Search Results
Abstract
Increasing evidence suggests that the Gulf Stream system is the origin for much of the eddy variability observed in the northwestern Atlantic Ocean. However, the dynamical mechanisms by which eddy energy, once generated in the neighborhood of the Gulf Stream, penetrates into the midocean regions are not fully understood. Here we explore the proposition that radiation away from the Gulf Stream can be interpreted as an oscillatory response of the ocean gyre interior to the forcing associated with translation and temporal evolution of the Gulf Stream current and its meanders. Specifically, we propose as a possible mechanism responsible for pules of Rossby wave radiation the sudden growth to finite amplitude and successive amplitude pulsations of quasi-stationary or eastward-moving finite-amplitude meanders. To examine this mechanism in detail, we construct a model for radiation in which the quasi-geostrophic equivalent barotropic potential vorticity equation is forced to its northern boundary by assigned distributions of streamfunction and vorticity corresponding to 1) a stationary pulsating meander, 2) a slowly propagating meander, and 3) a combination of 1 and 2.
We use both analytical and numerical techniques to solve the linear boundary-forced initial value problem with and without lateral friction and with and without bottom topography. We focus not only on the steady forced response but also on the transient component of the interior Rossby radiation field. On the β-plane without topography, it is shown that radiation into the far field is only possible for meander pulsation below a critical frequency. Below this frequency, the transient far-field response is large and force basin modes are necessary, together with the forced equilibrium solution, to accommodate the prescribed initial state of the system. With the addition of viscosity to damp the transient basin modes, and for frequencies higher than the critical value, the response is trapped at the northern wall and no radiation can be supported in the far field.
The inclusion of a simple parabolic relief along the full channel does not modify the qualitative behavior of the interior field. The only effect of the parabolic relief is to modify the effective value of planetary β and the cross-channel structure of the westward-propagating Rossby modes. The above results are, however, profoundly altered with the addition of nonlinearity. In particular, new mechanisms are possible for the development of far-field radiation and for the appearance of nonlinear, coherent solutions, as will he shown in Part II of this paper.
Abstract
Increasing evidence suggests that the Gulf Stream system is the origin for much of the eddy variability observed in the northwestern Atlantic Ocean. However, the dynamical mechanisms by which eddy energy, once generated in the neighborhood of the Gulf Stream, penetrates into the midocean regions are not fully understood. Here we explore the proposition that radiation away from the Gulf Stream can be interpreted as an oscillatory response of the ocean gyre interior to the forcing associated with translation and temporal evolution of the Gulf Stream current and its meanders. Specifically, we propose as a possible mechanism responsible for pules of Rossby wave radiation the sudden growth to finite amplitude and successive amplitude pulsations of quasi-stationary or eastward-moving finite-amplitude meanders. To examine this mechanism in detail, we construct a model for radiation in which the quasi-geostrophic equivalent barotropic potential vorticity equation is forced to its northern boundary by assigned distributions of streamfunction and vorticity corresponding to 1) a stationary pulsating meander, 2) a slowly propagating meander, and 3) a combination of 1 and 2.
We use both analytical and numerical techniques to solve the linear boundary-forced initial value problem with and without lateral friction and with and without bottom topography. We focus not only on the steady forced response but also on the transient component of the interior Rossby radiation field. On the β-plane without topography, it is shown that radiation into the far field is only possible for meander pulsation below a critical frequency. Below this frequency, the transient far-field response is large and force basin modes are necessary, together with the forced equilibrium solution, to accommodate the prescribed initial state of the system. With the addition of viscosity to damp the transient basin modes, and for frequencies higher than the critical value, the response is trapped at the northern wall and no radiation can be supported in the far field.
The inclusion of a simple parabolic relief along the full channel does not modify the qualitative behavior of the interior field. The only effect of the parabolic relief is to modify the effective value of planetary β and the cross-channel structure of the westward-propagating Rossby modes. The above results are, however, profoundly altered with the addition of nonlinearity. In particular, new mechanisms are possible for the development of far-field radiation and for the appearance of nonlinear, coherent solutions, as will he shown in Part II of this paper.
