar flux. Differences arise due to varying geometrical constraints on ocean circulation influencing its ability to transport heat meridionally. Without complex land configurations, the results prove easier to diagnose and compare to theory and simple models and, hence, provide a useful test bed for ideas about heat transport and its partition within the climate system. In particular, the results are discussed in the context of a 1978 study by Stone, who argued that for a planet with Earth’s astronomical parameters and rotation rate, the total meridional heat transport would be independent of the detailed dynamical processes responsible for that transport and depend primarily on the distribution of incoming solar radiation and the mean planetary albedo. The authors find that in warm climates in which there is no ice, Stone’s result is a useful guide. In cold climates with significant polar ice caps, however, meridional gradients in albedo significantly affect the absorption of solar radiation and need to be included in any detailed calculation or discussion of total heat transport. Since the meridional extent of polar ice caps is sensitive to details of atmospheric and oceanic circulation, these cannot be ignored. Finally, what has been learned is applied to a study of the total heat transport estimated from the Earth Radiation Budget Experiment (ERBE) data.

## Abstract

The degree to which total meridional heat transport is sensitive to the details of its atmospheric and oceanic components is explored. A coupled atmosphere, ocean, and sea ice model of an aquaplanet is employed to simulate very different climates—some with polar ice caps, some without—even though they are driven by the same incoming solar flux. Differences arise due to varying geometrical constraints on ocean circulation influencing its ability to transport heat meridionally. Without complex land configurations, the results prove easier to diagnose and compare to theory and simple models and, hence, provide a useful test bed for ideas about heat transport and its partition within the climate system. In particular, the results are discussed in the context of a 1978 study by Stone, who argued that for a planet with Earth’s astronomical parameters and rotation rate, the total meridional heat transport would be independent of the detailed dynamical processes responsible for that transport and depend primarily on the distribution of incoming solar radiation and the mean planetary albedo. The authors find that in warm climates in which there is no ice, Stone’s result is a useful guide. In cold climates with significant polar ice caps, however, meridional gradients in albedo significantly affect the absorption of solar radiation and need to be included in any detailed calculation or discussion of total heat transport. Since the meridional extent of polar ice caps is sensitive to details of atmospheric and oceanic circulation, these cannot be ignored. Finally, what has been learned is applied to a study of the total heat transport estimated from the Earth Radiation Budget Experiment (ERBE) data.

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## Abstract

A hierarchy of models is used to explore the role of the ocean in mediating the response of the climate to a single volcanic eruption and to a series of eruptions by drawing cold temperature anomalies into its interior, as measured by the ocean heat exchange parameter *q* (W m^{−2} K^{−1}). The response to a single (Pinatubo-like) eruption comprises two primary time scales: one fast (year) and one slow (decadal). Over the fast time scale, the ocean sequesters cooling anomalies induced by the eruption into its depth, enhancing the damping rate of sea surface temperature (SST) relative to that which would be expected if the atmosphere acted alone. This compromises the ability to constrain atmospheric feedback rates measured by *λ* (~1 W m^{−2} K^{−1}) from study of the relaxation of SST back toward equilibrium, but yields information about the transient climate sensitivity proportional to *λ* + *q*. Our study suggests that *q* can significantly exceed *λ* in the immediate aftermath of an eruption. Shielded from damping to the atmosphere, the effect of the volcanic eruption persists on longer decadal time scales. We contrast the response to an “impulse” from that of a “step” in which the forcing is kept constant in time. Finally, we assess the “accumulation potential” of a succession of volcanic eruptions over time, a process that may in part explain the prolongation of cold surface temperatures experienced during, for example, the Little Ice Age.

