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Abstract
The Argo profiling float network has repeatedly sampled much of the World Ocean. This study uses Argo temperature and salinity data to form the tracer structure function of ocean variability at the macroscale (10–1000 km, mesoscale and above). Here, second-order temperature and salinity structure functions over horizontal separations are calculated along either pressure or potential density surfaces, which allows analysis of both active and passive tracer structure functions. Using Argo data, a map of global variance is created from the climatological average and each datum. When turbulence is homogeneous, the structure function slope from Argo can be related to the wavenumber spectrum slope in ocean temperature or salinity variability. This first application of structure function techniques to Argo data gives physically meaningful results based on bootstrapped confidence intervals, showing geographical dependence of the structure functions with slopes near ⅔ on average, independent of depth.
Abstract
The Argo profiling float network has repeatedly sampled much of the World Ocean. This study uses Argo temperature and salinity data to form the tracer structure function of ocean variability at the macroscale (10–1000 km, mesoscale and above). Here, second-order temperature and salinity structure functions over horizontal separations are calculated along either pressure or potential density surfaces, which allows analysis of both active and passive tracer structure functions. Using Argo data, a map of global variance is created from the climatological average and each datum. When turbulence is homogeneous, the structure function slope from Argo can be related to the wavenumber spectrum slope in ocean temperature or salinity variability. This first application of structure function techniques to Argo data gives physically meaningful results based on bootstrapped confidence intervals, showing geographical dependence of the structure functions with slopes near ⅔ on average, independent of depth.
Abstract
The study of the mechanical energy budget of the oceans using the Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically rearranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which is illustrated using climatological data, the authors show that compressibility effects are in fact minor. The reference state can be regarded as a well-defined one-dimensional function of depth, which forms a surface in temperature, salinity, and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. This study shows that the reference state obtained by standard sorting methods is equivalent to, though computationally more expensive than, the volume frequency distribution approach. The approach that is presented can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.
Abstract
The study of the mechanical energy budget of the oceans using the Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically rearranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which is illustrated using climatological data, the authors show that compressibility effects are in fact minor. The reference state can be regarded as a well-defined one-dimensional function of depth, which forms a surface in temperature, salinity, and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. This study shows that the reference state obtained by standard sorting methods is equivalent to, though computationally more expensive than, the volume frequency distribution approach. The approach that is presented can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.
Abstract
Small-scale turbulent mixing in the upper Equatorial Undercurrent (EUC) of the eastern Pacific cold tongue is a critical component of the SST budget that drives variations in SST on a range of time scales. Recent observations have shown that turbulent mixing within the EUC is modulated by tropical instability waves (TIWs). A regional ocean model is used to investigate the mechanisms through which large-scale TIW circulation modulates the small-scale shear, stratification, and shear-driven turbulence in the EUC. Eulerian analyses of time series taken from both the model and the Tropical Atmosphere Ocean (TAO) array suggest that increases in the zonal shear of the EUC drive increased mixing on the leading edge of the TIW warm phase. A Lagrangian vorticity analysis attributes this increased zonal shear to horizontal vortex stretching driven by the strain in the TIW horizontal velocity field acting on the existing EUC shear. To investigate the impact of horizontal vortex stretching on the turbulent heat flux averaged over a TIW period the effects of periodic TIW strain are included as forcing in a simple 1D mixing model of the EUC. Model runs with TIW forcing show turbulent heat fluxes up to 30% larger than runs without TIW forcing, with the magnitude of the increase being sensitive to the vertical mixing scheme used in the model. These results emphasize the importance of coupling between the large-scale circulation and small-scale turbulence in the equatorial regions, with implications for the SST budget of the equatorial Pacific.
Abstract
Small-scale turbulent mixing in the upper Equatorial Undercurrent (EUC) of the eastern Pacific cold tongue is a critical component of the SST budget that drives variations in SST on a range of time scales. Recent observations have shown that turbulent mixing within the EUC is modulated by tropical instability waves (TIWs). A regional ocean model is used to investigate the mechanisms through which large-scale TIW circulation modulates the small-scale shear, stratification, and shear-driven turbulence in the EUC. Eulerian analyses of time series taken from both the model and the Tropical Atmosphere Ocean (TAO) array suggest that increases in the zonal shear of the EUC drive increased mixing on the leading edge of the TIW warm phase. A Lagrangian vorticity analysis attributes this increased zonal shear to horizontal vortex stretching driven by the strain in the TIW horizontal velocity field acting on the existing EUC shear. To investigate the impact of horizontal vortex stretching on the turbulent heat flux averaged over a TIW period the effects of periodic TIW strain are included as forcing in a simple 1D mixing model of the EUC. Model runs with TIW forcing show turbulent heat fluxes up to 30% larger than runs without TIW forcing, with the magnitude of the increase being sensitive to the vertical mixing scheme used in the model. These results emphasize the importance of coupling between the large-scale circulation and small-scale turbulence in the equatorial regions, with implications for the SST budget of the equatorial Pacific.