Abstract
The improvement in the climatological behavior of a numerical model as a consequence of the assimilation of surface data is investigated. The model used for this study is a quasigeostrophic (QG) model of the Gulf Stream region. The data that have been assimilated are maps of sea surface height that have been obtained as the superposition of sea surface height variability deduced from the Geosat altimeter measurements and a mean field constructed from historical hydrographic data. The method used for assimilating the data is the nudging technique. Nudging has been implemented in such a way as to achieve a high degree of convergence of the surface model fields toward the observations.
Comparisons of the assimilation results with available in situ observations show a significant improvement in the degree of realism of the climatological model behavior, with respect to the model in which no data are assimilated. The remaining discrepancies in the model mean circulation seem to be mainly associated with deficiencies in the mean component of the surface data that are assimilated. On the other hand, the possibility of building into the model more realistic eddy characteristics through the assimilation of the surface eddy field proves very successful in driving components of the mean model circulation that are in relatively good agreement with the available observations. Comparisons with current meter time series during a time period partially overlapping the Geosat mission show that the model is able to “correctly” extrapolate the instantaneous surface eddy signals to depths of approximately 1500 m. The correlation coefficient between current meter and model time series varies from values close to 0.7 in the top 1500 m to values as low as 0.1–0.2 in the deep ocean.
Abstract
The improvement in the climatological behavior of a numerical model as a consequence of the assimilation of surface data is investigated. The model used for this study is a quasigeostrophic (QG) model of the Gulf Stream region. The data that have been assimilated are maps of sea surface height that have been obtained as the superposition of sea surface height variability deduced from the Geosat altimeter measurements and a mean field constructed from historical hydrographic data. The method used for assimilating the data is the nudging technique. Nudging has been implemented in such a way as to achieve a high degree of convergence of the surface model fields toward the observations.
Comparisons of the assimilation results with available in situ observations show a significant improvement in the degree of realism of the climatological model behavior, with respect to the model in which no data are assimilated. The remaining discrepancies in the model mean circulation seem to be mainly associated with deficiencies in the mean component of the surface data that are assimilated. On the other hand, the possibility of building into the model more realistic eddy characteristics through the assimilation of the surface eddy field proves very successful in driving components of the mean model circulation that are in relatively good agreement with the available observations. Comparisons with current meter time series during a time period partially overlapping the Geosat mission show that the model is able to “correctly” extrapolate the instantaneous surface eddy signals to depths of approximately 1500 m. The correlation coefficient between current meter and model time series varies from values close to 0.7 in the top 1500 m to values as low as 0.1–0.2 in the deep ocean.
Abstract
In Part I of the present work we studied the transient Rossby wave radiation excited in the far field by a northern boundary forcing. We proposed as a possible mechanism responsible for transient pulses of Rossby waves the sudden growth to finite amplitude and successive amplitude pulsations of a stationary or eastward moving meander of an intense current like the Gulf Stream. In Part I the linear regime was thoroughly analyzed and the major findings were: 1) the transient part of the response initially excited by “switching on” the meander is the one responsible for the Rossby waves radiating and being clearly detectable in the far field; 2) the Rossby radiation is excited only when the meander pulsation frequency is below a critical value.
In this paper, we extend the results of Part I to the highly nonlinear regime addressing the problem of the production of nonlinear, coherent structures through the same boundary forcing mechanisms. The model used is the quasi-geostrophic, potential vorticity equation on a β-plane with or without topography, in a periodic channel forced by a northern boundary function. The forcing functions are designed to simulate (i) a stationary pulsating meander, (ii) a slowly propagating meander, (iii) a combination of both. This may constitute the simplest possible idealization of meander growth to finite amplitude, its successive steepening and bending with pinching off of eddies as frequently observed in the Gulf Stream system.
Using a boundary forcing idealizing a steady meander with a pulsating amplitude, we excite nonlinear vortices on the β-plane without topography. The related regime is called the “modon” regime as, at every pulsation cycle, two circulation patterns are produced, one cyclonic, the other anticyclonic. These vortices are part of a dipole pair and self-advect eastward or westward depending on their polarity (low-above-high or inverse). Through diagnostic tools we show that these vortices are ‘reasonable’ modons, that is highly nonlinear, exact solutions of the equivalent barotropic model on the β-plane.