## Abstract

A hierarchy of models is used to explore the role of the ocean in mediating the response of the climate to a single volcanic eruption and to a series of eruptions by drawing cold temperature anomalies into its interior, as measured by the ocean heat exchange parameter *q* (W m^{−2} K^{−1}). The response to a single (Pinatubo-like) eruption comprises two primary time scales: one fast (year) and one slow (decadal). Over the fast time scale, the ocean sequesters cooling anomalies induced by the eruption into its depth, enhancing the damping rate of sea surface temperature (SST) relative to that which would be expected if the atmosphere acted alone. This compromises the ability to constrain atmospheric feedback rates measured by *λ* (~1 W m^{−2} K^{−1}) from study of the relaxation of SST back toward equilibrium, but yields information about the transient climate sensitivity proportional to *λ* + *q*. Our study suggests that *q* can significantly exceed *λ* in the immediate aftermath of an eruption. Shielded from damping to the atmosphere, the effect of the volcanic eruption persists on longer decadal time scales. We contrast the response to an “impulse” from that of a “step” in which the forcing is kept constant in time. Finally, we assess the “accumulation potential” of a succession of volcanic eruptions over time, a process that may in part explain the prolongation of cold surface temperatures experienced during, for example, the Little Ice Age.

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## Abstract

The position of the intertropical convergence zone (ITCZ) is sensitive to the atmosphere’s hemispheric energy balance, lying in the hemisphere most strongly heated by radiative and turbulent surface energy fluxes. This study examines how the ocean circulation, through its cross-equatorial energy transport and associated surface energy fluxes, affects the ITCZ’s response to an imposed interhemispheric heating contrast in a coupled atmosphere–ocean general circulation model. Shifts of the ITCZ are strongly damped owing to a robust coupling between the atmosphere’s Hadley cells and the ocean’s subtropical cells by the trade winds and their associated surface stresses. An anomalous oceanic wind-driven cross-equatorial cell transports energy across the equator, strongly offsetting the imposed heating contrast. The circulation of this cell can be described by the combination of trade wind anomalies and the meridional gradient of sea surface temperature, which sets the temperature contrast between its upper and lower branches. The ability of the wind-driven ocean circulation to damp ITCZ shifts represents a previously unappreciated constraint on the atmosphere’s energy budget and indicates that the position of the ITCZ may be much less sensitive to interhemispheric heating contrasts than previously thought. Climatic implications of this damping are discussed.

## Abstract

The position of the intertropical convergence zone (ITCZ) is sensitive to the atmosphere’s hemispheric energy balance, lying in the hemisphere most strongly heated by radiative and turbulent surface energy fluxes. This study examines how the ocean circulation, through its cross-equatorial energy transport and associated surface energy fluxes, affects the ITCZ’s response to an imposed interhemispheric heating contrast in a coupled atmosphere–ocean general circulation model. Shifts of the ITCZ are strongly damped owing to a robust coupling between the atmosphere’s Hadley cells and the ocean’s subtropical cells by the trade winds and their associated surface stresses. An anomalous oceanic wind-driven cross-equatorial cell transports energy across the equator, strongly offsetting the imposed heating contrast. The circulation of this cell can be described by the combination of trade wind anomalies and the meridional gradient of sea surface temperature, which sets the temperature contrast between its upper and lower branches. The ability of the wind-driven ocean circulation to damp ITCZ shifts represents a previously unappreciated constraint on the atmosphere’s energy budget and indicates that the position of the ITCZ may be much less sensitive to interhemispheric heating contrasts than previously thought. Climatic implications of this damping are discussed.

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## Abstract

Multidecadal variability in the Atlantic meridional overturning circulation (AMOC) of the ocean is diagnosed in the NCAR Community Climate System Model, version 3 (CCSM3), and the GFDL Coupled Model (CM2.1). Common diagnostic approaches are applied to draw out similarities and differences between the two models. An index of AMOC variability is defined, and the manner in which key variables covary with it is determined. In both models the following is found. (i) AMOC variability is associated with upper-ocean (top 1 km) density anomalies (dominated by temperature) on the western margin of the basin in the region of the Mann eddy with a period of about 20 years. These anomalies modulate the trajectory and strength of the North Atlantic Current. The importance of the western margin is a direct consequence of the thermal wind relation and is independent of the mechanisms that create those density anomalies. (ii) Density anomalies in this key region are part of a larger-scale pattern that propagates around the subpolar gyre and acts as a “pacemaker” of AMOC variability. (iii) The observed variability is consistent with the primary driving mechanism being stochastic wind curl forcing, with Labrador Sea convection playing a secondary role. Also, “toy models” of delayed oscillator form are fitted to power spectra of key variables and are used to infer “quality factors” (Q-factors), which characterize the bandwidth relative to the center frequency and hence AMOC predictability horizons. The two models studied here have Q-factors of around 2, suggesting that prediction is possible out to about two cycles, which is likely larger than the real AMOC.

