Browse
Abstract
The internal wave (IW) continuum of a regional ocean model is studied in terms of the vertical spectral kinetic energy (KE) fluxes and transfers at high vertical wavenumbers. Previous work has shown that this model permits a partial representation of the IW cascade. In this work, vertical spectral KE flux is decomposed into catalyst, source, and destination vertical modes and frequency bands of nonlinear scattering, a framework that allows for the discernment of different types of nonlinear interactions involving both waves and eddies. Energy transfer within the supertidal IW continuum is found to be strongly dependent on resolution. Specifically, at a horizontal grid spacing of 1/48°, most KE in the supertidal continuum arrives there from lower-frequency modes through a single nonlinear interaction, whereas at 1/384° and with sufficient vertical resolution KE transfers within the supertidal IW continuum are comparable in size to KE transfer from lower-frequency modes. Additionally, comparisons are made with existing theoretical and observational work on energy pathways in the IW continuum. Induced diffusion (ID) is found to be associated with a weak forward frequency transfer within the supertidal IW continuum. ID is also limited to the highest vertical wavenumbers and is more sensitive to resolution relative to spectrally local interactions. At the same time, ID-like processes involving high-vertical-wavenumber near-inertial and tidal waves as well as low-vertical-wavenumber eddy fields are substantial, suggesting that the processes giving rise to a Garrett–Munk-like spectra in the present numerical simulation and perhaps the real ocean may be more varied than in idealized or wave-only frameworks.
Abstract
The internal wave (IW) continuum of a regional ocean model is studied in terms of the vertical spectral kinetic energy (KE) fluxes and transfers at high vertical wavenumbers. Previous work has shown that this model permits a partial representation of the IW cascade. In this work, vertical spectral KE flux is decomposed into catalyst, source, and destination vertical modes and frequency bands of nonlinear scattering, a framework that allows for the discernment of different types of nonlinear interactions involving both waves and eddies. Energy transfer within the supertidal IW continuum is found to be strongly dependent on resolution. Specifically, at a horizontal grid spacing of 1/48°, most KE in the supertidal continuum arrives there from lower-frequency modes through a single nonlinear interaction, whereas at 1/384° and with sufficient vertical resolution KE transfers within the supertidal IW continuum are comparable in size to KE transfer from lower-frequency modes. Additionally, comparisons are made with existing theoretical and observational work on energy pathways in the IW continuum. Induced diffusion (ID) is found to be associated with a weak forward frequency transfer within the supertidal IW continuum. ID is also limited to the highest vertical wavenumbers and is more sensitive to resolution relative to spectrally local interactions. At the same time, ID-like processes involving high-vertical-wavenumber near-inertial and tidal waves as well as low-vertical-wavenumber eddy fields are substantial, suggesting that the processes giving rise to a Garrett–Munk-like spectra in the present numerical simulation and perhaps the real ocean may be more varied than in idealized or wave-only frameworks.
Abstract
The simple scaling relation for internal-tide generation proposed by Jayne and St. Laurent is widely used for parameterizing turbulent mixing induced by breaking of internal tides. Based on the internal-tide generation derived from a 0.1° ocean general circulation model, we show that depending on which stratification is used, this relation produces different vertical distributions of internal-tide generation. When using the buoyancy frequency at the seafloor, which is a common practice, the scaling relation produces, relative to the model, too-strong internal-tide generation in the upper 2000 m and too-weak internal-tide generation in the lower 2000 m. Moreover, the different vertical distributions in the different ocean basins, characterized by a generally decreasing internal tide generation with increasing depth in the Indo-Pacific but not-decreasing or even increasing internal tide generation with increasing depth in the upper 3000 m of the Atlantic, cannot be captured when using bottom stratification. These unsatisfactory features can be easily removed by replacing the buoyancy frequency at the seafloor by a buoyancy frequency averaged over a large part of the water column. To our knowledge, this sensitivity to stratification has not been explicitly quantified for the global ocean. Because of this sensitivity, the scaling relation of Jayne and St. Laurent should be used with an averaged stratification to ensure a more adequate representation of turbulent diffusivity due to tidal mixing and water mass transformation in the deep oceans.