Abstract
A large fraction of the kinetic energy in the ocean is stored in the “quasigeostrophic” eddy field. This “balanced” eddy field is expected, according to geostrophic turbulence theory, to transfer energy to larger scales. In order for the general circulation to remain approximately steady, instability mechanisms leading to loss of balance (LOB) have been hypothesized to take place so that the eddy kinetic energy (EKE) may be transferred to small scales where it can be dissipated. This study examines the kinetic energy pathways in fully resolved direct numerical simulations of flow in a flat-bottomed reentrant channel, externally forced by surface buoyancy fluxes and wind stress in a configuration that resembles the Antarctic Circumpolar Current. The flow is allowed to reach a statistical steady state at which point it exhibits both a forward and an inverse energy cascade. Flow interactions with irregular bathymetry are excluded so that bottom drag is the sole mechanism available to dissipate the upscale EKE transfer. The authors show that EKE is dissipated preferentially at small scales near the surface via frontal instabilities associated with LOB and a forward energy cascade rather than by bottom drag after an inverse energy cascade. This is true both with and without forcing by the wind. These results suggest that LOB caused by frontal instabilities near the ocean surface could provide an efficient mechanism, independent of boundary effects, by which EKE is dissipated. Ageostrophic anticyclonic instability is the dominant frontal instability mechanism in these simulations. Symmetric instability is also important in a “deep convection” region, where it can be sustained by buoyancy loss.
Abstract
A large fraction of the kinetic energy in the ocean is stored in the “quasigeostrophic” eddy field. This “balanced” eddy field is expected, according to geostrophic turbulence theory, to transfer energy to larger scales. In order for the general circulation to remain approximately steady, instability mechanisms leading to loss of balance (LOB) have been hypothesized to take place so that the eddy kinetic energy (EKE) may be transferred to small scales where it can be dissipated. This study examines the kinetic energy pathways in fully resolved direct numerical simulations of flow in a flat-bottomed reentrant channel, externally forced by surface buoyancy fluxes and wind stress in a configuration that resembles the Antarctic Circumpolar Current. The flow is allowed to reach a statistical steady state at which point it exhibits both a forward and an inverse energy cascade. Flow interactions with irregular bathymetry are excluded so that bottom drag is the sole mechanism available to dissipate the upscale EKE transfer. The authors show that EKE is dissipated preferentially at small scales near the surface via frontal instabilities associated with LOB and a forward energy cascade rather than by bottom drag after an inverse energy cascade. This is true both with and without forcing by the wind. These results suggest that LOB caused by frontal instabilities near the ocean surface could provide an efficient mechanism, independent of boundary effects, by which EKE is dissipated. Ageostrophic anticyclonic instability is the dominant frontal instability mechanism in these simulations. Symmetric instability is also important in a “deep convection” region, where it can be sustained by buoyancy loss.
Abstract
A set of realistic, very high-resolution simulations is made for the Gulf Stream region using the oceanic model Regional Oceanic Modeling System (ROMS) to study the life cycle of the intense submesoscale cold filaments that form on the subtropical gyre, interior wall of the Gulf Stream. The surface buoyancy gradients and ageostrophic secondary circulations intensify in response to the mesoscale strain field as predicted by the theory of filamentogenesis. It can be understood in terms of a dual frontogenetic process, along the lines understood for a single front. There is, however, a stronger secondary circulation due to the amplification at the center of a cold filament. Filament dynamics in the presence of a mixed layer are not adequately described by the classical thermal wind balance. The effect of vertical mixing of momentum due to turbulence in the surface layer is of the same order of magnitude as the pressure gradient and Coriolis force and contributes equally to a so-called turbulent thermal wind balance. Filamentogenesis is disrupted by vigorous submesoscale instabilities. The cause of the instability is the lateral shear as energy production by the horizontal Reynolds stress is the primary fluctuation source during the process; this contrasts with the usual baroclinic instability of submesoscale surface fronts. The filaments are lines of strong oceanic surface convergence as illustrated by the release of Lagrangian parcels in the Gulf Stream. Diabatic mixing is strong as parcels move across the filaments and downwell into the pycnocline. The life cycle of a filament is typically a few days in duration, from intensification to quasi stationarity to instability to dissipation.
