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## Abstract

The influence of the beta effect, that is, the variation of the Coriolis parameter with latitude on the energy flux from moving storms to the oceanic internal wave field is considered. Large-scale, fast-moving storms are emphasized, and the oceanic internal wave field is considered. Large-scale, fast-moving storms are emphasized, and the oceanic response is described as forced inertial oscillations on a beta plane. An analytical solution to the energy flux is obtained and discussed for a simple wind stress field.

The beta effect introduces a difference between westward and eastward moving storms. It is most pronounced for storm speeds that move the storms past a fixed point in about an inertial period. In this regime, the energy flux to the internal wave field is, relative to the *f*-plane case, increased when the storm moves eastward and decreased when it moves westward. However, the influence of the beta effect on the energy flux to the internal wave field is generally small, and the *f*-plane approximation is expected to give a good description of the energy flux.

## Abstract

The influence of the beta effect, that is, the variation of the Coriolis parameter with latitude on the energy flux from moving storms to the oceanic internal wave field is considered. Large-scale, fast-moving storms are emphasized, and the oceanic internal wave field is considered. Large-scale, fast-moving storms are emphasized, and the oceanic response is described as forced inertial oscillations on a beta plane. An analytical solution to the energy flux is obtained and discussed for a simple wind stress field.

The beta effect introduces a difference between westward and eastward moving storms. It is most pronounced for storm speeds that move the storms past a fixed point in about an inertial period. In this regime, the energy flux to the internal wave field is, relative to the *f*-plane case, increased when the storm moves eastward and decreased when it moves westward. However, the influence of the beta effect on the energy flux to the internal wave field is generally small, and the *f*-plane approximation is expected to give a good description of the energy flux.

## Abstract

A simple conceptual model is used to illustrate aspects of how the midlatitude atmosphere, in the absence of ocean dynamics, responds to and feeds back on sea surface temperature (SST) anomalies. In the model, a dynamically passive ocean mixed layer of fixed depth exchanges heat with a single-level, energy-balance atmosphere with a constant mean wind, *U.* The temperatures of the two subsystems, *T*
_{O} and *T*
_{A}, respectively, strive to equilibrate through surface heat exchange, which is parameterized as *λ*(*T*
_{O} − *T*
_{A}).

Atmospheric advection of heat has two important effects on the evolution of SST anomalies. First, the SST anomalies propagate downwind at the speed (*c*
_{A}/*c*
_{O})*U,* where *c*
_{A} and *c*
_{O} are the heat capacities of the atmosphere and the oceanic mixed layer, respectively. Second, the damping rate of SST anomalies is scale dependent: the distance an atmospheric column travels before it equilibrates with the ocean through surface heat exchange (*Uc*
_{A}/*λ*) introduces a length scale that discriminates between small-scale and large-scale SST anomalies. Local bulk formulas of surface heat exchange determine the damping of small-scale anomalies, which decay exponentially over the timescale *c*
_{O}/*λ.* Large-scale anomalies, on the other hand, decay essentially diffusively and propagate downwind, until longwave radiation finally extinguishes them. The apparent diffusive decay results from the joint effect of atmospheric advection and surface heat exchange. And the effect becomes significant when the distance the atmosphere carries heat downwind is small compared to the scale of the SST anomaly. The kinematical diffusion coefficient associated with the phenomena is *c*^{2}_{A}*c*^{−1}_{O}*U*
^{2}
*λ*
^{−1}.

## Abstract

A simple conceptual model is used to illustrate aspects of how the midlatitude atmosphere, in the absence of ocean dynamics, responds to and feeds back on sea surface temperature (SST) anomalies. In the model, a dynamically passive ocean mixed layer of fixed depth exchanges heat with a single-level, energy-balance atmosphere with a constant mean wind, *U.* The temperatures of the two subsystems, *T*
_{O} and *T*
_{A}, respectively, strive to equilibrate through surface heat exchange, which is parameterized as *λ*(*T*
_{O} − *T*
_{A}).

