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- Author or Editor: Sonya Legg x
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Abstract
Recent measurements in a region of continental slope characterized by ridges and valleys running up and down the slope reveal interesting high mode structure in the tidal band velocity signals, with enhanced mixing above the corrugations. In order to understand these observations, numerical simulations of the internal tide generation in this region of topography were performed. Here the focus is on the response of the flow to along;chslope barotropic tidal forcing. For small-amplitude barotropic forcing, internal waves are generated over the continental slope that propagate toward the ocean surface and toward shallower water. When higher-amplitude forcing is combined with large-amplitude corrugations, the flow is locally supercritical downstream of ridges, and transient internal hydraulic jumps result. As the flow relaxes each half tidal period, these jumps are released as internal wave packets, which propagate up into the thermocline. The internal hydraulic jumps are a source of mixing in the valleys, while the small-scale shears associated with the internal waves could lead to mixing higher up the water column. Over the forcing range considered, the response is dominated by slightly higher harmonics of the tidal forcing frequency than predicted by existing analytic theories.
Abstract
Recent measurements in a region of continental slope characterized by ridges and valleys running up and down the slope reveal interesting high mode structure in the tidal band velocity signals, with enhanced mixing above the corrugations. In order to understand these observations, numerical simulations of the internal tide generation in this region of topography were performed. Here the focus is on the response of the flow to along;chslope barotropic tidal forcing. For small-amplitude barotropic forcing, internal waves are generated over the continental slope that propagate toward the ocean surface and toward shallower water. When higher-amplitude forcing is combined with large-amplitude corrugations, the flow is locally supercritical downstream of ridges, and transient internal hydraulic jumps result. As the flow relaxes each half tidal period, these jumps are released as internal wave packets, which propagate up into the thermocline. The internal hydraulic jumps are a source of mixing in the valleys, while the small-scale shears associated with the internal waves could lead to mixing higher up the water column. Over the forcing range considered, the response is dominated by slightly higher harmonics of the tidal forcing frequency than predicted by existing analytic theories.
Abstract
Recent measurements in a region of continental slope characterized by ridges and valleys running up and down the slope reveal interesting high-mode structure in the tidal band velocity signals and enhanced mixing over the corrugations. To deduce the processes responsible for the observed phenomena, numerical simulations of the internal tide generation in this region of topography were performed, focused on the response of the flow to cross-slope barotropic tidal forcing. The flow response is characterized by an internal tide generated at the shelf break that subsequently reflects from the corrugated slope. Above the corrugated slope, a high-mode structure may be created, but only if the Coriolis force is included. It is proposed that interference between the primary internal tide and secondary internal waves forced by the Coriolis-driven along-slope component of primary wave flow field is the cause of the high-mode structure in the simulations. Under suitable conditions of forcing, topography, and stratification, the shear generated by the interference may lead to local mixing. Hence complex topography may be an important contributor to boundary mixing in the ocean.
Abstract
Recent measurements in a region of continental slope characterized by ridges and valleys running up and down the slope reveal interesting high-mode structure in the tidal band velocity signals and enhanced mixing over the corrugations. To deduce the processes responsible for the observed phenomena, numerical simulations of the internal tide generation in this region of topography were performed, focused on the response of the flow to cross-slope barotropic tidal forcing. The flow response is characterized by an internal tide generated at the shelf break that subsequently reflects from the corrugated slope. Above the corrugated slope, a high-mode structure may be created, but only if the Coriolis force is included. It is proposed that interference between the primary internal tide and secondary internal waves forced by the Coriolis-driven along-slope component of primary wave flow field is the cause of the high-mode structure in the simulations. Under suitable conditions of forcing, topography, and stratification, the shear generated by the interference may lead to local mixing. Hence complex topography may be an important contributor to boundary mixing in the ocean.
