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Abstract
The high-resolution mooring observations reported here reveal a cascade process from internal solitary waves (ISWs) to turbulent mixing via high-frequency internal waves near the maximum local buoyancy frequency (near-N waves) in the deep water of the northern South China Sea (SCS). Riding on the parent ISW, near-N waves with a peak frequency of 20 cph emerged at the trough of the ISW and extended to the rear face of the ISW. Most of the near-N waves occurred around the thermocline, where the isothermal displacements induced by the near-N waves were largest with an amplitude of 12 m. The energy of near-N waves was 5% of that of the parent ISW, and instability investigations showed that due to the strong shear, Ri in the region of strong near-N waves was less than 1/4, suggesting that the near-N waves were unstable and might dissipate rapidly. Simulations based on the Korteweg–de Vries (KdV)–Burgers equation reproduced the formation of observed near-N waves due to the energy cascade from ISWs. Our observational results demonstrate a new energy cascade route from ISWs to turbulence in the deep water, deepening the understanding of the energy dissipation process of ISWs and their roles in the enhanced mixing in the northern SCS.
Abstract
The high-resolution mooring observations reported here reveal a cascade process from internal solitary waves (ISWs) to turbulent mixing via high-frequency internal waves near the maximum local buoyancy frequency (near-N waves) in the deep water of the northern South China Sea (SCS). Riding on the parent ISW, near-N waves with a peak frequency of 20 cph emerged at the trough of the ISW and extended to the rear face of the ISW. Most of the near-N waves occurred around the thermocline, where the isothermal displacements induced by the near-N waves were largest with an amplitude of 12 m. The energy of near-N waves was 5% of that of the parent ISW, and instability investigations showed that due to the strong shear, Ri in the region of strong near-N waves was less than 1/4, suggesting that the near-N waves were unstable and might dissipate rapidly. Simulations based on the Korteweg–de Vries (KdV)–Burgers equation reproduced the formation of observed near-N waves due to the energy cascade from ISWs. Our observational results demonstrate a new energy cascade route from ISWs to turbulence in the deep water, deepening the understanding of the energy dissipation process of ISWs and their roles in the enhanced mixing in the northern SCS.
Abstract
An existing approximately neutral surface, the ω surface, minimizes the neutrality error and hence also exhibits very small fictitious dianeutral diffusivity Df
that arises when lateral diffusion is applied along the surface, in nonneutral directions. However, there is also a spurious dianeutral advection that arises when lateral advection is applied nonneutrally along the surface; equivalently, lateral advection applied along the neutral tangent planes creates a vertical velocity e
sp through the ω surface. Mathematically, e
sp = u ⋅ s, where u is the lateral velocity and s is the slope error of the surface. We find that e
sp produces a leading-order term in the evolution equations of temperature and salinity, being similar in magnitude to the influence of cabbeling and thermobaricity. We introduce a new method to form an approximately neutral surface, called an ω
u
·
s
surface, that minimizes e
sp by adjusting its depth so that the slope error is nearly perpendicular to the lateral velocity. The e
sp on a surface cannot be reduced to zero when closed streamlines contain nonzero neutral helicity. While e
sp on the ω
u
·
s
surface is over 100 times smaller than that on the ω surface, the fictitious dianeutral diffusivity on the ω
u
·
s
surface is larger, nearly equal to the canonical 10−5 m2 s−1 background diffusivity. Thus, we also develop a method to minimize a combination of e
sp and Df
, yielding the
Abstract
An existing approximately neutral surface, the ω surface, minimizes the neutrality error and hence also exhibits very small fictitious dianeutral diffusivity Df
that arises when lateral diffusion is applied along the surface, in nonneutral directions. However, there is also a spurious dianeutral advection that arises when lateral advection is applied nonneutrally along the surface; equivalently, lateral advection applied along the neutral tangent planes creates a vertical velocity e
sp through the ω surface. Mathematically, e
sp = u ⋅ s, where u is the lateral velocity and s is the slope error of the surface. We find that e
sp produces a leading-order term in the evolution equations of temperature and salinity, being similar in magnitude to the influence of cabbeling and thermobaricity. We introduce a new method to form an approximately neutral surface, called an ω
u
·
s
surface, that minimizes e
sp by adjusting its depth so that the slope error is nearly perpendicular to the lateral velocity. The e
sp on a surface cannot be reduced to zero when closed streamlines contain nonzero neutral helicity. While e
sp on the ω
u
·
s
surface is over 100 times smaller than that on the ω surface, the fictitious dianeutral diffusivity on the ω
u
·
s
surface is larger, nearly equal to the canonical 10−5 m2 s−1 background diffusivity. Thus, we also develop a method to minimize a combination of e
sp and Df
, yielding the
Abstract
Simplified descriptions of the ocean are useful both for formulating explanatory theories and for conveying meaningful global attributes. Here, using a 26-yr average of a global state estimate from ECCO, the basis for Munk’s “abyssal recipes” is evaluated on a global scale between 1000- and 3000-m depth. The two specific hydrographic stations he used prove untypical, with potential temperature and salinity more generally displaying different vertical scale heights, and thus differing in one-dimensional (in the vertical) values of mixing coefficients and/or vertical velocities. The simplest explanation is that the circulation is fully three-dimensional with temperature and salinity fields not describable with a one-dimensional steady balance. In contrast, the potential density and buoyancy are quantitatively describable through a one-dimensional exponential balance, and which calls for an explanation in terms of turbulent mixing processes.