Atmospheric advection of heat has two important effects on the evolution of SST anomalies. First, the SST anomalies propagate downwind at the speed (*c*
_{A}/*c*
_{O})*U,* where *c*
_{A} and *c*
_{O} are the heat capacities of the atmosphere and the oceanic mixed layer, respectively. Second, the damping rate of SST anomalies is scale dependent: the distance an atmospheric column travels before it equilibrates with the ocean through surface heat exchange (*Uc*
_{A}/*λ*) introduces a length scale that discriminates between small-scale and large-scale SST anomalies. Local bulk formulas of surface heat exchange determine the damping of small-scale anomalies, which decay exponentially over the timescale *c*
_{O}/*λ.* Large-scale anomalies, on the other hand, decay essentially diffusively and propagate downwind, until longwave radiation finally extinguishes them. The apparent diffusive decay results from the joint effect of atmospheric advection and surface heat exchange. And the effect becomes significant when the distance the atmosphere carries heat downwind is small compared to the scale of the SST anomaly. The kinematical diffusion coefficient associated with the phenomena is *c*^{2}_{A}*c*^{−1}_{O}*U*
^{2}
*λ*
^{−1}.

## Abstract

The generation of long interval waves by traveling hurricanes on an *f* plane is studied within the context of linear theory. The emphasis of the present work is on the interval wave power, that is, the fraction of the energy input from the hurricane that is absorbed by the internal wave field in the ocean. Particular attention is paid to the dependence of the interval wave power on the hurricane speed, the oceanic stratification, and the Coriolis parameter. A formula for the wave power, expressed in terms of the wind-forcing spectrum, is derived.

The wave power can be divided in two parts: one part generated by the divergence of the wind stress and one part generated by the curl of the wind stress. The latter part, which is dominating for hurricanes, is always decreased when the strength of the stratification is increased, while the former part may either increase or decrease depending on the speed of the hurricane.

It is shown that, for a specified stratification and a fixed latitude, the wave power exhibits a maximum for a certain speed of the hurricane. The maximum occurs when the forcing is optimally tuned with the internal waves. When the strength of the stratification is increased, the maximum is found at a higher hurricane velocity, and the wave power is generally reduced.

An estimate, based on the derived results, of the global energy flux from hurricanes to the internal wave field is presented. An average energy flux of the order 10^{10} watts is suggested by this calculation.

## Abstract

The generation of long interval waves by traveling hurricanes on an *f* plane is studied within the context of linear theory. The emphasis of the present work is on the interval wave power, that is, the fraction of the energy input from the hurricane that is absorbed by the internal wave field in the ocean. Particular attention is paid to the dependence of the interval wave power on the hurricane speed, the oceanic stratification, and the Coriolis parameter. A formula for the wave power, expressed in terms of the wind-forcing spectrum, is derived.

The wave power can be divided in two parts: one part generated by the divergence of the wind stress and one part generated by the curl of the wind stress. The latter part, which is dominating for hurricanes, is always decreased when the strength of the stratification is increased, while the former part may either increase or decrease depending on the speed of the hurricane.

It is shown that, for a specified stratification and a fixed latitude, the wave power exhibits a maximum for a certain speed of the hurricane. The maximum occurs when the forcing is optimally tuned with the internal waves. When the strength of the stratification is increased, the maximum is found at a higher hurricane velocity, and the wave power is generally reduced.

An estimate, based on the derived results, of the global energy flux from hurricanes to the internal wave field is presented. An average energy flux of the order 10^{10} watts is suggested by this calculation.