The second type of boundary forcing capitalizes upon a resonance mechanism which was previously studied analytically in the weakly nonlinear regime. In it, an interior vortex is resonantly excited by a meander with constant amplitude which propagates at one of the eigenspeeds of the free linear modes of the channel. This mechanism needs topography to be effective when using quasi-geostrophic dynamics. With parabolic relief all along the channel, a resonantly forced nonlinear eddy is excited in the interior which propagates eastward leaving the forcing wave trailing behind it. In the highly nonlinear limit, the excited vortex remains coherent against the effects of dispersion even when the northern boundary forcing is turned off. Through a process of Rossby-wave shedding, it adjusts itself to the free-modon solution of the potential vorticity equation with a parabolic topography, as shown by using modon diagnostics.
Abstract
In Part I of the present work we studied the transient Rossby wave radiation excited in the far field by a northern boundary forcing. We proposed as a possible mechanism responsible for transient pulses of Rossby waves the sudden growth to finite amplitude and successive amplitude pulsations of a stationary or eastward moving meander of an intense current like the Gulf Stream. In Part I the linear regime was thoroughly analyzed and the major findings were: 1) the transient part of the response initially excited by “switching on” the meander is the one responsible for the Rossby waves radiating and being clearly detectable in the far field; 2) the Rossby radiation is excited only when the meander pulsation frequency is below a critical value.
In this paper, we extend the results of Part I to the highly nonlinear regime addressing the problem of the production of nonlinear, coherent structures through the same boundary forcing mechanisms. The model used is the quasi-geostrophic, potential vorticity equation on a β-plane with or without topography, in a periodic channel forced by a northern boundary function. The forcing functions are designed to simulate (i) a stationary pulsating meander, (ii) a slowly propagating meander, (iii) a combination of both. This may constitute the simplest possible idealization of meander growth to finite amplitude, its successive steepening and bending with pinching off of eddies as frequently observed in the Gulf Stream system.
Using a boundary forcing idealizing a steady meander with a pulsating amplitude, we excite nonlinear vortices on the β-plane without topography. The related regime is called the “modon” regime as, at every pulsation cycle, two circulation patterns are produced, one cyclonic, the other anticyclonic. These vortices are part of a dipole pair and self-advect eastward or westward depending on their polarity (low-above-high or inverse). Through diagnostic tools we show that these vortices are ‘reasonable’ modons, that is highly nonlinear, exact solutions of the equivalent barotropic model on the β-plane.
The second type of boundary forcing capitalizes upon a resonance mechanism which was previously studied analytically in the weakly nonlinear regime. In it, an interior vortex is resonantly excited by a meander with constant amplitude which propagates at one of the eigenspeeds of the free linear modes of the channel. This mechanism needs topography to be effective when using quasi-geostrophic dynamics. With parabolic relief all along the channel, a resonantly forced nonlinear eddy is excited in the interior which propagates eastward leaving the forcing wave trailing behind it. In the highly nonlinear limit, the excited vortex remains coherent against the effects of dispersion even when the northern boundary forcing is turned off. Through a process of Rossby-wave shedding, it adjusts itself to the free-modon solution of the potential vorticity equation with a parabolic topography, as shown by using modon diagnostics.
Abstract
The dynamical consequences of constraining a numerical model with sea surface height data have been investigated. The model used for this study is a quasigeostrophic model of the Gulf Stream region. The data that have been assimilated are maps of sea surface height obtained as the superposition of sea surface height variability deduced from the Geosat altimeter measurements and a mean field constructed from historical hydrographic data. The method used for assimilating the data is the nudging technique. Nudging has been implemented in such a way as to achieve a high degree of convergence of the surface model fields toward the observations. The assimilations of the surface data is thus equivalent to the prescription of a surface pressure boundary condition. The authors analyzed the mechanisms of the model adjustment and the characteristics of the resultant equilibrium state when the surface data are assimilated. Since the surface data are the superposition of a mean component and an eddy component, in order to understand the relative role of these two components in determining the characteristics of the final equilibrium state, two different experiments have been considered: in the first experiment only the climatological mean field is assimilated, while in the second experiment the total surface streamfunction field (mean plus eddies) has been used. It is shown that the model behavior in the presence of the surface data constraint can be conveniently described in terms of baroclinic Fofonoff modes. The prescribed mean component of the surface data acts as a “surface topography” in this problem. Its presence determines a distortion of the geostrophic contours in the subsurface layers, thus constraining the mean circulation in those layers. The intensity of the mean flow is determined by the inflow/outflow conditions at the open boundaries, as well as by eddy forcing and dissipation.