Abstract
The simple scaling relation for internal-tide generation proposed by Jayne and St. Laurent is widely used for parameterizing turbulent mixing induced by breaking of internal tides. Based on the internal-tide generation derived from a 0.1° ocean general circulation model, we show that depending on which stratification is used, this relation produces different vertical distributions of internal-tide generation. When using the buoyancy frequency at the seafloor, which is a common practice, the scaling relation produces, relative to the model, too-strong internal-tide generation in the upper 2000 m and too-weak internal-tide generation in the lower 2000 m. Moreover, the different vertical distributions in the different ocean basins, characterized by a generally decreasing internal tide generation with increasing depth in the Indo-Pacific but not-decreasing or even increasing internal tide generation with increasing depth in the upper 3000 m of the Atlantic, cannot be captured when using bottom stratification. These unsatisfactory features can be easily removed by replacing the buoyancy frequency at the seafloor by a buoyancy frequency averaged over a large part of the water column. To our knowledge, this sensitivity to stratification has not been explicitly quantified for the global ocean. Because of this sensitivity, the scaling relation of Jayne and St. Laurent should be used with an averaged stratification to ensure a more adequate representation of turbulent diffusivity due to tidal mixing and water mass transformation in the deep oceans.
Abstract
A variety of submesoscale coherent vortices (SCVs) in the Kuroshio Extension region have been reported by recent observational studies, and the preliminary understanding of their properties, spatial distribution, and possible origins has progressively improved. However, due to relatively sparse in situ observations, the generation mechanisms of these SCVs and associated dynamic processes remain unclear. In this study, we use high-resolution model simulations to fill the gaps of the in situ observations in terms of the three-dimensional structures and life cycles of SCVs. Vortex detection and tracking algorithms are adopted and the characteristics of warm-core and cold-core SCVs are revealed. These vortices have finite Rossby numbers (0.25–0.4), and their horizontal structures can be well described by the Taylor vortex model in terms of the gradient wind balance. The vertical velocity field is characterized by a distinct dipole pattern with upwelling and downwelling cells at the vortex edge. It is very likely that both types of SCVs are generated along the eastern Japan coast through flow–topography interactions, and the Izu–Ogasawara Ridge and Hokkaido slope are found to be two important generation sites where topography friction produces extremely low potential vorticity. After leaving the boundary, SCVs can propagate over long distances and trap a water volume of ∼1011 m3.
Abstract
A variety of submesoscale coherent vortices (SCVs) in the Kuroshio Extension region have been reported by recent observational studies, and the preliminary understanding of their properties, spatial distribution, and possible origins has progressively improved. However, due to relatively sparse in situ observations, the generation mechanisms of these SCVs and associated dynamic processes remain unclear. In this study, we use high-resolution model simulations to fill the gaps of the in situ observations in terms of the three-dimensional structures and life cycles of SCVs. Vortex detection and tracking algorithms are adopted and the characteristics of warm-core and cold-core SCVs are revealed. These vortices have finite Rossby numbers (0.25–0.4), and their horizontal structures can be well described by the Taylor vortex model in terms of the gradient wind balance. The vertical velocity field is characterized by a distinct dipole pattern with upwelling and downwelling cells at the vortex edge. It is very likely that both types of SCVs are generated along the eastern Japan coast through flow–topography interactions, and the Izu–Ogasawara Ridge and Hokkaido slope are found to be two important generation sites where topography friction produces extremely low potential vorticity. After leaving the boundary, SCVs can propagate over long distances and trap a water volume of ∼1011 m3.