## Abstract

A conceptual model of the salinity distribution in the oceanic Hadley cell is presented. The model pertains to the region of tropical easterly surface winds, where the surface salinity increases poleward from a local salinity minimum near the equator to a subtropical salinity maximum. A fundamental constraint is that the meridional freshwater transports in the atmosphere and the ocean have the same magnitude but opposite directions. A key assumption is that the strength of the meridional overturning cells in the atmosphere and the ocean is proportional and set by the surface layer Ekman transport. It is further assumed that, to the lowest order of approximation, the zonal-mean Ekman transports accomplish the meridional freshwater transports, that is, eddy fluxes and gyre-induced transports are ignored. The model predicts that the salinity variation in the oceanic cell is directly proportional to the specific humidity of the near-surface air, but independent of the meridional mass transport (as long as the atmospheric and oceanic mass transports remain proportional). If the relative humidity of the near-surface air is constant, the salinity variation in the oceanic Hadley cell varies essentially with the surface temperature according to the Clausius–Clapeyron expression for the saturation vapor pressure. Further, the model is compared to observations and a global warming simulation and found to give a leading-order description of the tropical surface salinity range.

## Abstract

A conceptual model of the salinity distribution in the oceanic Hadley cell is presented. The model pertains to the region of tropical easterly surface winds, where the surface salinity increases poleward from a local salinity minimum near the equator to a subtropical salinity maximum. A fundamental constraint is that the meridional freshwater transports in the atmosphere and the ocean have the same magnitude but opposite directions. A key assumption is that the strength of the meridional overturning cells in the atmosphere and the ocean is proportional and set by the surface layer Ekman transport. It is further assumed that, to the lowest order of approximation, the zonal-mean Ekman transports accomplish the meridional freshwater transports, that is, eddy fluxes and gyre-induced transports are ignored. The model predicts that the salinity variation in the oceanic cell is directly proportional to the specific humidity of the near-surface air, but independent of the meridional mass transport (as long as the atmospheric and oceanic mass transports remain proportional). If the relative humidity of the near-surface air is constant, the salinity variation in the oceanic Hadley cell varies essentially with the surface temperature according to the Clausius–Clapeyron expression for the saturation vapor pressure. Further, the model is compared to observations and a global warming simulation and found to give a leading-order description of the tropical surface salinity range.

## Abstract

The atmospheric meridional overturning circulation is computed using the interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim) data. Meridional mass transport streamfunctions are calculated not only using pressure as a vertical coordinate but also using temperature, specific humidity, and geopotential height as generalized vertical coordinates. Moreover, mass transport streamfunctions are calculated using the latent, the dry static, or the moist static energy as generalized vertical coordinates. The total meridional energy transport can be obtained by integrating these streamfunctions “vertically” over their entire energy range. The time-averaged mass transport streamfunctions are also decomposed into mean-flow and eddy-induced components. The meridional mass transport streamfunctions with temperature and specific humidity as independent variables yield a two-cell structure with a tropical Hadley-like cell and a pronounced extratropical Ferrel-like cell, which carries warm and moist air poleward. These Ferrel-like cells are much stronger than the Eulerian zonal-mean Ferrel cell, a feature that can be understood by considering the residual circulation related to specific humidity or temperature. Regardless of the generalized vertical coordinate, the present meridional mass transport streamfunctions yield essentially a two-layer structure with one poleward and one equatorward branch. The strongest meridional overturning in the midlatitudes is obtained when the specific humidity or the moist static energy is used as the vertical coordinate, indicating that the specific humidity is the variable that best distinguishes between poleward- and equatorward-moving air in the lower troposphere.