Abstract
Simplified descriptions of the ocean are useful both for formulating explanatory theories and for conveying meaningful global attributes. Here, using a 26-yr average of a global state estimate from ECCO, the basis for Munk’s “abyssal recipes” is evaluated on a global scale between 1000- and 3000-m depth. The two specific hydrographic stations he used prove untypical, with potential temperature and salinity more generally displaying different vertical scale heights, and thus differing in one-dimensional (in the vertical) values of mixing coefficients and/or vertical velocities. The simplest explanation is that the circulation is fully three-dimensional with temperature and salinity fields not describable with a one-dimensional steady balance. In contrast, the potential density and buoyancy are quantitatively describable through a one-dimensional exponential balance, and which calls for an explanation in terms of turbulent mixing processes.
Abstract
Subinertial, topographically trapped diurnal internal tides are an important energy source for turbulent mixing in the subarctic oceans. However, their generation may not be estimated by the conventional barotropic-to-baroclinic conversion because their vertical structure is sometimes barotropic, unlike superinertial internal tides that are always baroclinic. Here, a new energy diagram is presented, in which the barotropic mode is decomposed into the surface and topographic modes, with the latter being classified as part of the internal modes together with the baroclinic mode. The energy equation for the newly defined topographic mode is then derived, providing an appropriate formulation of the energy conversion rate from the subinertial surface tides to the topographically trapped internal tides. A series of numerical experiments confirm that the formulation successfully predicts the energy conversion rate for various cases, with the relative contribution of the baroclinic and topographic modes varying significantly depending on the bottom topography and stratification. Furthermore, this surface-to-internal conversion is demonstrated to give a significantly larger estimate than the barotropic-to-baroclinic conversion for subinertial tides. Applying the formulation to the results of a realistic numerical simulation in the Kuril Straits, an area with the strongest mixing due to subinertial diurnal tides, shows that the surface mode is converted into the baroclinic and topographic modes with comparable magnitudes, responsible for most of the energy dissipation in this area. These results indicate the need to reestimate the global distribution of the generation rate of the subinertial internal tides using our new formulation and to clarify their dissipation mechanisms.
Significance Statement
Diurnal internal tides in mid- to high-latitude oceans are very different from semidiurnal internal tides, in that they are trapped by topographic features and characterized by uniform rotation throughout the water column rather than by vertical oscillations within the water column. Focusing on this character, we formulate for the first time the generation rate of diurnal internal tides trapped over variable bottom topography. A series of idealized numerical experiments and application to the Kuril Straits show the validity and usefulness of this formulation, which provides a significantly larger generation estimate than previous studies. The results of this study are important for accurate global mapping of turbulent mixing induced by the breaking of internal tides.