Abstract
The dynamical consequences of constraining a numerical model with sea surface height data have been investigated. The model used for this study is a quasigeostrophic model of the Gulf Stream region. The data that have been assimilated are maps of sea surface height obtained as the superposition of sea surface height variability deduced from the Geosat altimeter measurements and a mean field constructed from historical hydrographic data. The method used for assimilating the data is the nudging technique. Nudging has been implemented in such a way as to achieve a high degree of convergence of the surface model fields toward the observations. The assimilations of the surface data is thus equivalent to the prescription of a surface pressure boundary condition. The authors analyzed the mechanisms of the model adjustment and the characteristics of the resultant equilibrium state when the surface data are assimilated. Since the surface data are the superposition of a mean component and an eddy component, in order to understand the relative role of these two components in determining the characteristics of the final equilibrium state, two different experiments have been considered: in the first experiment only the climatological mean field is assimilated, while in the second experiment the total surface streamfunction field (mean plus eddies) has been used. It is shown that the model behavior in the presence of the surface data constraint can be conveniently described in terms of baroclinic Fofonoff modes. The prescribed mean component of the surface data acts as a “surface topography” in this problem. Its presence determines a distortion of the geostrophic contours in the subsurface layers, thus constraining the mean circulation in those layers. The intensity of the mean flow is determined by the inflow/outflow conditions at the open boundaries, as well as by eddy forcing and dissipation.
Abstract
A reduced-gravity, primitive equation, upper-ocean GCM is used to study subduction pathways in the Atlantic subtropical and tropical gyres. In order to compare the different responses in the pathways to strong and weak wind stress forcings, Hellerman and Rosenstein (HR) and da Silva (DSV) climatological annual-mean and monthly wind stress forcings are used to force the model. It is shown that subtropical–tropical communication is dependent on both the strength and structure of the wind forcing. A comparison between the two experiments shows two results for the North Atlantic: 1) the full communication window between the subtropical and tropical gyres is similar in width despite the difference in the intensity of the winds and 2) the interior exchange window width is substantially larger in the weak forcing experiment (DSV) than the strong forcing experiment (HR), accompanied by a larger transport as well. The South Atlantic exhibits a similar communication between the subtropics and Tropics in both cases. The annual-mean of the seasonally varying forcing also supports these results. A two-layer ventilated thermocline model is developed with a zonally varying, even though idealized, wind stress in the North Atlantic, which includes the upward Ekman pumping region absent from the classical ventilated thermocline model. The model shows that the communication window for subduction pathways is a function of the zonal gradient of the Ekman pumping velocity, not the Ekman pumping itself, at outcrop lines and at the boundary between the subtropical and tropical gyres. This solution is validated using three additional GCM experiments. It is shown that the communication windows are primarily explained by the ventilated thermocline model without considering the buoyancy effects. From the GCM experiments, the interior exchange window, which is a part of the communication window and cannot be explained by the ventilated thermocline model, is widened by two factors: 1) eliminating part of the positive Ekman pumping region in the eastern North Atlantic and 2) weakening the Ekman pumping over the whole region. The implications of these results suggest that changes in the wind forcing on the order of the difference in the wind products used here can have a significant effect on the attributes of the communication window and, hence, the thermocline structure at lower latitudes.
