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Abstract
We examine the ocean energy cycle where the eddies are defined about the ensemble mean of a partially air–sea coupled, eddy-rich ensemble simulation of the North Atlantic. The decomposition about the ensemble mean leads to a parameter-free definition of eddies, which is interpreted as the expression of oceanic chaos. Using the ensemble framework, we define the reservoirs of mean and eddy kinetic energy (MKE and EKE, respectively) and mean total dynamic enthalpy (MTDE). We opt for the usage of dynamic enthalpy (DE) as a proxy for potential energy due to its dynamically consistent relation to hydrostatic pressure in Boussinesq fluids and nonreliance on any reference stratification. The curious result that emerges is that the potential energy reservoir cannot be decomposed into its mean and eddy components, and the eddy flux of DE can be absorbed into the EKE budget as pressure work. We find from the energy cycle that while baroclinic instability, associated with a positive vertical eddy buoyancy flux, tends to peak around February, EKE takes its maximum around September in the wind-driven gyre. Interestingly, the energy input from MKE to EKE, a process sometimes associated with barotropic processes, becomes larger than the vertical eddy buoyancy flux during the summer and autumn. Our results question the common notion that the inverse energy cascade of wintertime EKE energized by baroclinic instability within the mixed layer is solely responsible for the summer-to-autumn peak in EKE and suggest that both the eddy transport of DE and transfer of energy from MKE to EKE contribute to the seasonal EKE maxima.
Significance Statement
The Earth system, including the ocean, is chaotic. Namely, the state to be realized is highly sensitive to minute perturbations, a phenomenon commonly known as the “butterfly effect.” Here, we run a sweep of ocean simulations that allow us to disentangle the oceanic expression of chaos from the oceanic response to the atmosphere. We investigate the energy pathways between the two in a physically consistent manner in the North Atlantic region. Our approach can be extended to robustly examine the temporal change of oceanic energy and heat distribution under a warming climate.
Abstract
We examine the ocean energy cycle where the eddies are defined about the ensemble mean of a partially air–sea coupled, eddy-rich ensemble simulation of the North Atlantic. The decomposition about the ensemble mean leads to a parameter-free definition of eddies, which is interpreted as the expression of oceanic chaos. Using the ensemble framework, we define the reservoirs of mean and eddy kinetic energy (MKE and EKE, respectively) and mean total dynamic enthalpy (MTDE). We opt for the usage of dynamic enthalpy (DE) as a proxy for potential energy due to its dynamically consistent relation to hydrostatic pressure in Boussinesq fluids and nonreliance on any reference stratification. The curious result that emerges is that the potential energy reservoir cannot be decomposed into its mean and eddy components, and the eddy flux of DE can be absorbed into the EKE budget as pressure work. We find from the energy cycle that while baroclinic instability, associated with a positive vertical eddy buoyancy flux, tends to peak around February, EKE takes its maximum around September in the wind-driven gyre. Interestingly, the energy input from MKE to EKE, a process sometimes associated with barotropic processes, becomes larger than the vertical eddy buoyancy flux during the summer and autumn. Our results question the common notion that the inverse energy cascade of wintertime EKE energized by baroclinic instability within the mixed layer is solely responsible for the summer-to-autumn peak in EKE and suggest that both the eddy transport of DE and transfer of energy from MKE to EKE contribute to the seasonal EKE maxima.
Significance Statement
The Earth system, including the ocean, is chaotic. Namely, the state to be realized is highly sensitive to minute perturbations, a phenomenon commonly known as the “butterfly effect.” Here, we run a sweep of ocean simulations that allow us to disentangle the oceanic expression of chaos from the oceanic response to the atmosphere. We investigate the energy pathways between the two in a physically consistent manner in the North Atlantic region. Our approach can be extended to robustly examine the temporal change of oceanic energy and heat distribution under a warming climate.