Abstract
A set of realistic, very high-resolution simulations is made for the Gulf Stream region using the oceanic model Regional Oceanic Modeling System (ROMS) to study the life cycle of the intense submesoscale cold filaments that form on the subtropical gyre, interior wall of the Gulf Stream. The surface buoyancy gradients and ageostrophic secondary circulations intensify in response to the mesoscale strain field as predicted by the theory of filamentogenesis. It can be understood in terms of a dual frontogenetic process, along the lines understood for a single front. There is, however, a stronger secondary circulation due to the amplification at the center of a cold filament. Filament dynamics in the presence of a mixed layer are not adequately described by the classical thermal wind balance. The effect of vertical mixing of momentum due to turbulence in the surface layer is of the same order of magnitude as the pressure gradient and Coriolis force and contributes equally to a so-called turbulent thermal wind balance. Filamentogenesis is disrupted by vigorous submesoscale instabilities. The cause of the instability is the lateral shear as energy production by the horizontal Reynolds stress is the primary fluctuation source during the process; this contrasts with the usual baroclinic instability of submesoscale surface fronts. The filaments are lines of strong oceanic surface convergence as illustrated by the release of Lagrangian parcels in the Gulf Stream. Diabatic mixing is strong as parcels move across the filaments and downwell into the pycnocline. The life cycle of a filament is typically a few days in duration, from intensification to quasi stationarity to instability to dissipation.
Abstract
The interactions between boundary layer turbulence, including Langmuir turbulence, and submesoscale processes in the oceanic mixed layer are described using large-eddy simulations of the spindown of a temperature front in the presence of submesoscale eddies, winds, and waves. The simulations solve the surface-wave-averaged Boussinesq equations with Stokes drift wave forcing at a resolution that is sufficiently fine to capture small-scale Langmuir turbulence. A simulation without Stokes drift forcing is also performed for comparison. Spatial and spectral properties of temperature, velocity, and vorticity fields are described, and these fields are scale decomposed in order to examine multiscale fluxes of momentum and buoyancy. Buoyancy flux results indicate that Langmuir turbulence counters the restratifying effects of submesoscale eddies, leading to small-scale vertical transport and mixing that is 4 times greater than in the simulations without Stokes drift forcing. The observed fluxes are also shown to be in good agreement with results from an asymptotic analysis of the surface-wave-averaged, or Craik–Leibovich, equations. Regions of potential instability in the flow are identified using Richardson and Rossby numbers, and it is found that mixed gravitational/symmetric instabilities are nearly twice as prevalent when Langmuir turbulence is present, in contrast to simulations without Stokes drift forcing, which are dominated by symmetric instabilities. Mixed layer depth calculations based on potential vorticity and temperature show that the mixed layer is up to 2 times deeper in the presence of Langmuir turbulence. Differences between measures of the mixed layer depth based on potential vorticity and temperature are smaller in the simulations with Stokes drift forcing, indicating a reduced incidence of symmetric instabilities in the presence of Langmuir turbulence.
Abstract
The interactions between boundary layer turbulence, including Langmuir turbulence, and submesoscale processes in the oceanic mixed layer are described using large-eddy simulations of the spindown of a temperature front in the presence of submesoscale eddies, winds, and waves. The simulations solve the surface-wave-averaged Boussinesq equations with Stokes drift wave forcing at a resolution that is sufficiently fine to capture small-scale Langmuir turbulence. A simulation without Stokes drift forcing is also performed for comparison. Spatial and spectral properties of temperature, velocity, and vorticity fields are described, and these fields are scale decomposed in order to examine multiscale fluxes of momentum and buoyancy. Buoyancy flux results indicate that Langmuir turbulence counters the restratifying effects of submesoscale eddies, leading to small-scale vertical transport and mixing that is 4 times greater than in the simulations without Stokes drift forcing. The observed fluxes are also shown to be in good agreement with results from an asymptotic analysis of the surface-wave-averaged, or Craik–Leibovich, equations. Regions of potential instability in the flow are identified using Richardson and Rossby numbers, and it is found that mixed gravitational/symmetric instabilities are nearly twice as prevalent when Langmuir turbulence is present, in contrast to simulations without Stokes drift forcing, which are dominated by symmetric instabilities. Mixed layer depth calculations based on potential vorticity and temperature show that the mixed layer is up to 2 times deeper in the presence of Langmuir turbulence. Differences between measures of the mixed layer depth based on potential vorticity and temperature are smaller in the simulations with Stokes drift forcing, indicating a reduced incidence of symmetric instabilities in the presence of Langmuir turbulence.