Abstract
In global ocean circulation and climate models, bottom-enhanced turbulent mixing is often parameterized such that the vertical decay scale of the energy dissipation rate ζ is universally constant at 500 m. In this study, using a nonhydrostatic two-dimensional numerical model in the horizontal–vertical plane that incorporates a monochromatic sinusoidal seafloor topography and the Garrett–Munk (GM) background internal wave field, we find that ζ of the internal lee-wave-driven bottom-enhanced mixing is actually variable depending on the magnitude of the steady flow U 0, the horizontal wavenumber kH , and the height hT of the seafloor topography. When the steepness parameter (Sp = NhT /U 0 where N is the buoyancy frequency near the seafloor) is less than 0.3, internal lee waves propagate upward from the seafloor while interacting with the GM internal wave field to create a turbulent mixing region with ζ that extends farther upward from the seafloor as U 0 increases, but is nearly independent of kH . In contrast, when Sp exceeds 0.3, inertial oscillations (IOs) not far above the seafloor are enhanced by the intermittent supply of internal lee-wave energy Doppler-shifted to the near-inertial frequency, which occurs depending on the sign and magnitude of the background IO shear. The composite flow, consisting of the superposition of U 0 and the IOs, interacts with the seafloor topography to efficiently generate internal lee waves during the period centered on the time of the composite flow maximum, but their upward propagation is inhibited by the increased IO shear, creating a turbulent mixing region of small ζ.
Abstract
In global ocean circulation and climate models, bottom-enhanced turbulent mixing is often parameterized such that the vertical decay scale of the energy dissipation rate ζ is universally constant at 500 m. In this study, using a nonhydrostatic two-dimensional numerical model in the horizontal–vertical plane that incorporates a monochromatic sinusoidal seafloor topography and the Garrett–Munk (GM) background internal wave field, we find that ζ of the internal lee-wave-driven bottom-enhanced mixing is actually variable depending on the magnitude of the steady flow U 0, the horizontal wavenumber kH , and the height hT of the seafloor topography. When the steepness parameter (Sp = NhT /U 0 where N is the buoyancy frequency near the seafloor) is less than 0.3, internal lee waves propagate upward from the seafloor while interacting with the GM internal wave field to create a turbulent mixing region with ζ that extends farther upward from the seafloor as U 0 increases, but is nearly independent of kH . In contrast, when Sp exceeds 0.3, inertial oscillations (IOs) not far above the seafloor are enhanced by the intermittent supply of internal lee-wave energy Doppler-shifted to the near-inertial frequency, which occurs depending on the sign and magnitude of the background IO shear. The composite flow, consisting of the superposition of U 0 and the IOs, interacts with the seafloor topography to efficiently generate internal lee waves during the period centered on the time of the composite flow maximum, but their upward propagation is inhibited by the increased IO shear, creating a turbulent mixing region of small ζ.
Abstract
Submesoscale currents and internal gravity waves achieve an intense turbulent cascade near the ocean surface [depth of 0–O(100) m], which is thought to give rise to significant energy sources and sinks for mesoscale eddies. Here, we characterize the contributions of nonwave currents (NWCs; including eddies and fronts) and internal gravity waves (IGWs; including near-inertial motions, lee waves, and the internal wave continuum) to near-surface submesoscale turbulence in the Drake Passage. Using a numerical simulation, we combine Lagrangian filtering and a Helmholtz decomposition to identify NWCs and IGWs and to characterize their dynamics (rotational versus divergent). We show that NWCs and IGWs contribute in different proportions to the inverse and forward turbulent kinetic energy cascades, based on their dynamics and spatiotemporal scales. Purely rotational NWCs cause most of the inverse cascade, while coupled rotational–divergent components of NWCs and coupled NWC–IGWs cause the forward cascade. The cascade changes direction at a spatial scale at which motions become increasingly divergent. However, the forward cascade is ultimately limited by the motions’ spatiotemporal scales. The bulk of the forward cascade (80%–95%) is caused by NWCs and IGWs of small spatiotemporal scales (L < 10 km; T < 6 h), which are primarily rotational: submesoscale eddies, fronts, and the internal wave continuum. These motions also cause a significant part of the inverse cascade (30%). Our results highlight the requirement for high spatiotemporal resolutions to diagnose the properties and large-scale impacts of near-surface submesoscale turbulence accurately, with significant implications for ocean energy cycle study strategies.