Abstract
A reduced-gravity, primitive equation, upper-ocean GCM is used to study subduction pathways in the Atlantic subtropical and tropical gyres. In order to compare the different responses in the pathways to strong and weak wind stress forcings, Hellerman and Rosenstein (HR) and da Silva (DSV) climatological annual-mean and monthly wind stress forcings are used to force the model. It is shown that subtropical–tropical communication is dependent on both the strength and structure of the wind forcing. A comparison between the two experiments shows two results for the North Atlantic: 1) the full communication window between the subtropical and tropical gyres is similar in width despite the difference in the intensity of the winds and 2) the interior exchange window width is substantially larger in the weak forcing experiment (DSV) than the strong forcing experiment (HR), accompanied by a larger transport as well. The South Atlantic exhibits a similar communication between the subtropics and Tropics in both cases. The annual-mean of the seasonally varying forcing also supports these results. A two-layer ventilated thermocline model is developed with a zonally varying, even though idealized, wind stress in the North Atlantic, which includes the upward Ekman pumping region absent from the classical ventilated thermocline model. The model shows that the communication window for subduction pathways is a function of the zonal gradient of the Ekman pumping velocity, not the Ekman pumping itself, at outcrop lines and at the boundary between the subtropical and tropical gyres. This solution is validated using three additional GCM experiments. It is shown that the communication windows are primarily explained by the ventilated thermocline model without considering the buoyancy effects. From the GCM experiments, the interior exchange window, which is a part of the communication window and cannot be explained by the ventilated thermocline model, is widened by two factors: 1) eliminating part of the positive Ekman pumping region in the eastern North Atlantic and 2) weakening the Ekman pumping over the whole region. The implications of these results suggest that changes in the wind forcing on the order of the difference in the wind products used here can have a significant effect on the attributes of the communication window and, hence, the thermocline structure at lower latitudes.
Abstract
A numerical model, with quasigeostrophic and barotropic dynamics, is used to study the forcing of mean flows by an unstable jet. The initially zonal jet has specified shape and transport at the western inflow boundary and is sufficiently intense and narrow that the potential vorticity gradient changes sign, giving rise to barotropic instabilities. The resulting eddies act to smooth the potential vorticity anomalies transported into the domain and produce homogenized regions in which recirculations develop to the north and south of the jet. The intensity of these recirculations, as a function of nondimensional beta, is investigated and a simple, kinematic interpretation offered.
Abstract
A numerical model, with quasigeostrophic and barotropic dynamics, is used to study the forcing of mean flows by an unstable jet. The initially zonal jet has specified shape and transport at the western inflow boundary and is sufficiently intense and narrow that the potential vorticity gradient changes sign, giving rise to barotropic instabilities. The resulting eddies act to smooth the potential vorticity anomalies transported into the domain and produce homogenized regions in which recirculations develop to the north and south of the jet. The intensity of these recirculations, as a function of nondimensional beta, is investigated and a simple, kinematic interpretation offered.
Abstract
Linear and nonlinear radiating instabilities of an eastern boundary current are studied using a barotropic quasigeostrophic model in an idealized meridional channel. The eastern boundary current is meridionally uniform and produces unstable modes in which long waves are most able to radiate. These long radiating modes are easily suppressed by friction because of their small growth rates. However, the long radiating modes can overcome friction by nonlinear energy input transferred from the more unstable trapped mode and play an important role in the energy budget of the boundary current system. The nonlinearly powered long radiating modes take away part of the perturbation energy from the instability origin to the ocean interior. The radiated instabilities can generate zonal striations in the ocean interior that are comparable to features observed in the ocean. Subharmonic instability is identified to be responsible for the nonlinear resonance between the radiating and trapped modes, but more general nonlinear triad interactions are expected to apply in a highly nonlinear environment.
Abstract
Linear and nonlinear radiating instabilities of an eastern boundary current are studied using a barotropic quasigeostrophic model in an idealized meridional channel. The eastern boundary current is meridionally uniform and produces unstable modes in which long waves are most able to radiate. These long radiating modes are easily suppressed by friction because of their small growth rates. However, the long radiating modes can overcome friction by nonlinear energy input transferred from the more unstable trapped mode and play an important role in the energy budget of the boundary current system. The nonlinearly powered long radiating modes take away part of the perturbation energy from the instability origin to the ocean interior. The radiated instabilities can generate zonal striations in the ocean interior that are comparable to features observed in the ocean. Subharmonic instability is identified to be responsible for the nonlinear resonance between the radiating and trapped modes, but more general nonlinear triad interactions are expected to apply in a highly nonlinear environment.
