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Abstract
Subsurface eddies are a special type of oceanic eddy that display the maximum velocity in the subsurface layer. Based on field observations, a lens-shaped subsurface anticyclonic eddy (SAE) was detected in the northern South China Sea (SCS) in May 2021. The SAE was located between 20 and 200 m, with a shoaling of the seasonal thermocline and deepening of the main thermocline. Satellite images showed that the SAE exhibited positive sea level anomaly (SLA) and negative sea surface temperature (SST) anomaly. Eddy track indicated that this SAE originated from the Luzon Strait and was generated in the Kuroshio Loop Current (KLC) last winter. The evolution of the SAE was related to the anomalous water properties inside the eddy and the seasonal change of sea surface heat flux. In winter, the continuous surface cooling and Kuroshio intrusion led to a cold, salty core in the upper part of the anticyclonic eddy, which resulted in a subsurface-intensified structure through geostrophic adjustment. As the season changed from winter to spring, sea surface temperature increased. The lens-shaped structure was formed when the seasonal thermocline appeared near the surface that capped the winter well-mixed water inside the eddy. From 1993 to 2021, nearly half of the winter KLC shedding eddies (12/25) survived to late spring and evolved into subsurface lens-shaped structures. This result indicates that the transition of KLC shedding eddy to SAE is a common phenomenon in the northern SCS, which is potentially important for local air–sea interaction, heat–salt balance, and biogeochemical processes.
Significance Statement
Subsurface eddies are lens-shaped eddies with anomalous water properties in the subsurface layer. While such eddies have been reported in many regions of the World Ocean, they are poorly investigated in the SCS, especially the periodic subsurface eddies that appear in a fixed time frame with similar patterns and trajectories. This study reported a subsurface anticyclonic eddy (SAE) in the northern SCS and elucidated its generation and evolution processes. Statistical results confirm that this is a periodic SAE, which occurs nearly annually in late spring and evolves from the Kuroshio shedding eddy with seasonal changes. This study provides a new perspective on the evolution of subsurface eddies in the SCS and will benefit targeted observations in the future.
Abstract
Subsurface eddies are a special type of oceanic eddy that display the maximum velocity in the subsurface layer. Based on field observations, a lens-shaped subsurface anticyclonic eddy (SAE) was detected in the northern South China Sea (SCS) in May 2021. The SAE was located between 20 and 200 m, with a shoaling of the seasonal thermocline and deepening of the main thermocline. Satellite images showed that the SAE exhibited positive sea level anomaly (SLA) and negative sea surface temperature (SST) anomaly. Eddy track indicated that this SAE originated from the Luzon Strait and was generated in the Kuroshio Loop Current (KLC) last winter. The evolution of the SAE was related to the anomalous water properties inside the eddy and the seasonal change of sea surface heat flux. In winter, the continuous surface cooling and Kuroshio intrusion led to a cold, salty core in the upper part of the anticyclonic eddy, which resulted in a subsurface-intensified structure through geostrophic adjustment. As the season changed from winter to spring, sea surface temperature increased. The lens-shaped structure was formed when the seasonal thermocline appeared near the surface that capped the winter well-mixed water inside the eddy. From 1993 to 2021, nearly half of the winter KLC shedding eddies (12/25) survived to late spring and evolved into subsurface lens-shaped structures. This result indicates that the transition of KLC shedding eddy to SAE is a common phenomenon in the northern SCS, which is potentially important for local air–sea interaction, heat–salt balance, and biogeochemical processes.
Significance Statement
Subsurface eddies are lens-shaped eddies with anomalous water properties in the subsurface layer. While such eddies have been reported in many regions of the World Ocean, they are poorly investigated in the SCS, especially the periodic subsurface eddies that appear in a fixed time frame with similar patterns and trajectories. This study reported a subsurface anticyclonic eddy (SAE) in the northern SCS and elucidated its generation and evolution processes. Statistical results confirm that this is a periodic SAE, which occurs nearly annually in late spring and evolves from the Kuroshio shedding eddy with seasonal changes. This study provides a new perspective on the evolution of subsurface eddies in the SCS and will benefit targeted observations in the future.