Abstract
Submesoscale currents and internal gravity waves achieve an intense turbulent cascade near the ocean surface [depth of 0–O(100) m], which is thought to give rise to significant energy sources and sinks for mesoscale eddies. Here, we characterize the contributions of nonwave currents (NWCs; including eddies and fronts) and internal gravity waves (IGWs; including near-inertial motions, lee waves, and the internal wave continuum) to near-surface submesoscale turbulence in the Drake Passage. Using a numerical simulation, we combine Lagrangian filtering and a Helmholtz decomposition to identify NWCs and IGWs and to characterize their dynamics (rotational versus divergent). We show that NWCs and IGWs contribute in different proportions to the inverse and forward turbulent kinetic energy cascades, based on their dynamics and spatiotemporal scales. Purely rotational NWCs cause most of the inverse cascade, while coupled rotational–divergent components of NWCs and coupled NWC–IGWs cause the forward cascade. The cascade changes direction at a spatial scale at which motions become increasingly divergent. However, the forward cascade is ultimately limited by the motions’ spatiotemporal scales. The bulk of the forward cascade (80%–95%) is caused by NWCs and IGWs of small spatiotemporal scales (L < 10 km; T < 6 h), which are primarily rotational: submesoscale eddies, fronts, and the internal wave continuum. These motions also cause a significant part of the inverse cascade (30%). Our results highlight the requirement for high spatiotemporal resolutions to diagnose the properties and large-scale impacts of near-surface submesoscale turbulence accurately, with significant implications for ocean energy cycle study strategies.
Abstract
The mechanism of initial and transient perturbations of symmetric instability (SI) in a hydrostatic flow with lateral shear is analyzed by applying the generalized stability analysis. It is well known that the SI’s most rapidly growing motion is along isopycnals, and the growth rates consist of growing, neutral, and decaying modes. The eigenvectors of these three modes are not orthogonal to each other, hence the initial and transient perturbations bear little resemblance to the normal mode. Our findings indicate that the emergence of normal modes occurs within a time span of 1–3 inertial periods, which we refer to as the transient state. The overall growth of perturbation energy is divided into three components: geostrophic shear production (GSP), lateral shear production (LSP), and meridional buoyancy flux (MB). During the transient state, the perturbation energy is partly driven by MB, contrary to the normal mode which has zero MB. The relative energy contribution is evaluated through the ratio to GSP. While the MB-to-GSP ratio of the initial mode is higher than that of the normal mode, the LSP-to-GSP ratio remains constant. In the absence of the fastest-growing normal mode, MB can serve as the predominant initial energy source. The precise transition in the energy regime is contingent upon the geostrophic Richardson number and Rossby number.
Significance Statement
Fronts can be unstable to instabilities, which generate disturbance growth and lead to the mixing of water masses. We wanted to understand the initial and transient development of disturbance growth leading to the well-known exponentially growing state. While the exponentially growing disturbance is dominant in the long run, the disturbance growth may not have enough time to achieve the exponentially growing state. We find that the initial disturbance growth bears little resemblance to the exponentially growing state. Capturing the complete spectrum of front evolution remains challenging, and observations have thus far been limited to short-term records. The insights learned from this study can aid in better characterizing the disturbance growth captured in these short-term records.