## Abstract

The atmospheric meridional overturning circulation is computed using the interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim) data. Meridional mass transport streamfunctions are calculated not only using pressure as a vertical coordinate but also using temperature, specific humidity, and geopotential height as generalized vertical coordinates. Moreover, mass transport streamfunctions are calculated using the latent, the dry static, or the moist static energy as generalized vertical coordinates. The total meridional energy transport can be obtained by integrating these streamfunctions “vertically” over their entire energy range. The time-averaged mass transport streamfunctions are also decomposed into mean-flow and eddy-induced components. The meridional mass transport streamfunctions with temperature and specific humidity as independent variables yield a two-cell structure with a tropical Hadley-like cell and a pronounced extratropical Ferrel-like cell, which carries warm and moist air poleward. These Ferrel-like cells are much stronger than the Eulerian zonal-mean Ferrel cell, a feature that can be understood by considering the residual circulation related to specific humidity or temperature. Regardless of the generalized vertical coordinate, the present meridional mass transport streamfunctions yield essentially a two-layer structure with one poleward and one equatorward branch. The strongest meridional overturning in the midlatitudes is obtained when the specific humidity or the moist static energy is used as the vertical coordinate, indicating that the specific humidity is the variable that best distinguishes between poleward- and equatorward-moving air in the lower troposphere.

## Abstract

In high-latitude subpolar seas, such as the Nordic seas and the Labrador Sea, time-mean geostrophic currents mediate the bulk of the meridional oceanic heat transport. These currents are primarily encountered along the continental slopes as intense cyclonic boundary currents, which, because of the relatively weak stratification, should be strongly steered by the bottom topography. However, analyses of hydrographic and satellite altimetric data along depth contours in Nordic seas boundary currents reveal some remarkable, stationary, along-stream variations in the depth-integrated buoyancy and bottom pressure. A closer examination shows that these variations are linked to changes in steepness and curvature of the continental slope. To examine the underlying dynamics, a steady-state model of a cyclonic stratified boundary current over a topographic slope is developed in the limit of small Rossby numbers. Based on potential vorticity conservation, equations for the zeroth- and first-order pressure and buoyancy fields are derived. To the lowest order, the flow is completely aligned with the bottom topography. However, the first-order results show that where the lowest-order flow increases (decreases) its relative vorticity along a depth contour, the first-order pressure and depth-integrated buoyancy increase (decrease). This response is associated with cross-isobath flows, which induce stretching/compression of fluid elements that compensates for the changes in relative vorticity. The model-predicted along-isobath variations in pressure and depth-integrated buoyancy are comparable in magnitude to the ones found in the observational data from the Nordics Seas.

## Abstract

In high-latitude subpolar seas, such as the Nordic seas and the Labrador Sea, time-mean geostrophic currents mediate the bulk of the meridional oceanic heat transport. These currents are primarily encountered along the continental slopes as intense cyclonic boundary currents, which, because of the relatively weak stratification, should be strongly steered by the bottom topography. However, analyses of hydrographic and satellite altimetric data along depth contours in Nordic seas boundary currents reveal some remarkable, stationary, along-stream variations in the depth-integrated buoyancy and bottom pressure. A closer examination shows that these variations are linked to changes in steepness and curvature of the continental slope. To examine the underlying dynamics, a steady-state model of a cyclonic stratified boundary current over a topographic slope is developed in the limit of small Rossby numbers. Based on potential vorticity conservation, equations for the zeroth- and first-order pressure and buoyancy fields are derived. To the lowest order, the flow is completely aligned with the bottom topography. However, the first-order results show that where the lowest-order flow increases (decreases) its relative vorticity along a depth contour, the first-order pressure and depth-integrated buoyancy increase (decrease). This response is associated with cross-isobath flows, which induce stretching/compression of fluid elements that compensates for the changes in relative vorticity. The model-predicted along-isobath variations in pressure and depth-integrated buoyancy are comparable in magnitude to the ones found in the observational data from the Nordics Seas.