Abstract
Subinertial, topographically trapped diurnal internal tides are an important energy source for turbulent mixing in the subarctic oceans. However, their generation may not be estimated by the conventional barotropic-to-baroclinic conversion because their vertical structure is sometimes barotropic, unlike superinertial internal tides that are always baroclinic. Here, a new energy diagram is presented, in which the barotropic mode is decomposed into the surface and topographic modes, with the latter being classified as part of the internal modes together with the baroclinic mode. The energy equation for the newly defined topographic mode is then derived, providing an appropriate formulation of the energy conversion rate from the subinertial surface tides to the topographically trapped internal tides. A series of numerical experiments confirm that the formulation successfully predicts the energy conversion rate for various cases, with the relative contribution of the baroclinic and topographic modes varying significantly depending on the bottom topography and stratification. Furthermore, this surface-to-internal conversion is demonstrated to give a significantly larger estimate than the barotropic-to-baroclinic conversion for subinertial tides. Applying the formulation to the results of a realistic numerical simulation in the Kuril Straits, an area with the strongest mixing due to subinertial diurnal tides, shows that the surface mode is converted into the baroclinic and topographic modes with comparable magnitudes, responsible for most of the energy dissipation in this area. These results indicate the need to reestimate the global distribution of the generation rate of the subinertial internal tides using our new formulation and to clarify their dissipation mechanisms.
Significance Statement
Diurnal internal tides in mid- to high-latitude oceans are very different from semidiurnal internal tides, in that they are trapped by topographic features and characterized by uniform rotation throughout the water column rather than by vertical oscillations within the water column. Focusing on this character, we formulate for the first time the generation rate of diurnal internal tides trapped over variable bottom topography. A series of idealized numerical experiments and application to the Kuril Straits show the validity and usefulness of this formulation, which provides a significantly larger generation estimate than previous studies. The results of this study are important for accurate global mapping of turbulent mixing induced by the breaking of internal tides.
Abstract
The deep channel north of New Guinea (NG) is the choke site for the upper deep branches of the Pacific meridional overturning circulation (U-PMOC). The U-PMOC is a crucial element of the ocean’s climate and biogeochemical systems. It carries the mixed water of the Upper Circumpolar Water and North Pacific Deep Water with a potential temperature over 1.2°–2.2°C. The pathway and volume transport of U-PMOC through the deep channel north of NG are revealed by mooring measurements from 2014 to 2019. Mean U-PMOC is located at ∼2000–3500 m with a velocity core at 2550 m and is directed eastward. The U-PMOC shows a strong seasonal variability with a direction reversal from June to September. The oceanic reanalysis product GLORYS12V1 well reproduces the observed U-PMOC and is thus used to estimate the mean and standard deviation of U-PMOC’s volume transport as 2.19 ± 11.4 Sv (1 Sv ≡ 106 m3 s−1) and to explore the underlying dynamics of the U-PMOC. The seasonality of U-PMOC is induced by the vertical propagation of the Rossby energy through the upper ocean in the eastern Pacific to the deep ocean in the western Pacific. The mean eastward U-PMOC transport is forced by the zonal deep pressure gradient, which is mainly determined by the local upper-ocean processes above 500 m.
Abstract
The deep channel north of New Guinea (NG) is the choke site for the upper deep branches of the Pacific meridional overturning circulation (U-PMOC). The U-PMOC is a crucial element of the ocean’s climate and biogeochemical systems. It carries the mixed water of the Upper Circumpolar Water and North Pacific Deep Water with a potential temperature over 1.2°–2.2°C. The pathway and volume transport of U-PMOC through the deep channel north of NG are revealed by mooring measurements from 2014 to 2019. Mean U-PMOC is located at ∼2000–3500 m with a velocity core at 2550 m and is directed eastward. The U-PMOC shows a strong seasonal variability with a direction reversal from June to September. The oceanic reanalysis product GLORYS12V1 well reproduces the observed U-PMOC and is thus used to estimate the mean and standard deviation of U-PMOC’s volume transport as 2.19 ± 11.4 Sv (1 Sv ≡ 106 m3 s−1) and to explore the underlying dynamics of the U-PMOC. The seasonality of U-PMOC is induced by the vertical propagation of the Rossby energy through the upper ocean in the eastern Pacific to the deep ocean in the western Pacific. The mean eastward U-PMOC transport is forced by the zonal deep pressure gradient, which is mainly determined by the local upper-ocean processes above 500 m.