Abstract
A laboratory experiment of multiple baroclinic zonal jets is described, thought to be dynamically similar to flow observed in the Antarctic Circumpolar Current. Differential heating sets the overall temperature difference and drives unstable baroclinic flow, but the circulation is free to determine its own structure and local stratification; experiments were run to a stationary state and extend the dynamical regime of previous experiments. A topographic analog to the planetary β effect is imposed by the gradient of fluid depth with radius supplied by a sloping bottom and a parabolic free surface. New regimes of a low thermal Rossby number (RoT ~ 10−3) and high Taylor number (Ta ~ 1011) are explored such that the deformation radius Lρ is much smaller than the annulus gap width L and similar to the Rhines length. Multiple jets emerge in rough proportion to the smallness of the Rhines scale, relatively insensitive to the Taylor number; a regime diagram taking the β effect into account better reflects the emergence of the jets. Eddy momentum fluxes are consistent with an active role in maintaining the jets, and jet development appears to follow the Vallis and Maltrud phenomenology of anisotropic wave–turbulence interaction on a β plane. Intermittency and episodes of coherent meridional jet migration occur, especially during spinup.
Abstract
A laboratory experiment of multiple baroclinic zonal jets is described, thought to be dynamically similar to flow observed in the Antarctic Circumpolar Current. Differential heating sets the overall temperature difference and drives unstable baroclinic flow, but the circulation is free to determine its own structure and local stratification; experiments were run to a stationary state and extend the dynamical regime of previous experiments. A topographic analog to the planetary β effect is imposed by the gradient of fluid depth with radius supplied by a sloping bottom and a parabolic free surface. New regimes of a low thermal Rossby number (RoT ~ 10−3) and high Taylor number (Ta ~ 1011) are explored such that the deformation radius Lρ is much smaller than the annulus gap width L and similar to the Rhines length. Multiple jets emerge in rough proportion to the smallness of the Rhines scale, relatively insensitive to the Taylor number; a regime diagram taking the β effect into account better reflects the emergence of the jets. Eddy momentum fluxes are consistent with an active role in maintaining the jets, and jet development appears to follow the Vallis and Maltrud phenomenology of anisotropic wave–turbulence interaction on a β plane. Intermittency and episodes of coherent meridional jet migration occur, especially during spinup.
Abstract
The processes that determine the depth of the Southern Ocean thermocline are considered. In existing conceptual frameworks, the thermocline depth is determined by competition between the mean and eddy heat transport, with a contribution from the interaction with the stratification in the enclosed portion of the ocean. Using numerical simulations, this study examines the equilibration of an idealized circumpolar current with and without topography. The authors find that eddies are much more efficient when topography is present, leading to a shallower thermocline than in the flat case. A simple quasigeostrophic analytical model shows that the topographically induced standing wave increases the effective eddy diffusivity by increasing the local buoyancy gradients and lengthening the buoyancy contours across which the eddies transport heat. In addition to this local heat flux intensification, transient eddy heat fluxes are suppressed away from the topography, especially upstream, indicating that localized topography leads to local (absolute) baroclinic instability and its subsequent finite-amplitude equilibration, which extracts available potential energy very efficiently from the time-mean flow.
Abstract
The processes that determine the depth of the Southern Ocean thermocline are considered. In existing conceptual frameworks, the thermocline depth is determined by competition between the mean and eddy heat transport, with a contribution from the interaction with the stratification in the enclosed portion of the ocean. Using numerical simulations, this study examines the equilibration of an idealized circumpolar current with and without topography. The authors find that eddies are much more efficient when topography is present, leading to a shallower thermocline than in the flat case. A simple quasigeostrophic analytical model shows that the topographically induced standing wave increases the effective eddy diffusivity by increasing the local buoyancy gradients and lengthening the buoyancy contours across which the eddies transport heat. In addition to this local heat flux intensification, transient eddy heat fluxes are suppressed away from the topography, especially upstream, indicating that localized topography leads to local (absolute) baroclinic instability and its subsequent finite-amplitude equilibration, which extracts available potential energy very efficiently from the time-mean flow.