## Abstract

This article presents a new framework for studying water mass transformations in salinity–temperature space that can, with equal ease, be applied to study water mass transformation in spaces defined by any two conservative tracers. It is shown how the flow across isothermal and isohaline surfaces in the ocean can be quantified from knowledge of the nonadvective fluxes of heat and salt. It is also shown how these cross-isothermal and cross-isohaline flows can be used to form a continuity equation in salinity–temperature space. These flows are then quantified in a state-of-the-art ocean model. Two major transformation cells are found: a tropical cell driven primarily by surface fluxes and dianeutral diffusion and a conveyor belt cell where isoneutral diffusion is also important. Both cells are similar to cells found in earlier work on the thermohaline streamfunction. A key benefit with this framework over a streamfunction approach is that transformation due to different diabatic processes can be studied individually. The distributions of volume and surface area in *S*–*T* space are found to be useful for determining how transformations due to these different processes affect the water masses in the model. The surface area distribution shows that the water mass transformations due to surface fluxes tend to be directed away from *S*–*T* regions that occupy large areas at the sea surface.

## Abstract

This article presents a new framework for studying water mass transformations in salinity–temperature space that can, with equal ease, be applied to study water mass transformation in spaces defined by any two conservative tracers. It is shown how the flow across isothermal and isohaline surfaces in the ocean can be quantified from knowledge of the nonadvective fluxes of heat and salt. It is also shown how these cross-isothermal and cross-isohaline flows can be used to form a continuity equation in salinity–temperature space. These flows are then quantified in a state-of-the-art ocean model. Two major transformation cells are found: a tropical cell driven primarily by surface fluxes and dianeutral diffusion and a conveyor belt cell where isoneutral diffusion is also important. Both cells are similar to cells found in earlier work on the thermohaline streamfunction. A key benefit with this framework over a streamfunction approach is that transformation due to different diabatic processes can be studied individually. The distributions of volume and surface area in *S*–*T* space are found to be useful for determining how transformations due to these different processes affect the water masses in the model. The surface area distribution shows that the water mass transformations due to surface fluxes tend to be directed away from *S*–*T* regions that occupy large areas at the sea surface.

## Abstract

The possibility that a decreased equator-to-Pole surface density difference could imply stronger rather than weaker thermohaline circulation (THC) is explored theoretically as well as with the aid of numerical simulations. The idea builds on the classical thermocline scaling, stating that the THC should increase with density difference as well as with vertical diffusivity. To explore possible changes in vertical diffusivity that would follow a change in the oceanic density difference, simple models of internal wave mixing are considered. For reasonable assumptions concerning the energy supply to vertical mixing, the overall diffusivity tends to increase with decreasing density difference. This enhancement of the vertical diffusivity acts to deepen the thermocline, an effect that can cause the THC to amplify despite that the surface density difference is reduced. This remarkable state of affairs is illustrated with simulations from a one-hemisphere ocean circulation model. In the simulations, two stratification-dependent diffusivity representations are investigated, which both imply that a weaker density difference will be associated with a stronger THC. The more common mixing representation, where the diffusivity is taken to be fixed, yields the opposite and well-known result: a weaker density difference will be associated with a weaker THC.

## Abstract

The possibility that a decreased equator-to-Pole surface density difference could imply stronger rather than weaker thermohaline circulation (THC) is explored theoretically as well as with the aid of numerical simulations. The idea builds on the classical thermocline scaling, stating that the THC should increase with density difference as well as with vertical diffusivity. To explore possible changes in vertical diffusivity that would follow a change in the oceanic density difference, simple models of internal wave mixing are considered. For reasonable assumptions concerning the energy supply to vertical mixing, the overall diffusivity tends to increase with decreasing density difference. This enhancement of the vertical diffusivity acts to deepen the thermocline, an effect that can cause the THC to amplify despite that the surface density difference is reduced. This remarkable state of affairs is illustrated with simulations from a one-hemisphere ocean circulation model. In the simulations, two stratification-dependent diffusivity representations are investigated, which both imply that a weaker density difference will be associated with a stronger THC. The more common mixing representation, where the diffusivity is taken to be fixed, yields the opposite and well-known result: a weaker density difference will be associated with a weaker THC.

## Abstract

The flux form of the potential vorticity (PV) equation is employed to derive simple expressions for the boundary and interior flux of PV in ocean circulation using Bernoulli functions. The formulas are discussed and physically interpreted and used to map the flux of PV through a model of ocean circulation.