## Abstract

Multidecadal variability in the Atlantic meridional overturning circulation (AMOC) of the ocean is diagnosed in the NCAR Community Climate System Model, version 3 (CCSM3), and the GFDL Coupled Model (CM2.1). Common diagnostic approaches are applied to draw out similarities and differences between the two models. An index of AMOC variability is defined, and the manner in which key variables covary with it is determined. In both models the following is found. (i) AMOC variability is associated with upper-ocean (top 1 km) density anomalies (dominated by temperature) on the western margin of the basin in the region of the Mann eddy with a period of about 20 years. These anomalies modulate the trajectory and strength of the North Atlantic Current. The importance of the western margin is a direct consequence of the thermal wind relation and is independent of the mechanisms that create those density anomalies. (ii) Density anomalies in this key region are part of a larger-scale pattern that propagates around the subpolar gyre and acts as a “pacemaker” of AMOC variability. (iii) The observed variability is consistent with the primary driving mechanism being stochastic wind curl forcing, with Labrador Sea convection playing a secondary role. Also, “toy models” of delayed oscillator form are fitted to power spectra of key variables and are used to infer “quality factors” (Q-factors), which characterize the bandwidth relative to the center frequency and hence AMOC predictability horizons. The two models studied here have Q-factors of around 2, suggesting that prediction is possible out to about two cycles, which is likely larger than the real AMOC.

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## Abstract

The parametric representation of buoyancy and momentum transport by baroclinic eddies in a primitive equation “*β* plane” channel is studied through a transformation of the governing equations. Adoption of the“transformed Eulerian mean” and the assumption that the eddies (but not the mean flow) are quasigeostrophic in nature leads to 1) the eddies being represented symbolically by one term, an eddy potential vorticity flux, rendering a representation that incorporates both eddy momentum and eddy buoyancy fluxes, and 2) the advecting velocities being those of the residual mean circulation. A closure is employed for the eddy potential vorticity flux that directs it down the mean potential vorticity gradient. Care is taken to ensure that the resulting force does not generate any net momentum in the channel but only acts to redistribute it.

The approach is investigated by comparing a zonally averaged parameterized model with a three-dimensional eddy-resolving calculation of flow in a stress-driven channel. The stress at the upper surface is communicated down the water column to the bottom by eddy form drag. Moreover, lateral eddy momentum fluxes act to strengthen and sharpen the mean flow, transporting eastward momentum from the flanks to the center of the jet, up its large-scale gradient. Both vertical momentum transfer and lateral, upgradient momentum transfer by eddies, is captured in the parameterized model.

Finally, advantages of the parametric approach are demonstrated in two further contexts: 1) the spindown of a baroclinic zone and 2) the maintenance of surface winds by eddy momentum flux in the atmosphere.

## Abstract

The parametric representation of buoyancy and momentum transport by baroclinic eddies in a primitive equation “*β* plane” channel is studied through a transformation of the governing equations. Adoption of the“transformed Eulerian mean” and the assumption that the eddies (but not the mean flow) are quasigeostrophic in nature leads to 1) the eddies being represented symbolically by one term, an eddy potential vorticity flux, rendering a representation that incorporates both eddy momentum and eddy buoyancy fluxes, and 2) the advecting velocities being those of the residual mean circulation. A closure is employed for the eddy potential vorticity flux that directs it down the mean potential vorticity gradient. Care is taken to ensure that the resulting force does not generate any net momentum in the channel but only acts to redistribute it.

The approach is investigated by comparing a zonally averaged parameterized model with a three-dimensional eddy-resolving calculation of flow in a stress-driven channel. The stress at the upper surface is communicated down the water column to the bottom by eddy form drag. Moreover, lateral eddy momentum fluxes act to strengthen and sharpen the mean flow, transporting eastward momentum from the flanks to the center of the jet, up its large-scale gradient. Both vertical momentum transfer and lateral, upgradient momentum transfer by eddies, is captured in the parameterized model.

Finally, advantages of the parametric approach are demonstrated in two further contexts: 1) the spindown of a baroclinic zone and 2) the maintenance of surface winds by eddy momentum flux in the atmosphere.