Abstract
Recent studies suggest that the eddy kinetic energy is localized in the lee of significant topographic features in the Antarctic Circumpolar Current (ACC). Here we explore the importance of the local dynamics quantitatively using the outputs from the realistic ocean general circulation model hindcast with the aid of the modified Lorentz energy cycle. Results confirm the importance of energy transfer among reservoirs in the downstream region of standing meanders, showing that the major five standing meanders are responsible for more than 70% of the kinetic energy transfer to eddies and dissipation over the Antarctic Circumpolar Current region. The eddy kinetic energy is generated in the upper 3000-m depth downstream of the standing meanders and transported due to the vertical energy redistribution governed by the vertical pressure flux toward the deeper layer where the eddy energy is dissipated. Moreover, we also calculate the work done by the Ekman transport to confirm that the wind energy input works as the dominant energy source for the baroclinic energy pathway. The advantage of this quantity against the vertical mean density flux is that it is independent of the reference states defined arbitrarily. It is shown that the westerlies can supply sufficient energy locally to initiate baroclinic instability in the Indian and Pacific sectors of the ACC, whereas the nonlocal process is important in the Atlantic sector. Our results suggest that the five narrow regions associated with significant topography play key roles in the energy balance of the ACC region.
Significance Statement
The purpose of this study is to understand the eddy–mean flow interactions in the Antarctic Circumpolar Current from the energetic viewpoint. Our results show that the five narrow regions called “hotspots” in our study are responsible for the energy transfer from the mean flow to eddies. It is also found that the hotspots are important for the energy sink in the Southern Ocean. These findings suggest that the five hotspots are likely to play key roles in the responses of the Antarctic Circumpolar Current to the changes in westerlies in these decades.
Abstract
Recent studies suggest that the eddy kinetic energy is localized in the lee of significant topographic features in the Antarctic Circumpolar Current (ACC). Here we explore the importance of the local dynamics quantitatively using the outputs from the realistic ocean general circulation model hindcast with the aid of the modified Lorentz energy cycle. Results confirm the importance of energy transfer among reservoirs in the downstream region of standing meanders, showing that the major five standing meanders are responsible for more than 70% of the kinetic energy transfer to eddies and dissipation over the Antarctic Circumpolar Current region. The eddy kinetic energy is generated in the upper 3000-m depth downstream of the standing meanders and transported due to the vertical energy redistribution governed by the vertical pressure flux toward the deeper layer where the eddy energy is dissipated. Moreover, we also calculate the work done by the Ekman transport to confirm that the wind energy input works as the dominant energy source for the baroclinic energy pathway. The advantage of this quantity against the vertical mean density flux is that it is independent of the reference states defined arbitrarily. It is shown that the westerlies can supply sufficient energy locally to initiate baroclinic instability in the Indian and Pacific sectors of the ACC, whereas the nonlocal process is important in the Atlantic sector. Our results suggest that the five narrow regions associated with significant topography play key roles in the energy balance of the ACC region.
Significance Statement
The purpose of this study is to understand the eddy–mean flow interactions in the Antarctic Circumpolar Current from the energetic viewpoint. Our results show that the five narrow regions called “hotspots” in our study are responsible for the energy transfer from the mean flow to eddies. It is also found that the hotspots are important for the energy sink in the Southern Ocean. These findings suggest that the five hotspots are likely to play key roles in the responses of the Antarctic Circumpolar Current to the changes in westerlies in these decades.
Abstract
Based on the Regional Ocean Modeling System (ROMS) and the conditional nonlinear optimal perturbation (CNOP) method, we explore the nonlinear optimal triggering perturbation of the Kuroshio large meander (LM) and its evolution, and reveal the role of nonlinear physical processes in the formation of the LM path. The results show that the large amplitudes of the perturbations are mainly located in the upper 2000 m in the southeastern area of Kyushu (29°–32°N, 131°–134°E), where the eastward propagation of the cold anomaly is vital to the formation of the LM path. By analyzing the depth-integrated vorticity equation of the perturbation, we find that linear advection, namely, the interaction between the perturbation and the reference field, tends to move the cyclonic eddy induced by the optimal triggering perturbation eastward, while the nonlinear advection associated with the interaction of perturbations tends to move the cyclonic eddy westward. The opposing effects of the nonlinear advection and the linear advection slow the eastward movement of the cyclonic eddy so that the eddy has a chance to effectively develop, eventually leading to the formation of the Kuroshio LM path.