Abstract
The spectral description of the energy of oceanic internal gravity waves is generally represented by the Garrett–Munk (GM) model, a function with a power-law decrease of spectral energy in wavenumber–frequency space. Besides the slopes of these power laws, the spectrum is expressed as a function of energy and a bandwidth parameter that fixes the range of vertical modes excited in the respective state. Whereas concepts have been developed and agreed upon of what processes feed the wave spectrum and what dissipates energy, there is no explanation of what shapes the spectral distribution, i.e., how the power laws come about and what sets the bandwidth. The present study develops a parametric spectral model of energy and bandwidth from the basic underlying energy balance in terms of forcing, propagation, refraction, spectral transfer, and dissipation. The model is an extension of the IDEMIX (Internal Wave Dissipation, Energy and Mixing) models where bandwidth was taken as a constant parameter. The current version of the model is restricted to single-column mode and the slopes of the spectral power laws are fixed. A coupled system of predictive equations for energy and bandwidth (for up- and downward propagating waves) results. The equations imply that bandwidth relates to energy by a power law with an exponent given by the dynamical parameters. It agrees favorably with energy, bandwidth, and slope data from previously published fits of the GM model to Argo float observations. Numerical solutions of the coupled energy–bandwidth model in stand-alone modus are presented.
Abstract
The spectral description of the energy of oceanic internal gravity waves is generally represented by the Garrett–Munk (GM) model, a function with a power-law decrease of spectral energy in wavenumber–frequency space. Besides the slopes of these power laws, the spectrum is expressed as a function of energy and a bandwidth parameter that fixes the range of vertical modes excited in the respective state. Whereas concepts have been developed and agreed upon of what processes feed the wave spectrum and what dissipates energy, there is no explanation of what shapes the spectral distribution, i.e., how the power laws come about and what sets the bandwidth. The present study develops a parametric spectral model of energy and bandwidth from the basic underlying energy balance in terms of forcing, propagation, refraction, spectral transfer, and dissipation. The model is an extension of the IDEMIX (Internal Wave Dissipation, Energy and Mixing) models where bandwidth was taken as a constant parameter. The current version of the model is restricted to single-column mode and the slopes of the spectral power laws are fixed. A coupled system of predictive equations for energy and bandwidth (for up- and downward propagating waves) results. The equations imply that bandwidth relates to energy by a power law with an exponent given by the dynamical parameters. It agrees favorably with energy, bandwidth, and slope data from previously published fits of the GM model to Argo float observations. Numerical solutions of the coupled energy–bandwidth model in stand-alone modus are presented.
Abstract
The Arctic Ocean is characterized by an ice-covered layer of cold and relatively fresh water above layers of warmer and saltier water. It is estimated that enough heat is stored in these deeper layers to melt all the Arctic sea ice many times over, but they are isolated from the surface by a stable halocline. Current vertical mixing rates across the Arctic Ocean halocline are small, due in part to sea ice reducing wind–ocean momentum transfer and damping internal waves. However, recent observational studies have argued that sea ice retreat results in enhanced mixing. This could create a positive feedback whereby increased vertical mixing due to sea ice retreat causes the previously isolated subsurface heat to melt more sea ice. Here, we use an idealized climate model to investigate the impacts of such a feedback. We find that an abrupt “tipping point” can occur under global warming, with an associated hysteresis window bounded by saddle-node bifurcations. We show that the presence and magnitude of the hysteresis are sensitive to the choice of model parameters, and the hysteresis occurs for only a limited range of parameters. During the critical transition at the bifurcation point, we find that only a small percentage of the heat stored in the deep layer is released, although this is still enough to lead to substantial sea ice melt. Furthermore, no clear relationship is apparent between this change in heat storage and the level of hysteresis when the parameters are varied.
Abstract
The Arctic Ocean is characterized by an ice-covered layer of cold and relatively fresh water above layers of warmer and saltier water. It is estimated that enough heat is stored in these deeper layers to melt all the Arctic sea ice many times over, but they are isolated from the surface by a stable halocline. Current vertical mixing rates across the Arctic Ocean halocline are small, due in part to sea ice reducing wind–ocean momentum transfer and damping internal waves. However, recent observational studies have argued that sea ice retreat results in enhanced mixing. This could create a positive feedback whereby increased vertical mixing due to sea ice retreat causes the previously isolated subsurface heat to melt more sea ice. Here, we use an idealized climate model to investigate the impacts of such a feedback. We find that an abrupt “tipping point” can occur under global warming, with an associated hysteresis window bounded by saddle-node bifurcations. We show that the presence and magnitude of the hysteresis are sensitive to the choice of model parameters, and the hysteresis occurs for only a limited range of parameters. During the critical transition at the bifurcation point, we find that only a small percentage of the heat stored in the deep layer is released, although this is still enough to lead to substantial sea ice melt. Furthermore, no clear relationship is apparent between this change in heat storage and the level of hysteresis when the parameters are varied.