Abstract
A recent numerical study by Noh et al. of open-ocean deep convection in the presence of a single geostrophic eddy showed that two possible regimes exist: 1) the localized convection regime in which baroclinic instability of the eddy dominates, with slantwise fluxes and restratification, and 2) the distributed convection regime in which vertical mixing dominates. Noh et al. found that localized convection dominates for relatively small buoyancy forcing, strong eddies, and strong surface ambient stratification. Here it is shown that this regime transition can be expressed in terms of a ratio of time scales: the localized convection regime appears when the time scale for lateral fluxes from eddy interior to exterior t
L
is short in comparison with the time scale for convective erosion of the exterior stratification t
c
. Scaling arguments give this ratio of time scales as t
L
/t
c
∼ f β
2
R
2
B/(A
2
γ) where f is the Coriolis parameter, R is the radius of the eddy, B is the buoyancy forcing, 1/β is the depth scale of the exponentially decaying surface-intensified stratification, γ is the relative amplitude of the eddy, and Aβ is the value of the surface stratification
Abstract
A recent numerical study by Noh et al. of open-ocean deep convection in the presence of a single geostrophic eddy showed that two possible regimes exist: 1) the localized convection regime in which baroclinic instability of the eddy dominates, with slantwise fluxes and restratification, and 2) the distributed convection regime in which vertical mixing dominates. Noh et al. found that localized convection dominates for relatively small buoyancy forcing, strong eddies, and strong surface ambient stratification. Here it is shown that this regime transition can be expressed in terms of a ratio of time scales: the localized convection regime appears when the time scale for lateral fluxes from eddy interior to exterior t
L
is short in comparison with the time scale for convective erosion of the exterior stratification t
c
. Scaling arguments give this ratio of time scales as t
L
/t
c
∼ f β
2
R
2
B/(A
2
γ) where f is the Coriolis parameter, R is the radius of the eddy, B is the buoyancy forcing, 1/β is the depth scale of the exponentially decaying surface-intensified stratification, γ is the relative amplitude of the eddy, and Aβ is the value of the surface stratification
Abstract
A series of two-dimensional numerical simulations examine the breaking of first-mode internal waves at isolated ridges, independently varying the relative height of the topography compared to the depth of the ocean h 0/H 0; the relative steepness of the topographic slope compared to the slope of the internal wave group velocity γ; and the Froude number of the incoming internal wave Fr0. The fraction of the incoming wave energy, which is reflected back toward deep water, transmitted beyond the ridge, and lost to dissipation and mixing, is diagnosed from the simulations. For critical slopes, with γ = 1, the fraction of incoming energy lost at the slope scales approximately like h 0/H 0, independent of the incoming wave Froude number. For subcritical slopes, with γ < 1, waves break and lose a substantial proportion of their energy if the maximum Froude number, estimated as Frmax = Fr0/(1 − h 0/H 0)2, exceeds a critical value, found empirically to be about 0.3. The dissipation at subcritical slopes therefore increases as both incoming wave Froude number and topographic height increase. At critical slopes, the dissipation is enhanced along the slope facing the incoming wave. In contrast, at subcritical slopes, dissipation is small until the wave amplitude is sufficiently enhanced by the shoaling topography to exceed the critical Froude number; then large dissipation extends all the way to the surface. The results are shown to generalize to variable stratification and different topographies, including axisymmetric seamounts. The regimes for low-mode internal wave breaking at isolated critical and subcritical topography identified by these simulations provide guidance for the parameterization of the mixing due to radiated internal tides.
Abstract
A series of two-dimensional numerical simulations examine the breaking of first-mode internal waves at isolated ridges, independently varying the relative height of the topography compared to the depth of the ocean h 0/H 0; the relative steepness of the topographic slope compared to the slope of the internal wave group velocity γ; and the Froude number of the incoming internal wave Fr0. The fraction of the incoming wave energy, which is reflected back toward deep water, transmitted beyond the ridge, and lost to dissipation and mixing, is diagnosed from the simulations. For critical slopes, with γ = 1, the fraction of incoming energy lost at the slope scales approximately like h 0/H 0, independent of the incoming wave Froude number. For subcritical slopes, with γ < 1, waves break and lose a substantial proportion of their energy if the maximum Froude number, estimated as Frmax = Fr0/(1 − h 0/H 0)2, exceeds a critical value, found empirically to be about 0.3. The dissipation at subcritical slopes therefore increases as both incoming wave Froude number and topographic height increase. At critical slopes, the dissipation is enhanced along the slope facing the incoming wave. In contrast, at subcritical slopes, dissipation is small until the wave amplitude is sufficiently enhanced by the shoaling topography to exceed the critical Froude number; then large dissipation extends all the way to the surface. The results are shown to generalize to variable stratification and different topographies, including axisymmetric seamounts. The regimes for low-mode internal wave breaking at isolated critical and subcritical topography identified by these simulations provide guidance for the parameterization of the mixing due to radiated internal tides.