Abstract
The mechanism of initial and transient perturbations of symmetric instability (SI) in a hydrostatic flow with lateral shear is analyzed by applying the generalized stability analysis. It is well known that the SI’s most rapidly growing motion is along isopycnals, and the growth rates consist of growing, neutral, and decaying modes. The eigenvectors of these three modes are not orthogonal to each other, hence the initial and transient perturbations bear little resemblance to the normal mode. Our findings indicate that the emergence of normal modes occurs within a time span of 1–3 inertial periods, which we refer to as the transient state. The overall growth of perturbation energy is divided into three components: geostrophic shear production (GSP), lateral shear production (LSP), and meridional buoyancy flux (MB). During the transient state, the perturbation energy is partly driven by MB, contrary to the normal mode which has zero MB. The relative energy contribution is evaluated through the ratio to GSP. While the MB-to-GSP ratio of the initial mode is higher than that of the normal mode, the LSP-to-GSP ratio remains constant. In the absence of the fastest-growing normal mode, MB can serve as the predominant initial energy source. The precise transition in the energy regime is contingent upon the geostrophic Richardson number and Rossby number.
Significance Statement
Fronts can be unstable to instabilities, which generate disturbance growth and lead to the mixing of water masses. We wanted to understand the initial and transient development of disturbance growth leading to the well-known exponentially growing state. While the exponentially growing disturbance is dominant in the long run, the disturbance growth may not have enough time to achieve the exponentially growing state. We find that the initial disturbance growth bears little resemblance to the exponentially growing state. Capturing the complete spectrum of front evolution remains challenging, and observations have thus far been limited to short-term records. The insights learned from this study can aid in better characterizing the disturbance growth captured in these short-term records.
Abstract
This study quantifies the overturning circulation in the Arctic Ocean and associated heat transport (HT) and freshwater transport (FWT) from October 2004 to May 2010 based on hydrographic and current observations. Our main data source consists of 1165 moored instrument records in the four Arctic main gateways: Davis Strait, Fram Strait, Bering Strait, and the Barents Sea Opening. We employ a box inverse model to obtain mass and salt balanced velocity fields, which are then used to quantify the overturning circulation as well as HT and FWT. Atlantic Water is transformed into two different water masses in the Arctic Ocean at a rate of 4.3 Sv (1 Sv ≡ 106 m3 s−1). Combined with 0.7 Sv of Bering Strait inflow and 0.15 Sv of surface freshwater flux, 2.2 Sv flows back to the south through Davis Strait and western Fram Strait as the upper limb of the overturning circulation, and 2.9 Sv returns southward through Fram Strait as the lower limb of the overturning. The Arctic Ocean imports heat of 180 ± 57 TW (long-term mean ± standard deviation of monthly means) with a methodological uncertainty of 20 TW and exports FW of 156 ± 91 mSv with an uncertainty of 61 mSv over the 6 years with a potential offset of ∼30 mSv. The HT and FWT have large seasonalities ranging between 110 and 260 TW (maximum in winter) and between 40 and 260 mSv (maximum in winter), respectively. The obtained overturning circulation and associated HT and FWT presented here are vital information to better understand the northern extent of the Atlantic meridional overturning circulation.
Abstract
This study quantifies the overturning circulation in the Arctic Ocean and associated heat transport (HT) and freshwater transport (FWT) from October 2004 to May 2010 based on hydrographic and current observations. Our main data source consists of 1165 moored instrument records in the four Arctic main gateways: Davis Strait, Fram Strait, Bering Strait, and the Barents Sea Opening. We employ a box inverse model to obtain mass and salt balanced velocity fields, which are then used to quantify the overturning circulation as well as HT and FWT. Atlantic Water is transformed into two different water masses in the Arctic Ocean at a rate of 4.3 Sv (1 Sv ≡ 106 m3 s−1). Combined with 0.7 Sv of Bering Strait inflow and 0.15 Sv of surface freshwater flux, 2.2 Sv flows back to the south through Davis Strait and western Fram Strait as the upper limb of the overturning circulation, and 2.9 Sv returns southward through Fram Strait as the lower limb of the overturning. The Arctic Ocean imports heat of 180 ± 57 TW (long-term mean ± standard deviation of monthly means) with a methodological uncertainty of 20 TW and exports FW of 156 ± 91 mSv with an uncertainty of 61 mSv over the 6 years with a potential offset of ∼30 mSv. The HT and FWT have large seasonalities ranging between 110 and 260 TW (maximum in winter) and between 40 and 260 mSv (maximum in winter), respectively. The obtained overturning circulation and associated HT and FWT presented here are vital information to better understand the northern extent of the Atlantic meridional overturning circulation.