Abstract
A new three-dimensional method is proposed for calculating the annual mean subduction and obduction rate in the ocean and applied to the North Pacific Ocean. Due to the beta spiral, the subducted/obducted water at a given station can spread over/come from a wide range with different densities in the subsurface ocean. This new method can provide the three-dimensional feature of subduction/obduction and more accurate distribution of the annual subduction/obduction rate in density space. The spatial patterns of annual subduction/obduction rate obtained from both the classical and new methods are similar, although at individual stations the rate can be different; however, the new 3D method can greatly improve the density structure of subducted/obducted water mass. In spite of the assumption of idealized fluid in most previous studies, our analysis showed that subducted water masses can change their density due to diapycnal mixing, especially for water masses subducted at relatively shallow depths. In the North Pacific, the subduction process mainly takes place for about 1–2 months in most of the subtropical basin, while the time window for obduction is ∼100 days in the major obduction regions. Based on the SODA monthly mean climatology, the subducted/obducted water in the North Pacific is primarily distributed at depths of 80–120 m.
Significance Statement
The annual mean subduction/obduction rate is a term quantifying the large-scale irreversible downward/upward water transport between the mixed layer and the permanent pycnocline; these processes are crucially important for climate and the biogeochemical cycle in the oceans. However, the widely used classical Lagrangian method for calculating the annual subduction/obduction rate does not take the three-dimensional structure of ocean currents into consideration, which may induce errors in the destinations/sources of subducted/obducted water masses and the associated water properties. This study is focused on refining the three-dimensional features of subduction/obduction and providing a more accurate distribution of the annual subduction/obduction rate in the density space. In addition, the time window for subduction/obduction and the distribution of subducted/obducted water in the ocean interior are explored based on the SODA monthly mean climatology.
Abstract
A new three-dimensional method is proposed for calculating the annual mean subduction and obduction rate in the ocean and applied to the North Pacific Ocean. Due to the beta spiral, the subducted/obducted water at a given station can spread over/come from a wide range with different densities in the subsurface ocean. This new method can provide the three-dimensional feature of subduction/obduction and more accurate distribution of the annual subduction/obduction rate in density space. The spatial patterns of annual subduction/obduction rate obtained from both the classical and new methods are similar, although at individual stations the rate can be different; however, the new 3D method can greatly improve the density structure of subducted/obducted water mass. In spite of the assumption of idealized fluid in most previous studies, our analysis showed that subducted water masses can change their density due to diapycnal mixing, especially for water masses subducted at relatively shallow depths. In the North Pacific, the subduction process mainly takes place for about 1–2 months in most of the subtropical basin, while the time window for obduction is ∼100 days in the major obduction regions. Based on the SODA monthly mean climatology, the subducted/obducted water in the North Pacific is primarily distributed at depths of 80–120 m.
Significance Statement
The annual mean subduction/obduction rate is a term quantifying the large-scale irreversible downward/upward water transport between the mixed layer and the permanent pycnocline; these processes are crucially important for climate and the biogeochemical cycle in the oceans. However, the widely used classical Lagrangian method for calculating the annual subduction/obduction rate does not take the three-dimensional structure of ocean currents into consideration, which may induce errors in the destinations/sources of subducted/obducted water masses and the associated water properties. This study is focused on refining the three-dimensional features of subduction/obduction and providing a more accurate distribution of the annual subduction/obduction rate in the density space. In addition, the time window for subduction/obduction and the distribution of subducted/obducted water in the ocean interior are explored based on the SODA monthly mean climatology.
Abstract
In this paper, we revisit the problem of wind–wave interaction with emphasis on strong winds. For these events, it is assumed that nonlinearity is so large that the slope of the wind waves has reached a limiting steepness. Recent observations suggest that the drag decreases with wind in the strong wind speed regime. In this paper, we try to explain this. In the first step, we introduce a model for surface gravity waves and calculate explicitly the background roughness length from the original approach of Janssen. It is found that for young, steep wind sea, the background roughness length almost vanishes, giving a reduced drag. In addition, it is shown that for steep waves, the slowing down of the wind by waves is a nonlinear process; hence, the growth rate of the waves by wind depends in a nonlinear fashion on the wave spectrum. For strong winds, it is found that, as waves are typically steep, this nonlinear effect gives a further reduction of the wind input. As a consequence, in these extreme circumstances, the drag coefficient decreases with wind.