Abstract
A point-vortex heton model of the lateral dispersion of cold water formed in open-ocean deep convection is developed and studied as an idealized representation of the sinking and spreading phase of open-ocean deep convection. The overturning and geostrophic adjustment of dense fluid on and below the radius of deformation scale, formed by cooling on the large-scale, are parameterized in the model by introducing paired. discrete point vortices (hetons) of cyclonic sense in the surface layer, anticyclonic below, driving a cold baroclinic vortex. The convection site is imagined to be made up of many such baroclinic vortices, each with a vertically homogeneous core carrying cold, convectively tainted waters. The point vortices are introduced at a rate that depends on the large-scale cooling and the intensity assumed for each vortex. The interaction of many cold baroclinic vortices, making up a cloud, is studied using point-vortex Green's function techniques. The current solenoids of the individual elements sum together to drive a large-scale rim current around the convection site, cyclonic above, anticyclonic below, which is associated with a baroclinic zone on a scale of the order of the ambient radius of deformation. For parameters typical of open-ocean deep convection, the cloud of point vortices breaks down baroclinically on a time scale of a few days, into Rossby radius-scale “clumps.” These extended hetons efficiently flux the cold water away laterally from the convection site and affect an inward transfer of heat sufficient to offset loss to the atmosphere.
Abstract
A point-vortex heton model of the lateral dispersion of cold water formed in open-ocean deep convection is developed and studied as an idealized representation of the sinking and spreading phase of open-ocean deep convection. The overturning and geostrophic adjustment of dense fluid on and below the radius of deformation scale, formed by cooling on the large-scale, are parameterized in the model by introducing paired. discrete point vortices (hetons) of cyclonic sense in the surface layer, anticyclonic below, driving a cold baroclinic vortex. The convection site is imagined to be made up of many such baroclinic vortices, each with a vertically homogeneous core carrying cold, convectively tainted waters. The point vortices are introduced at a rate that depends on the large-scale cooling and the intensity assumed for each vortex. The interaction of many cold baroclinic vortices, making up a cloud, is studied using point-vortex Green's function techniques. The current solenoids of the individual elements sum together to drive a large-scale rim current around the convection site, cyclonic above, anticyclonic below, which is associated with a baroclinic zone on a scale of the order of the ambient radius of deformation. For parameters typical of open-ocean deep convection, the cloud of point vortices breaks down baroclinically on a time scale of a few days, into Rossby radius-scale “clumps.” These extended hetons efficiently flux the cold water away laterally from the convection site and affect an inward transfer of heat sufficient to offset loss to the atmosphere.
Abstract
Internal wave reflection from a sloping topographic boundary may lead to enhanced shear if the topographic angle to the horizontal is close to that of the internal wave group velocity vector. Previous analytic studies have suggested that shear enhancement is reduced at concave slopes as compared with convex and planar slopes near the critical angle. Here the internal wave reflection from concave and convex slopes that pass through the critical angle is investigated numerically using the nonhydrostatic Massachusetts Institute of Technology General Circulation Model (MITgcm). Overturning, shear instability, and resultant mixing are examined. Results are compared with simulations of wave reflection from planar slopes with angles greater than, less than, and equal to the critical angle. In contrast to the analytic predictions, no reduction in mixing is found for the concave slope as compared with the other slopes. In all cases, stratification is eroded in a band above the slope, bounded at its outer edge by the internal wave characteristic. The difference between numerical and analytic results is caused by the nonlinearity of the numerical calculations, where the finite-amplitude flow leads to generation of upslope-propagating bores for a wide range of topographic slopes around the critical angle.