Abstract
Accurate estimates of extreme waves are central for maritime activities, and stochastic wave models are the best option available for practical applications. However, the way currents influence the statistics of space–time extremes in spectral wave models has not been properly assessed. Here we demonstrate impacts of the wave modulation caused by one of the world’s strongest open ocean tidal currents, which reaches speeds of at least 3 m s−1. For a bimodal swell and wind sea state, we find that most intense interactions occur when the wind sea opposes the tidal current, with an increase in significant wave height and spectral steepness up to 45% and 167%, respectively. The steepness modulation strengthens the second-order Stokes contribution for the normalized extreme crests, which increases between 5% and 14% during opposing wind sea and current. The normalized extreme wave heights have a strong dependence on the narrow-bandedness parameter, which is sensitive to the variance distribution in the bimodal spectrum, and we find an increase up to 12% with currents opposing the wind sea. In another case of swell opposing a tidal jet, we find the spectral steepness to exceed the increase predicted by a simplified modulation model. We find support in single-point observations that using tidal currents as forcing in wave models improves the representation of the expected maximum waves, but that action must be taken to close the gap of measurements in strong currents.
Significance Statement
The purpose of this study is to investigate how a very strong tidal current affects the surface wave field, and how it changes the stochastic extreme waves formulated for a space–time domain. Our results suggest that the expected maximum waves become more realistic when tidal currents are added as forcing in wave models. Here, the expected extremes exceed traditional model estimates, i.e., without current forcing, by more than 10%. These differences have implications for maritime operations, both in terms of planning of marine structures and for navigational purposes. However, there is a significant lack of observations in environments with such strong currents, which are needed to further verify our results.
Abstract
Accurate estimates of extreme waves are central for maritime activities, and stochastic wave models are the best option available for practical applications. However, the way currents influence the statistics of space–time extremes in spectral wave models has not been properly assessed. Here we demonstrate impacts of the wave modulation caused by one of the world’s strongest open ocean tidal currents, which reaches speeds of at least 3 m s−1. For a bimodal swell and wind sea state, we find that most intense interactions occur when the wind sea opposes the tidal current, with an increase in significant wave height and spectral steepness up to 45% and 167%, respectively. The steepness modulation strengthens the second-order Stokes contribution for the normalized extreme crests, which increases between 5% and 14% during opposing wind sea and current. The normalized extreme wave heights have a strong dependence on the narrow-bandedness parameter, which is sensitive to the variance distribution in the bimodal spectrum, and we find an increase up to 12% with currents opposing the wind sea. In another case of swell opposing a tidal jet, we find the spectral steepness to exceed the increase predicted by a simplified modulation model. We find support in single-point observations that using tidal currents as forcing in wave models improves the representation of the expected maximum waves, but that action must be taken to close the gap of measurements in strong currents.
Significance Statement
The purpose of this study is to investigate how a very strong tidal current affects the surface wave field, and how it changes the stochastic extreme waves formulated for a space–time domain. Our results suggest that the expected maximum waves become more realistic when tidal currents are added as forcing in wave models. Here, the expected extremes exceed traditional model estimates, i.e., without current forcing, by more than 10%. These differences have implications for maritime operations, both in terms of planning of marine structures and for navigational purposes. However, there is a significant lack of observations in environments with such strong currents, which are needed to further verify our results.