Abstract
Based on the Regional Ocean Modeling System (ROMS) and the conditional nonlinear optimal perturbation (CNOP) method, we explore the nonlinear optimal triggering perturbation of the Kuroshio large meander (LM) and its evolution, and reveal the role of nonlinear physical processes in the formation of the LM path. The results show that the large amplitudes of the perturbations are mainly located in the upper 2000 m in the southeastern area of Kyushu (29°–32°N, 131°–134°E), where the eastward propagation of the cold anomaly is vital to the formation of the LM path. By analyzing the depth-integrated vorticity equation of the perturbation, we find that linear advection, namely, the interaction between the perturbation and the reference field, tends to move the cyclonic eddy induced by the optimal triggering perturbation eastward, while the nonlinear advection associated with the interaction of perturbations tends to move the cyclonic eddy westward. The opposing effects of the nonlinear advection and the linear advection slow the eastward movement of the cyclonic eddy so that the eddy has a chance to effectively develop, eventually leading to the formation of the Kuroshio LM path.
Abstract
Eddy saturation refers to a regime in which the total volume transport of an oceanic current is insensitive to the wind stress strength. Baroclinicity is currently believed to be the key to the development of an eddy-saturated state. In this paper, it is shown that eddy saturation can also occur in a purely barotropic flow over topography, without baroclinicity. Thus, eddy saturation is a fundamental property of barotropic dynamics above topography. It is demonstrated that the main factor controlling the appearance or not of eddy-saturated states in the barotropic setting is the structure of geostrophic contours, that is, the contours of f/H (the ratio of the Coriolis parameter to the ocean’s depth). Eddy-saturated states occur when the geostrophic contours are open, that is, when the geostrophic contours span the whole zonal extent of the domain. This minimal requirement for eddy-saturated states is demonstrated using numerical integrations of a single-layer quasigeostrophic flow over two different topographies characterized by either open or closed geostrophic contours with parameter values loosely inspired by the Southern Ocean. In this setting, transient eddies are produced through a barotropic–topographic instability that occurs because of the interaction of the large-scale zonal flow with the topography. By studying this barotropic–topographic instability insight is gained on how eddy-saturated states are established.
Abstract
Eddy saturation refers to a regime in which the total volume transport of an oceanic current is insensitive to the wind stress strength. Baroclinicity is currently believed to be the key to the development of an eddy-saturated state. In this paper, it is shown that eddy saturation can also occur in a purely barotropic flow over topography, without baroclinicity. Thus, eddy saturation is a fundamental property of barotropic dynamics above topography. It is demonstrated that the main factor controlling the appearance or not of eddy-saturated states in the barotropic setting is the structure of geostrophic contours, that is, the contours of f/H (the ratio of the Coriolis parameter to the ocean’s depth). Eddy-saturated states occur when the geostrophic contours are open, that is, when the geostrophic contours span the whole zonal extent of the domain. This minimal requirement for eddy-saturated states is demonstrated using numerical integrations of a single-layer quasigeostrophic flow over two different topographies characterized by either open or closed geostrophic contours with parameter values loosely inspired by the Southern Ocean. In this setting, transient eddies are produced through a barotropic–topographic instability that occurs because of the interaction of the large-scale zonal flow with the topography. By studying this barotropic–topographic instability insight is gained on how eddy-saturated states are established.
Abstract
Evidence in support of overturn-based methods, often used to infer turbulent dissipation rate from density profiles, is typically from regions with weaker turbulence than that at rough-topography hotspots. The present work uses direct numerical simulations (DNS) of an idealized problem of sloping topography as well as high-resolution large-eddy simulation (LES) of turbulent flow at more realistic topography in order to investigate the accuracy of overturn-based methods in sites with internal wave breaking. Two methods are assessed: Thorpe sorting, where the overturn length L T is based on local distortion of measured density from the background, and inversion sorting, where the inversion length scale L I measures the statically unstable local region. The overturn boundaries are different between the two methods. Thorpe sorting leads to an order of magnitude overestimate of the turbulent dissipation in the DNS during large convective overturn events when inversion sorting is more accurate. The LES of steep, realistic topography leads to a similar conclusion of a substantial overestimate of dissipation by Thorpe sorting. Energy arguments explain the better performance of inversion sorting in convectively driven turbulence and the better performance of Thorpe sorting in shear-driven turbulence.