Abstract
Internal wave reflection from a sloping topographic boundary may lead to enhanced shear if the topographic angle to the horizontal is close to that of the internal wave group velocity vector. Previous analytic studies have suggested that shear enhancement is reduced at concave slopes as compared with convex and planar slopes near the critical angle. Here the internal wave reflection from concave and convex slopes that pass through the critical angle is investigated numerically using the nonhydrostatic Massachusetts Institute of Technology General Circulation Model (MITgcm). Overturning, shear instability, and resultant mixing are examined. Results are compared with simulations of wave reflection from planar slopes with angles greater than, less than, and equal to the critical angle. In contrast to the analytic predictions, no reduction in mixing is found for the concave slope as compared with the other slopes. In all cases, stratification is eroded in a band above the slope, bounded at its outer edge by the internal wave characteristic. The difference between numerical and analytic results is caused by the nonlinearity of the numerical calculations, where the finite-amplitude flow leads to generation of upslope-propagating bores for a wide range of topographic slopes around the critical angle.
Abstract
The dissipation of low-mode internal tides as they propagate through mesoscale baroclinic eddies is examined using a series of numerical simulations, complemented by three-dimensional ray tracing calculations. The incident mode-1 internal tide is refracted into convergent energy beams, resulting in a zone of reduced energy flux in the lee of the eddy. The dissipation of internal tides is significantly enhanced in the upper water column within strongly baroclinic (anticyclonic) eddies, exhibiting a spatially asymmetric pattern, due to trapped high-mode internal tides. Where the eddy velocity opposes the internal tide propagation velocity, high-mode waves can be trapped within the eddy, whereas high modes can freely propagate away from regions where eddy and internal wave velocities are in the same direction. The trapped high modes with large vertical shear are then dissipated, with the asymmetric distribution of trapping leading to the asymmetric distribution of dissipation. Three-dimensional ray tracing solutions further illustrate the importance of the baroclinic current for wave trapping. Similar enhancement of dissipation is also found for a baroclinic cyclonic eddy. However, a barotropic eddy is incapable of facilitating robust high modes and thus cannot generate significant dissipation of internal tides, despite its strong velocities. Both energy transfer from low to high modes in the baroclinic eddy structure and trapping of those high modes by the eddy velocity field are therefore necessary to produce internal wave dissipation, a conclusion confirmed by examining the sensitivity of the internal tide dissipation to eddy radius, vorticity, and vertical scale.
Significance Statement
The oceanic tides drive underwater waves at the tidal frequency known as internal tides. When these waves break, or dissipate, they can lead to mixing of oceanic heat and salt which impacts the ocean circulation and climate. Accurate climate predictions require computer models that correctly represent the distribution of this mixing. Here we explore how an oceanic eddy, a swirling vortex of order 100–400 km across, can locally enhance the dissipation of oceanic internal tides. We find that strong ocean eddies can be hotspots for internal tide dissipation, for both clockwise and anticlockwise rotating vortices, and surface-enhanced eddies are most effective at internal tide dissipation. These results can improve climate model representations of tidally driven mixing, leading to more credible future predictions.
Abstract
The dissipation of low-mode internal tides as they propagate through mesoscale baroclinic eddies is examined using a series of numerical simulations, complemented by three-dimensional ray tracing calculations. The incident mode-1 internal tide is refracted into convergent energy beams, resulting in a zone of reduced energy flux in the lee of the eddy. The dissipation of internal tides is significantly enhanced in the upper water column within strongly baroclinic (anticyclonic) eddies, exhibiting a spatially asymmetric pattern, due to trapped high-mode internal tides. Where the eddy velocity opposes the internal tide propagation velocity, high-mode waves can be trapped within the eddy, whereas high modes can freely propagate away from regions where eddy and internal wave velocities are in the same direction. The trapped high modes with large vertical shear are then dissipated, with the asymmetric distribution of trapping leading to the asymmetric distribution of dissipation. Three-dimensional ray tracing solutions further illustrate the importance of the baroclinic current for wave trapping. Similar enhancement of dissipation is also found for a baroclinic cyclonic eddy. However, a barotropic eddy is incapable of facilitating robust high modes and thus cannot generate significant dissipation of internal tides, despite its strong velocities. Both energy transfer from low to high modes in the baroclinic eddy structure and trapping of those high modes by the eddy velocity field are therefore necessary to produce internal wave dissipation, a conclusion confirmed by examining the sensitivity of the internal tide dissipation to eddy radius, vorticity, and vertical scale.