Abstract
Salt mixing enables the transport of water between the inflow and outflow layers of estuarine circulation and therefore closes the circulation by driving a diahaline exchange flow. A recently derived universal law links the salt mixing inside an estuarine volume bounded by an isohaline surface to freshwater discharge: it states that on long-term average, the area-integrated mixing across the bounding isohaline is directly proportional to the freshwater discharge entering the estuary. However, even though numerous studies predict that periods of extreme discharge will become more frequent with climate change, the direct impact of such periods on estuarine mixing and circulation has yet to be investigated. Therefore, this numerical modeling study focuses on salinity mixing and diahaline exchange flows during a low-discharge and an extreme high-discharge period. To this end, we apply a realistic numerical setup of the Elbe estuary in northern Germany, using curvilinear coordinates that follow the navigational channel. This is the first time the direct relationship between diahaline exchange flow and salt mixing as well as the spatial distribution of the diahaline exchange flow is shown in a realistic tidal setup. The spatial distribution is highly correlated with the local mixing gradient for salinity, such that inflow occurs near the bottom at the upstream end of the isohaline. Meanwhile, outflow occurs near the surface at its downstream end. Last, increased vertical stratification occurs within the estuary during the high-discharge period, while estuarine-wide mixing strongly converges to the universal law for averaging periods of the discharge event time scale.
Significance Statement
Inside estuaries, such as river mouths, terrestrial freshwater is mixed with salty ocean water. This is accompanied by an estuarine circulation with inflow of saltwater into the estuary and outflow of brackish water toward the ocean. Here, we aim to better understand how salt mixing and estuarine circulation in a tidal estuary react to periods of extreme freshwater discharge. We find that even during extremely high or low discharge, salt mixing follows the freshwater discharge on time scales as short as days, and that estuarine circulation patterns are largely explained by the local distribution of mixing. As extreme runoff events are likely to occur more often with climate change, these findings may help to understand the dynamics inside future estuaries.
Abstract
Salt mixing enables the transport of water between the inflow and outflow layers of estuarine circulation and therefore closes the circulation by driving a diahaline exchange flow. A recently derived universal law links the salt mixing inside an estuarine volume bounded by an isohaline surface to freshwater discharge: it states that on long-term average, the area-integrated mixing across the bounding isohaline is directly proportional to the freshwater discharge entering the estuary. However, even though numerous studies predict that periods of extreme discharge will become more frequent with climate change, the direct impact of such periods on estuarine mixing and circulation has yet to be investigated. Therefore, this numerical modeling study focuses on salinity mixing and diahaline exchange flows during a low-discharge and an extreme high-discharge period. To this end, we apply a realistic numerical setup of the Elbe estuary in northern Germany, using curvilinear coordinates that follow the navigational channel. This is the first time the direct relationship between diahaline exchange flow and salt mixing as well as the spatial distribution of the diahaline exchange flow is shown in a realistic tidal setup. The spatial distribution is highly correlated with the local mixing gradient for salinity, such that inflow occurs near the bottom at the upstream end of the isohaline. Meanwhile, outflow occurs near the surface at its downstream end. Last, increased vertical stratification occurs within the estuary during the high-discharge period, while estuarine-wide mixing strongly converges to the universal law for averaging periods of the discharge event time scale.
Significance Statement
Inside estuaries, such as river mouths, terrestrial freshwater is mixed with salty ocean water. This is accompanied by an estuarine circulation with inflow of saltwater into the estuary and outflow of brackish water toward the ocean. Here, we aim to better understand how salt mixing and estuarine circulation in a tidal estuary react to periods of extreme freshwater discharge. We find that even during extremely high or low discharge, salt mixing follows the freshwater discharge on time scales as short as days, and that estuarine circulation patterns are largely explained by the local distribution of mixing. As extreme runoff events are likely to occur more often with climate change, these findings may help to understand the dynamics inside future estuaries.