Abstract
Evidence in support of overturn-based methods, often used to infer turbulent dissipation rate from density profiles, is typically from regions with weaker turbulence than that at rough-topography hotspots. The present work uses direct numerical simulations (DNS) of an idealized problem of sloping topography as well as high-resolution large-eddy simulation (LES) of turbulent flow at more realistic topography in order to investigate the accuracy of overturn-based methods in sites with internal wave breaking. Two methods are assessed: Thorpe sorting, where the overturn length L T is based on local distortion of measured density from the background, and inversion sorting, where the inversion length scale L I measures the statically unstable local region. The overturn boundaries are different between the two methods. Thorpe sorting leads to an order of magnitude overestimate of the turbulent dissipation in the DNS during large convective overturn events when inversion sorting is more accurate. The LES of steep, realistic topography leads to a similar conclusion of a substantial overestimate of dissipation by Thorpe sorting. Energy arguments explain the better performance of inversion sorting in convectively driven turbulence and the better performance of Thorpe sorting in shear-driven turbulence.
Abstract
The relative roles of advective processes and mixing on the temporal adjustment of the meridional overturning circulation are examined, in particular the effects of mixing in either the abyssal or upper ocean. Laboratory experiments with convectively driven overturning and imposed stirring rates show that the circulation adjusts toward an equilibrium state on time scales governed by mixing in the upper boundary layer region but independent of the mixing rate in the bulk of the interior. The equilibrium state of the stratification is dependent only on the rate of mixing in the boundary layer. An idealized high-resolution ocean model shows adjustment (of a two-cell circulation) dominated primarily by the advective ventilation time scale, consistent with a view of the circulation determined by water mass transformation occurring primarily near the surface. Both the experiments and the model results indicate that adjustments of the circulation are controlled by surface buoyancy uptake (or rejection) and that the nonequilibrium circulation is dominated by advective processes, especially if the average abyssal ocean diffusivity is less than 3 × 10−5 m2 s−1.
Abstract
The relative roles of advective processes and mixing on the temporal adjustment of the meridional overturning circulation are examined, in particular the effects of mixing in either the abyssal or upper ocean. Laboratory experiments with convectively driven overturning and imposed stirring rates show that the circulation adjusts toward an equilibrium state on time scales governed by mixing in the upper boundary layer region but independent of the mixing rate in the bulk of the interior. The equilibrium state of the stratification is dependent only on the rate of mixing in the boundary layer. An idealized high-resolution ocean model shows adjustment (of a two-cell circulation) dominated primarily by the advective ventilation time scale, consistent with a view of the circulation determined by water mass transformation occurring primarily near the surface. Both the experiments and the model results indicate that adjustments of the circulation are controlled by surface buoyancy uptake (or rejection) and that the nonequilibrium circulation is dominated by advective processes, especially if the average abyssal ocean diffusivity is less than 3 × 10−5 m2 s−1.
Abstract
Inertial waves propagating upward in a geostrophically balanced front experience critical reflections against the ocean surface. Such reflections naturally create oscillations with small vertical scales, and viscous friction becomes a dominant process. Here, friction modifies the polarization relations of internal waves and allows energy from the balanced front to be exchanged with the ageostrophic motions and eventually dissipated. In addition, while in the well-known inviscid case internal waves propagate on only two characteristics, this study demonstrates using an analytical model that strong viscous effects introduce additional oscillatory modes that can exchange energy with the front. Moreover, during a linear, near-critical reflection, the superposition of several of these oscillations induces an even stronger energy exchange with the front. When the Richardson number based on the frontal thermal wind shear is O(1), the rate of energy exchange peaks at wave frequencies that are near inertial and is comparable in magnitude to the energy flux of the incident, upward-propagating waves. Two-dimensional, linear numerical experiments confirm this finding. The analytical model also demonstrates that this process is qualitatively insensitive to the actual value of the viscosity or the form of the boundary condition at the surface. In fully nonlinear experiments, the authors recover these qualitative conclusions. However, nonlinear wave–wave interactions and turbulence in particular, strongly modify the amount of energy that is exchanged with the front. In practice, such nonlinear effects are only active when the incident waves have frequencies higher than the Coriolis frequency, since these configurations are conducive to near-resonant triad interactions between incident and reflected waves.