Significance Statement
The oceanic tides drive underwater waves at the tidal frequency known as internal tides. When these waves break, or dissipate, they can lead to mixing of oceanic heat and salt which impacts the ocean circulation and climate. Accurate climate predictions require computer models that correctly represent the distribution of this mixing. Here we explore how an oceanic eddy, a swirling vortex of order 100–400 km across, can locally enhance the dissipation of oceanic internal tides. We find that strong ocean eddies can be hotspots for internal tide dissipation, for both clockwise and anticlockwise rotating vortices, and surface-enhanced eddies are most effective at internal tide dissipation. These results can improve climate model representations of tidally driven mixing, leading to more credible future predictions.
Abstract
In this study, we revisit the problem of rotating dense overflow dynamics by performing nonhydrostatic numerical simulations, resolving submesoscale variability. Thermohaline stratification and buoyancy forcing are based on data from the Eurasian basin of the Arctic Ocean, where overflows are particularly crucial to the exchange of dense water between shelves and deep basins, yet have been studied relatively little. A nonlinear equation of state is used, allowing proper representation of thermohaline structure and mixing. We examine three increasingly complex scenarios: nonrotating 2D, rotating 2D, and rotating 3D. The nonrotating 2D case behaves according to known theory: the gravity current descends alongslope until reaching a relatively shallow neutral buoyancy level. However, in the rotating cases, we have identified novel dynamics: in both 2D and 3D, the submesoscale range is dominated by symmetric instability (SI). Rotation leads to geostrophic adjustment, causing dense water to be confined within the forcing region longer and attain a greater density anomaly. In the 2D case, Ekman drainage leads to descent of the geostrophic jet, forming a highly dense alongslope front. Beams of negative Ertel potential vorticity develop parallel to the slope, initiating SI and vigorous mixing in the overflow. In 3D, baroclinic eddies are responsible for cross-isobath dense water transport, but SI again develops along the slope and at eddy edges. Remarkably, through two different dynamics, the 2D SI-dominated case and 3D eddy-dominated case attain roughly the same final water mass distribution, highlighting the potential role of SI in driving mixing within certain regimes of dense overflows.
Abstract
In this study, we revisit the problem of rotating dense overflow dynamics by performing nonhydrostatic numerical simulations, resolving submesoscale variability. Thermohaline stratification and buoyancy forcing are based on data from the Eurasian basin of the Arctic Ocean, where overflows are particularly crucial to the exchange of dense water between shelves and deep basins, yet have been studied relatively little. A nonlinear equation of state is used, allowing proper representation of thermohaline structure and mixing. We examine three increasingly complex scenarios: nonrotating 2D, rotating 2D, and rotating 3D. The nonrotating 2D case behaves according to known theory: the gravity current descends alongslope until reaching a relatively shallow neutral buoyancy level. However, in the rotating cases, we have identified novel dynamics: in both 2D and 3D, the submesoscale range is dominated by symmetric instability (SI). Rotation leads to geostrophic adjustment, causing dense water to be confined within the forcing region longer and attain a greater density anomaly. In the 2D case, Ekman drainage leads to descent of the geostrophic jet, forming a highly dense alongslope front. Beams of negative Ertel potential vorticity develop parallel to the slope, initiating SI and vigorous mixing in the overflow. In 3D, baroclinic eddies are responsible for cross-isobath dense water transport, but SI again develops along the slope and at eddy edges. Remarkably, through two different dynamics, the 2D SI-dominated case and 3D eddy-dominated case attain roughly the same final water mass distribution, highlighting the potential role of SI in driving mixing within certain regimes of dense overflows.