Abstract
Mesoscale eddy buoyancy fluxes across continental slopes profoundly modulate the boundary current dynamics and shelf–ocean exchanges but have yet to be appropriately parameterized via the Gent–McWilliams (GM) scheme in predictive ocean models. In this work, we test the prognostic performance of multiple GM variants in noneddying simulations of upwelling slope fronts that are commonly found along the subtropical continental margins. The tested GM variants range from a set of constant eddy buoyancy diffusivities to recently developed energetically constrained, bathymetry-aware diffusivities, whose implementation is augmented by an artificial neural network (ANN) serving to predict the mesoscale eddy energy based on the topographic and mean flow quantities online. In addition, an ANN is employed to parameterize the cross-slope eddy momentum flux (EMF) that maintains a barotropic flow field analogous to that in an eddy-resolving model. Our tests reveal that noneddying simulations employing the bathymetry-aware forms of the Rhines scale–based scheme and GEOMETRIC scheme can most accurately reproduce the heat contents and along-slope baroclinic transports as those in the eddy-resolving simulations. Further analyses reveal certain degrees of physical consistency in the ANN-inferred eddy energy, which tends to grow (decay) as isopycnal slopes are steepened (flattened), and in the parameterized EMF, which exhibits the correct strength of shaping the flow baroclinicity if a bathymetry-aware GM variant is jointly used. These findings provide a recipe of GM variants for use in noneddying simulations with continental slopes and highlight the potential of machine learning techniques to augment physics-based mesoscale eddy parameterization schemes.
Significance Statement
This study evaluates the predictive skill of parameterization schemes of water mass transports induced by ocean mesoscale eddies across continental slopes. Correctly parameterizing these transports in noneddying ocean models (e.g., ocean climate models) is crucial for predicting the ocean circulation and shelf–ocean exchanges. This work highlights the importance of bathymetric effects on eddy transports, as parameterization schemes that account for the influence of a sloping seafloor outperform those developed specifically for a flat-bottomed ocean. This work also highlights the efficacy of machine learning techniques to augment physics-based mesoscale eddy parameterization schemes, for instance, by estimating the mesoscale eddy energy online to realize energy-dependent parameterization schemes in noneddying simulations.
Abstract
Mesoscale eddy buoyancy fluxes across continental slopes profoundly modulate the boundary current dynamics and shelf–ocean exchanges but have yet to be appropriately parameterized via the Gent–McWilliams (GM) scheme in predictive ocean models. In this work, we test the prognostic performance of multiple GM variants in noneddying simulations of upwelling slope fronts that are commonly found along the subtropical continental margins. The tested GM variants range from a set of constant eddy buoyancy diffusivities to recently developed energetically constrained, bathymetry-aware diffusivities, whose implementation is augmented by an artificial neural network (ANN) serving to predict the mesoscale eddy energy based on the topographic and mean flow quantities online. In addition, an ANN is employed to parameterize the cross-slope eddy momentum flux (EMF) that maintains a barotropic flow field analogous to that in an eddy-resolving model. Our tests reveal that noneddying simulations employing the bathymetry-aware forms of the Rhines scale–based scheme and GEOMETRIC scheme can most accurately reproduce the heat contents and along-slope baroclinic transports as those in the eddy-resolving simulations. Further analyses reveal certain degrees of physical consistency in the ANN-inferred eddy energy, which tends to grow (decay) as isopycnal slopes are steepened (flattened), and in the parameterized EMF, which exhibits the correct strength of shaping the flow baroclinicity if a bathymetry-aware GM variant is jointly used. These findings provide a recipe of GM variants for use in noneddying simulations with continental slopes and highlight the potential of machine learning techniques to augment physics-based mesoscale eddy parameterization schemes.
Significance Statement
This study evaluates the predictive skill of parameterization schemes of water mass transports induced by ocean mesoscale eddies across continental slopes. Correctly parameterizing these transports in noneddying ocean models (e.g., ocean climate models) is crucial for predicting the ocean circulation and shelf–ocean exchanges. This work highlights the importance of bathymetric effects on eddy transports, as parameterization schemes that account for the influence of a sloping seafloor outperform those developed specifically for a flat-bottomed ocean. This work also highlights the efficacy of machine learning techniques to augment physics-based mesoscale eddy parameterization schemes, for instance, by estimating the mesoscale eddy energy online to realize energy-dependent parameterization schemes in noneddying simulations.