Abstract
Freshwater from the Greenland Ice Sheet is routed to the ocean through narrow fjords along the coastline where it impacts ecosystems both within the fjord and on the continental shelf, regional circulation, and potentially the global overturning circulation. However, the timing of freshwater export is sensitive to the residence time of waters within glacial fjords. Here, we present evidence of seasonal freshwater storage in a tidewater glacial fjord using hydrographic and velocity data collected over 10 days during the summers of 2012 and 2013 in Saqqarleq (SQ), a midsize fjord in west Greenland. The data revealed a rapid freshening trend of −0.05 ± 0.01 and −0.04 ± 0.01 g kg−1 day−1 in 2012 and 2013, respectively, within the intermediate layer of the fjord (15–100 m) less than 2.5 km from the glacier terminus. The freshening trend is driven, in part, by the downward mixing of outflowing glacially modified water near the surface and increasingly stratifies the fjord from the surface downward over the summer melt season. We construct a box model that recreates the first-order dynamics of the fjord and describes freshwater storage as a balance between friction and density-driven exchange outside the fjord. The model can be used to diagnose the time scale for this balance to be reached, and for SQ we find a month lag between subglacial meltwater discharge and net freshwater export. These results indicate a fjord-induced delay in freshwater export to the ocean that should be represented in large-scale models seeking to understand the impact of Greenland freshwater on the regional climate system.
Abstract
Freshwater from the Greenland Ice Sheet is routed to the ocean through narrow fjords along the coastline where it impacts ecosystems both within the fjord and on the continental shelf, regional circulation, and potentially the global overturning circulation. However, the timing of freshwater export is sensitive to the residence time of waters within glacial fjords. Here, we present evidence of seasonal freshwater storage in a tidewater glacial fjord using hydrographic and velocity data collected over 10 days during the summers of 2012 and 2013 in Saqqarleq (SQ), a midsize fjord in west Greenland. The data revealed a rapid freshening trend of −0.05 ± 0.01 and −0.04 ± 0.01 g kg−1 day−1 in 2012 and 2013, respectively, within the intermediate layer of the fjord (15–100 m) less than 2.5 km from the glacier terminus. The freshening trend is driven, in part, by the downward mixing of outflowing glacially modified water near the surface and increasingly stratifies the fjord from the surface downward over the summer melt season. We construct a box model that recreates the first-order dynamics of the fjord and describes freshwater storage as a balance between friction and density-driven exchange outside the fjord. The model can be used to diagnose the time scale for this balance to be reached, and for SQ we find a month lag between subglacial meltwater discharge and net freshwater export. These results indicate a fjord-induced delay in freshwater export to the ocean that should be represented in large-scale models seeking to understand the impact of Greenland freshwater on the regional climate system.
Abstract
The generation of broadband wave energy frequency spectra from narrowband wave forcing in geophysical flows remains a conundrum. In contrast to the long-standing view that nonlinear wave–wave interactions drive the spreading of wave energy in frequency space, recent work suggests that Doppler-shifting by geostrophic flows may be the primary agent. We investigate this possibility by ray tracing a large number of inertia–gravity wave packets through three-dimensional, geostrophically turbulent flows generated either by a quasigeostrophic (QG) simulation or by synthetic random processes. We find that, in all cases investigated, a broadband quasi-stationary inertia–gravity wave frequency spectrum forms, irrespective of the initial frequencies and wave vectors of the packets. The frequency spectrum is well represented by a power law. A possible theoretical explanation relies on the analogy between the kinematic stretching of passive tracer gradients and the refraction of wave vectors. Consistent with this hypothesis, the spectrum of eigenvalues of the background flow velocity gradients predicts a frequency spectrum that is nearly identical to that found by integration of the ray tracing equations.