Abstract
Recent observations from the Hawaiian Ridge indicate episodes of overturning and strong dissipation coupled with the tidal cycle near the top of the ridge. Simulations with realistic topography and stratification suggest that this overturning has its origins in transient internal hydraulic jumps that occur below the shelf break at maximum ebb tide, and then propagate up the slope as internal bores when the flow reverses. A series of numerical simulations explores the parameter space of topographic slope, barotropic velocity, stratification, and forcing frequency to identify the parameter regime in which these internal jumps are possible. Theoretical analysis predicts that the tidally driven jumps may occur when the vertical tidal excursion is large, which is shown to imply steep topographic slopes, such that dh/dxN/ω > 1. The vertical length scale of the jumps is predicted to depend on the flow speed such that the jump Froude number is of order unity. The numerical results agree with the theoretical predictions, with finite-amplitude internal hydraulic jumps and overturning forming during strong offslope tidal flow over steep slopes. These results suggest that internal hydraulic jumps may be an important mechanism for local tidally generated mixing at tall steep topography.
Abstract
Recent observations from the Hawaiian Ridge indicate episodes of overturning and strong dissipation coupled with the tidal cycle near the top of the ridge. Simulations with realistic topography and stratification suggest that this overturning has its origins in transient internal hydraulic jumps that occur below the shelf break at maximum ebb tide, and then propagate up the slope as internal bores when the flow reverses. A series of numerical simulations explores the parameter space of topographic slope, barotropic velocity, stratification, and forcing frequency to identify the parameter regime in which these internal jumps are possible. Theoretical analysis predicts that the tidally driven jumps may occur when the vertical tidal excursion is large, which is shown to imply steep topographic slopes, such that dh/dxN/ω > 1. The vertical length scale of the jumps is predicted to depend on the flow speed such that the jump Froude number is of order unity. The numerical results agree with the theoretical predictions, with finite-amplitude internal hydraulic jumps and overturning forming during strong offslope tidal flow over steep slopes. These results suggest that internal hydraulic jumps may be an important mechanism for local tidally generated mixing at tall steep topography.
Abstract
Fine- and micro-structure observations indicate that turbulent mixing is enhanced within O(1) km above rough topography. Enhanced mixing is associated with internal wave breaking and, in many regions of the ocean, has been linked to the breaking and dissipation of internal tides. The generation and dissipation of internal tides are explored in this study using a high-resolution two-dimensional nonhydrostatic numerical model, which explicitly resolves the instabilities leading to wave breaking, configured in an idealized domain with a realistic multiscale topography and flow characteristics. The control simulation, chosen to represent the Brazil Basin region, produces a vertical profile of energy dissipation and temporal characteristics of finescale motions that are consistent with observations. Results suggest that a significant fraction of mixing in the bottom O(1) km of the ocean is sustained by the transfer of energy from the large-scale internal tides to smaller-scale internal waves by nonlinear wave–wave interactions. The time scale of the energy transfer to the smaller scales is estimated to be on the order of a few days. A suite of sensitivity experiments is carried out to examine the dependence of the energy transfer time scale and energy dissipation on topographic roughness, tidal amplitude, and Coriolis frequency parameters. Implications for tidal mixing parameterizations are discussed.
Abstract
Fine- and micro-structure observations indicate that turbulent mixing is enhanced within O(1) km above rough topography. Enhanced mixing is associated with internal wave breaking and, in many regions of the ocean, has been linked to the breaking and dissipation of internal tides. The generation and dissipation of internal tides are explored in this study using a high-resolution two-dimensional nonhydrostatic numerical model, which explicitly resolves the instabilities leading to wave breaking, configured in an idealized domain with a realistic multiscale topography and flow characteristics. The control simulation, chosen to represent the Brazil Basin region, produces a vertical profile of energy dissipation and temporal characteristics of finescale motions that are consistent with observations. Results suggest that a significant fraction of mixing in the bottom O(1) km of the ocean is sustained by the transfer of energy from the large-scale internal tides to smaller-scale internal waves by nonlinear wave–wave interactions. The time scale of the energy transfer to the smaller scales is estimated to be on the order of a few days. A suite of sensitivity experiments is carried out to examine the dependence of the energy transfer time scale and energy dissipation on topographic roughness, tidal amplitude, and Coriolis frequency parameters. Implications for tidal mixing parameterizations are discussed.