## Abstract

The flux form of the potential vorticity (PV) equation is employed to derive simple expressions for the boundary and interior flux of PV in ocean circulation using Bernoulli functions. The formulas are discussed and physically interpreted and used to map the flux of PV through a model of ocean circulation.

## Abstract

The authors present results from laboratory experiments and numerical simulations of the barotropic circulation in a basin with sloping boundaries forced by a surface stress. Focus is placed on flows with large-scale Rossby numbers that are significantly smaller than unity. The results of the laboratory experiments and simulations show that cyclonic circulation follows the isobaths, the flow pattern being independent of the strength of the forcing. For anticyclonic circulation, the flow pattern changes with forcing strength. It is similar to the cyclonic topographically steered pattern for weak forcing, and it develops strong cross-slope flows for strong forcing.

Linear dynamics are symmetric between cyclonic and anticyclonic circulations and give a good description of the cyclonic and weakly forced anticyclonic circulations. The analysis of the nonlinear dynamics shows that topographically steered cyclonic flows are all stable and steady energy-minimum solutions to the inviscid nonlinear equations. This implies that the nonlinear terms (advection of relative vorticity) are always small for the topographically steered cyclonic flow.

For anticyclonic flow, the situation is very different. It is possible that no anticyclonic topographically steered flow is ever a solution to the steady inviscid equations. And if such a steady anticyclonic flow does exist, it is likely to be unstable, since it must correspond to a saddle point in energy rather than to a minimum or a maximum. The nonlinear terms are important when the Rossby number is larger than the Ekman number, which is the case for the anticyclonic experiments with strongest forcing. For these experiments, the advection of relative vorticity prevents the flow from following topography, creating locations with strong relative vorticity and cross-slope flow. The development of cross-slope flow can be understood from the conservation of potential vorticity in basins with irregular topography.

The separation of anticyclonic flow from steep topography shown in the laboratory experiments and the theoretical analysis herein are in agreement with features like the Gulf Stream separation from the continental slope at Cape Hatteras, North Carolina.

## Abstract

The authors present results from laboratory experiments and numerical simulations of the barotropic circulation in a basin with sloping boundaries forced by a surface stress. Focus is placed on flows with large-scale Rossby numbers that are significantly smaller than unity. The results of the laboratory experiments and simulations show that cyclonic circulation follows the isobaths, the flow pattern being independent of the strength of the forcing. For anticyclonic circulation, the flow pattern changes with forcing strength. It is similar to the cyclonic topographically steered pattern for weak forcing, and it develops strong cross-slope flows for strong forcing.

Linear dynamics are symmetric between cyclonic and anticyclonic circulations and give a good description of the cyclonic and weakly forced anticyclonic circulations. The analysis of the nonlinear dynamics shows that topographically steered cyclonic flows are all stable and steady energy-minimum solutions to the inviscid nonlinear equations. This implies that the nonlinear terms (advection of relative vorticity) are always small for the topographically steered cyclonic flow.

For anticyclonic flow, the situation is very different. It is possible that no anticyclonic topographically steered flow is ever a solution to the steady inviscid equations. And if such a steady anticyclonic flow does exist, it is likely to be unstable, since it must correspond to a saddle point in energy rather than to a minimum or a maximum. The nonlinear terms are important when the Rossby number is larger than the Ekman number, which is the case for the anticyclonic experiments with strongest forcing. For these experiments, the advection of relative vorticity prevents the flow from following topography, creating locations with strong relative vorticity and cross-slope flow. The development of cross-slope flow can be understood from the conservation of potential vorticity in basins with irregular topography.

The separation of anticyclonic flow from steep topography shown in the laboratory experiments and the theoretical analysis herein are in agreement with features like the Gulf Stream separation from the continental slope at Cape Hatteras, North Carolina.