Abstract
Inertial waves propagating upward in a geostrophically balanced front experience critical reflections against the ocean surface. Such reflections naturally create oscillations with small vertical scales, and viscous friction becomes a dominant process. Here, friction modifies the polarization relations of internal waves and allows energy from the balanced front to be exchanged with the ageostrophic motions and eventually dissipated. In addition, while in the well-known inviscid case internal waves propagate on only two characteristics, this study demonstrates using an analytical model that strong viscous effects introduce additional oscillatory modes that can exchange energy with the front. Moreover, during a linear, near-critical reflection, the superposition of several of these oscillations induces an even stronger energy exchange with the front. When the Richardson number based on the frontal thermal wind shear is O(1), the rate of energy exchange peaks at wave frequencies that are near inertial and is comparable in magnitude to the energy flux of the incident, upward-propagating waves. Two-dimensional, linear numerical experiments confirm this finding. The analytical model also demonstrates that this process is qualitatively insensitive to the actual value of the viscosity or the form of the boundary condition at the surface. In fully nonlinear experiments, the authors recover these qualitative conclusions. However, nonlinear wave–wave interactions and turbulence in particular, strongly modify the amount of energy that is exchanged with the front. In practice, such nonlinear effects are only active when the incident waves have frequencies higher than the Coriolis frequency, since these configurations are conducive to near-resonant triad interactions between incident and reflected waves.
Abstract
Here, the effects of surface waves on submesoscale instabilities are studied through analytical and linear analyses as well as nonlinear large-eddy simulations of the wave-averaged Boussinesq equations. The wave averaging yields a surface-intensified current (Stokes drift) that advects momentum, adds to the total Coriolis force, and induces a Stokes shear force. The Stokes–Coriolis force alters the geostrophically balanced flow by reducing the burden on the Eulerian–Coriolis force to prop up the front, thereby potentially inciting an anti-Stokes Eulerian shear, while maintaining the Lagrangian (Eulerian plus Stokes) shear. Since the Lagrangian shear is maintained, the Charney–Stern–Pedlosky criteria for quasigeostrophic (QG) baroclinic instability are unchanged with the appropriate Lagrangian interpretation of the shear and QG potential vorticity. While the Stokes drift does not directly affect vorticity, the anti-Stokes Eulerian shear contributes to the Ertel potential vorticity (PV). When the Stokes shear and geostrophic shear are aligned (antialigned), the PV is more (less) cyclonic. If the Stokes-modified PV is anticyclonic, the flow is unstable to symmetric instabilities (SI). Stokes drift also weakly impacts SI through the Stokes shear force. When the Stokes and Eulerian shears are the same (opposite) sign, the Stokes shear force does positive (negative) work on the flow associated with SI. Stokes drift also allows SI to extract more potential energy from the front, providing an indirect mechanism for Stokes-induced restratification.
Abstract
Here, the effects of surface waves on submesoscale instabilities are studied through analytical and linear analyses as well as nonlinear large-eddy simulations of the wave-averaged Boussinesq equations. The wave averaging yields a surface-intensified current (Stokes drift) that advects momentum, adds to the total Coriolis force, and induces a Stokes shear force. The Stokes–Coriolis force alters the geostrophically balanced flow by reducing the burden on the Eulerian–Coriolis force to prop up the front, thereby potentially inciting an anti-Stokes Eulerian shear, while maintaining the Lagrangian (Eulerian plus Stokes) shear. Since the Lagrangian shear is maintained, the Charney–Stern–Pedlosky criteria for quasigeostrophic (QG) baroclinic instability are unchanged with the appropriate Lagrangian interpretation of the shear and QG potential vorticity. While the Stokes drift does not directly affect vorticity, the anti-Stokes Eulerian shear contributes to the Ertel potential vorticity (PV). When the Stokes shear and geostrophic shear are aligned (antialigned), the PV is more (less) cyclonic. If the Stokes-modified PV is anticyclonic, the flow is unstable to symmetric instabilities (SI). Stokes drift also weakly impacts SI through the Stokes shear force. When the Stokes and Eulerian shears are the same (opposite) sign, the Stokes shear force does positive (negative) work on the flow associated with SI. Stokes drift also allows SI to extract more potential energy from the front, providing an indirect mechanism for Stokes-induced restratification.