Abstract
Submesoscale (1–200 km) wavenumber spectra of kinetic and potential energy and tracer variance are obtained from in situ observations in the Gulf Stream region and in the eastern subtropical North Pacific. In the Gulf Stream region, steep kinetic energy spectra at scales between 200 and 20 km are consistent with predictions of interior quasigeostrophic–turbulence theory, both in the mixed layer and in the thermocline. At scales below 20 km, the spectra flatten out, consistent with a growing contribution of internal-wave energy at small scales. In the subtropical North Pacific, the energy spectra are flatter and inconsistent with predictions of interior quasigeostrophic–turbulence theory. The observed spectra and their dependence on depth are also inconsistent with predictions of surface quasigeostrophic–turbulence theory for the observed ocean stratification. It appears that unbalanced motions, most likely internal tides at large scales and the internal-wave continuum at small scales, dominate the energy spectrum throughout the submesoscale range. Spectra of temperature variance along density surfaces, which are not affected by internal tides, are also inconsistent with predictions of geostrophic-turbulence theories. Reasons for this inconsistency could be the injection of energy in the submesoscale range by small-scale baroclinic instabilities or modifications of the spectra by coupling between surface and interior dynamics or by ageostrophic frontal effects.
Abstract
Submesoscale (1–200 km) wavenumber spectra of kinetic and potential energy and tracer variance are obtained from in situ observations in the Gulf Stream region and in the eastern subtropical North Pacific. In the Gulf Stream region, steep kinetic energy spectra at scales between 200 and 20 km are consistent with predictions of interior quasigeostrophic–turbulence theory, both in the mixed layer and in the thermocline. At scales below 20 km, the spectra flatten out, consistent with a growing contribution of internal-wave energy at small scales. In the subtropical North Pacific, the energy spectra are flatter and inconsistent with predictions of interior quasigeostrophic–turbulence theory. The observed spectra and their dependence on depth are also inconsistent with predictions of surface quasigeostrophic–turbulence theory for the observed ocean stratification. It appears that unbalanced motions, most likely internal tides at large scales and the internal-wave continuum at small scales, dominate the energy spectrum throughout the submesoscale range. Spectra of temperature variance along density surfaces, which are not affected by internal tides, are also inconsistent with predictions of geostrophic-turbulence theories. Reasons for this inconsistency could be the injection of energy in the submesoscale range by small-scale baroclinic instabilities or modifications of the spectra by coupling between surface and interior dynamics or by ageostrophic frontal effects.
Abstract
An idealized eddy-resolving numerical model and an analytic three-layer model are used to develop ideas about what controls the circulation of Atlantic Water in the Arctic Ocean. The numerical model is forced with a surface heat flux, uniform winds, and a source of low-salinity water near the surface around the perimeter of an Arctic basin. Despite this idealized configuration, the model is able to reproduce many general aspects of the Arctic Ocean circulation and hydrography, including exchange through Fram Strait, circulation of Atlantic Water, a halocline, ice cover and transport, surface heat flux, and a Beaufort Gyre. The analytic model depends on a nondimensional number, and provides theoretical estimates of the halocline depth, stratification, freshwater content, and baroclinic shear in the boundary current. An empirical relationship between freshwater content and sea surface height allows for a prediction of the transport of Atlantic Water in the cyclonic boundary current. Parameters typical of the Arctic Ocean produce a cyclonic boundary current of Atlantic Water of O(1 − 2 Sv; where 1 Sv ≡ 106 m3 s−1) and a halocline depth of O(200 m), in reasonable agreement with observations. The theory compares well with a series of numerical model calculations in which mixing and environmental parameters are varied, thus lending credibility to the dynamics of the analytic model. In these models, lateral eddy fluxes from the boundary and vertical diffusion in the interior are important drivers of the halocline and the circulation of Atlantic Water in the Arctic Ocean.
Abstract
An idealized eddy-resolving numerical model and an analytic three-layer model are used to develop ideas about what controls the circulation of Atlantic Water in the Arctic Ocean. The numerical model is forced with a surface heat flux, uniform winds, and a source of low-salinity water near the surface around the perimeter of an Arctic basin. Despite this idealized configuration, the model is able to reproduce many general aspects of the Arctic Ocean circulation and hydrography, including exchange through Fram Strait, circulation of Atlantic Water, a halocline, ice cover and transport, surface heat flux, and a Beaufort Gyre. The analytic model depends on a nondimensional number, and provides theoretical estimates of the halocline depth, stratification, freshwater content, and baroclinic shear in the boundary current. An empirical relationship between freshwater content and sea surface height allows for a prediction of the transport of Atlantic Water in the cyclonic boundary current. Parameters typical of the Arctic Ocean produce a cyclonic boundary current of Atlantic Water of O(1 − 2 Sv; where 1 Sv ≡ 106 m3 s−1) and a halocline depth of O(200 m), in reasonable agreement with observations. The theory compares well with a series of numerical model calculations in which mixing and environmental parameters are varied, thus lending credibility to the dynamics of the analytic model. In these models, lateral eddy fluxes from the boundary and vertical diffusion in the interior are important drivers of the halocline and the circulation of Atlantic Water in the Arctic Ocean.