Abstract
The generation of broadband wave energy frequency spectra from narrowband wave forcing in geophysical flows remains a conundrum. In contrast to the long-standing view that nonlinear wave–wave interactions drive the spreading of wave energy in frequency space, recent work suggests that Doppler-shifting by geostrophic flows may be the primary agent. We investigate this possibility by ray tracing a large number of inertia–gravity wave packets through three-dimensional, geostrophically turbulent flows generated either by a quasigeostrophic (QG) simulation or by synthetic random processes. We find that, in all cases investigated, a broadband quasi-stationary inertia–gravity wave frequency spectrum forms, irrespective of the initial frequencies and wave vectors of the packets. The frequency spectrum is well represented by a power law. A possible theoretical explanation relies on the analogy between the kinematic stretching of passive tracer gradients and the refraction of wave vectors. Consistent with this hypothesis, the spectrum of eigenvalues of the background flow velocity gradients predicts a frequency spectrum that is nearly identical to that found by integration of the ray tracing equations.
Abstract
Energetic internal tides in the Pacific Ocean generated from multiple sources are the subject of many studies, although the subpolar North Pacific (SNP) is known as a high-latitude hotspot that remains less explored. The present study is the first detailed investigation on M2 internal tide energetics and dynamics in the SNP by high-resolution numerical simulations. The M2 internal tides in the SNP mainly originate from the Aleutian Ridge (area-integrated 5.51 GW and averaged ∼10−3 W m−2 of barotropic-to-baroclinic conversion rate), wherein the Amukta Pass is the most significant source. The Amukta Pass radiates northward 0.55 GW (averaged 2.3 kW m−1) to the Bering Sea and southward 1.40 GW (averaged 3.7 kW m−1) to the North Pacific. The subsequent south–north asymmetric radiation pattern is consistent with satellite altimeter detection. In the Bering basin, multiwave superposition in the near field between the Amukta Pass and adjacent sources generates two standing wave patterns. After approaching the Bering Sea slope, remote internal tides from Aleutian Ridge enhance local generation and dissipation. The dissipation field is relatively similar to the generation map, which is explained by the higher local dissipation efficiency q (>1/2) and the faster energy attenuation than in the midlatitudes. The simulated dissipation rates compare favorably with the estimate from fine-scale parameterization, indicating the dominance of internal tidal mixing. The averaged dissipation rate in SNP is O(10−10) W kg−1, and the depth-integrated dissipation rates reach O(10−1) W m−2 near the Amukta Pass. It is important to understand the unique physics and dissipative process of high-latitude internal tides to fully characterize the redistribution of global tidal energy and associated mixing.
Abstract
Energetic internal tides in the Pacific Ocean generated from multiple sources are the subject of many studies, although the subpolar North Pacific (SNP) is known as a high-latitude hotspot that remains less explored. The present study is the first detailed investigation on M2 internal tide energetics and dynamics in the SNP by high-resolution numerical simulations. The M2 internal tides in the SNP mainly originate from the Aleutian Ridge (area-integrated 5.51 GW and averaged ∼10−3 W m−2 of barotropic-to-baroclinic conversion rate), wherein the Amukta Pass is the most significant source. The Amukta Pass radiates northward 0.55 GW (averaged 2.3 kW m−1) to the Bering Sea and southward 1.40 GW (averaged 3.7 kW m−1) to the North Pacific. The subsequent south–north asymmetric radiation pattern is consistent with satellite altimeter detection. In the Bering basin, multiwave superposition in the near field between the Amukta Pass and adjacent sources generates two standing wave patterns. After approaching the Bering Sea slope, remote internal tides from Aleutian Ridge enhance local generation and dissipation. The dissipation field is relatively similar to the generation map, which is explained by the higher local dissipation efficiency q (>1/2) and the faster energy attenuation than in the midlatitudes. The simulated dissipation rates compare favorably with the estimate from fine-scale parameterization, indicating the dominance of internal tidal mixing. The averaged dissipation rate in SNP is O(10−10) W kg−1, and the depth-integrated dissipation rates reach O(10−1) W m−2 near the Amukta Pass. It is important to understand the unique physics and dissipative process of high-latitude internal tides to fully characterize the redistribution of global tidal energy and associated mixing.