Abstract
While near-inertial waves are known to be generated by atmospheric storms, recent observations in the Kuroshio Front find intense near-inertial internal-wave shear along sloping isopycnals, even during calm weather. Recent literature suggests that spontaneous generation of near-inertial waves by frontal instabilities could represent a major sink for the subinertial quasigeostrophic circulation. An unforced three-dimensional 1-km-resolution model, initialized with the observed cross-Kuroshio structure, is used to explore this mechanism. After several weeks, the model exhibits growth of 10–100-km-scale frontal meanders, accompanied by O(10) mW m−2 spontaneous generation of near-inertial waves associated with readjustment of submesoscale fronts forced out of balance by mesoscale confluent flows. These waves have properties resembling those in the observations. However, they are reabsorbed into the model Kuroshio Front with no more than 15% dissipating or radiating away. Thus, spontaneous generation of near-inertial waves represents a redistribution of quasigeostrophic energy rather than a significant sink.
Abstract
While near-inertial waves are known to be generated by atmospheric storms, recent observations in the Kuroshio Front find intense near-inertial internal-wave shear along sloping isopycnals, even during calm weather. Recent literature suggests that spontaneous generation of near-inertial waves by frontal instabilities could represent a major sink for the subinertial quasigeostrophic circulation. An unforced three-dimensional 1-km-resolution model, initialized with the observed cross-Kuroshio structure, is used to explore this mechanism. After several weeks, the model exhibits growth of 10–100-km-scale frontal meanders, accompanied by O(10) mW m−2 spontaneous generation of near-inertial waves associated with readjustment of submesoscale fronts forced out of balance by mesoscale confluent flows. These waves have properties resembling those in the observations. However, they are reabsorbed into the model Kuroshio Front with no more than 15% dissipating or radiating away. Thus, spontaneous generation of near-inertial waves represents a redistribution of quasigeostrophic energy rather than a significant sink.
Abstract
Direct numerical simulation (DNS) and large-eddy simulation (LES) are employed to study the mixing brought about by convective overturns in a stratified, oscillatory bottom layer underneath internal tides. The phasing of turbulence, the onset and breakdown of convective overturns, and the pathway to irreversible mixing are quantified. Mixing efficiency shows a systematic dependence on tidal phase, and during the breakdown of large convective overturns it is approximately 0.6, a value that is substantially larger than the commonly assumed value of 0.2 used for calculating scalar mixing from the turbulent dissipation rate. Diapycnal diffusivity is calculated using the irreversible diapycnal flux and, for tall overturns of O(50) m, the diffusivity is found to be almost 1000 times higher than the molecular diffusivity. The Thorpe (overturn) length scale is often used as a proxy for the Ozmidov length scale and thus infers the turbulent dissipation rate from overturns. The accuracy of overturn-based estimates of the dissipation rate is assessed for this flow. The Ozmidov length scale LO and Thorpe length scale LT are found to behave differently during a tidal cycle: LT decreases during the convective instability, while LO increases; there is a significant phase lag between the maxima of LT and LO; and finally LT is not linearly related to LO. Thus, the Thorpe-inferred dissipation rates are quite different from the actual values. Interestingly, the ratio of their cycle-averaged values is found to be O(1), a result explained on the basis of available potential energy.
Abstract
Direct numerical simulation (DNS) and large-eddy simulation (LES) are employed to study the mixing brought about by convective overturns in a stratified, oscillatory bottom layer underneath internal tides. The phasing of turbulence, the onset and breakdown of convective overturns, and the pathway to irreversible mixing are quantified. Mixing efficiency shows a systematic dependence on tidal phase, and during the breakdown of large convective overturns it is approximately 0.6, a value that is substantially larger than the commonly assumed value of 0.2 used for calculating scalar mixing from the turbulent dissipation rate. Diapycnal diffusivity is calculated using the irreversible diapycnal flux and, for tall overturns of O(50) m, the diffusivity is found to be almost 1000 times higher than the molecular diffusivity. The Thorpe (overturn) length scale is often used as a proxy for the Ozmidov length scale and thus infers the turbulent dissipation rate from overturns. The accuracy of overturn-based estimates of the dissipation rate is assessed for this flow. The Ozmidov length scale LO and Thorpe length scale LT are found to behave differently during a tidal cycle: LT decreases during the convective instability, while LO increases; there is a significant phase lag between the maxima of LT and LO; and finally LT is not linearly related to LO. Thus, the Thorpe-inferred dissipation rates are quite different from the actual values. Interestingly, the ratio of their cycle-averaged values is found to be O(1), a result explained on the basis of available potential energy.