Abstract
In this paper, we revisit the problem of wind–wave interaction with emphasis on strong winds. For these events, it is assumed that nonlinearity is so large that the slope of the wind waves has reached a limiting steepness. Recent observations suggest that the drag decreases with wind in the strong wind speed regime. In this paper, we try to explain this. In the first step, we introduce a model for surface gravity waves and calculate explicitly the background roughness length from the original approach of Janssen. It is found that for young, steep wind sea, the background roughness length almost vanishes, giving a reduced drag. In addition, it is shown that for steep waves, the slowing down of the wind by waves is a nonlinear process; hence, the growth rate of the waves by wind depends in a nonlinear fashion on the wave spectrum. For strong winds, it is found that, as waves are typically steep, this nonlinear effect gives a further reduction of the wind input. As a consequence, in these extreme circumstances, the drag coefficient decreases with wind.
Abstract
The circulation within marginal seas subject to periodic winds, and their exchange with the open ocean, are explored using idealized numerical models and theory. This is motivated by the strong seasonal cycle in winds over the Nordic Seas and the exchange with the subpolar North Atlantic Ocean through the Denmark Strait and Faroe Bank Channel. Two distinct regimes are identified: an interior with closed f/h contours and a shallow shelf region that connects to the open ocean. The interior develops a strong oscillating along-topography circulation with weaker ageostrophic radial flows. The relative importance of the bottom Ekman layer and interior ageostrophic flows depends only on ωh/Cd , where ω is the forcing frequency, h is the bottom depth, and Cd is a linear bottom drag coefficient. The dynamics on the shelf are controlled by the frictional decay of coastal waves over an along-shelf scale Ly = f 0 LsHs /Cd , where f 0 is the Coriolis parameter, and Ls and Hs are the shelf width and depth. For Ly much less than the perimeter of the basin, the surface Ekman transport is provided primarily by overturning within the marginal sea and there is little exchange with the open ocean. For Ly on the order of the basin perimeter or larger, most of the Ekman transport is provided from outside the marginal sea with an opposite exchange through the deep part of the strait. This demonstrates a direct connection between the dynamics of coastal waves on the shelf and the exchange of deep waters through the strait, some of which is derived from below sill depth.
Significance Statement
The purpose of this study is to understand how winds over marginal seas, which are semienclosed bodies of water around the perimeter of ocean basins, can force an exchange of water, heat, salt, and other tracers through narrow straits between the marginal sea and the open ocean. Understanding this exchange is important because marginal seas are often regions of net heat, freshwater, and carbon exchange with the atmosphere. The present results identify a direct connection between processes along the coast of the marginal sea and the flow of waters through deep straits into the open ocean.
Abstract
The circulation within marginal seas subject to periodic winds, and their exchange with the open ocean, are explored using idealized numerical models and theory. This is motivated by the strong seasonal cycle in winds over the Nordic Seas and the exchange with the subpolar North Atlantic Ocean through the Denmark Strait and Faroe Bank Channel. Two distinct regimes are identified: an interior with closed f/h contours and a shallow shelf region that connects to the open ocean. The interior develops a strong oscillating along-topography circulation with weaker ageostrophic radial flows. The relative importance of the bottom Ekman layer and interior ageostrophic flows depends only on ωh/Cd , where ω is the forcing frequency, h is the bottom depth, and Cd is a linear bottom drag coefficient. The dynamics on the shelf are controlled by the frictional decay of coastal waves over an along-shelf scale Ly = f 0 LsHs /Cd , where f 0 is the Coriolis parameter, and Ls and Hs are the shelf width and depth. For Ly much less than the perimeter of the basin, the surface Ekman transport is provided primarily by overturning within the marginal sea and there is little exchange with the open ocean. For Ly on the order of the basin perimeter or larger, most of the Ekman transport is provided from outside the marginal sea with an opposite exchange through the deep part of the strait. This demonstrates a direct connection between the dynamics of coastal waves on the shelf and the exchange of deep waters through the strait, some of which is derived from below sill depth.
Significance Statement
The purpose of this study is to understand how winds over marginal seas, which are semienclosed bodies of water around the perimeter of ocean basins, can force an exchange of water, heat, salt, and other tracers through narrow straits between the marginal sea and the open ocean. Understanding this exchange is important because marginal seas are often regions of net heat, freshwater, and carbon exchange with the atmosphere. The present results identify a direct connection between processes along the coast of the marginal sea and the flow of waters through deep straits into the open ocean.
Abstract
The formation of a sharp oceanic front located south-southeast of Sri Lanka during the southwest monsoon is examined through in situ and remote observations and high-resolution model output. Remote sensing and model output reveal that the front extends approximately 200 km eastward from the southeast coast of Sri Lanka toward the southern Bay of Bengal (BoB). This annually occurring front is associated with the boundary between the southwest monsoon current with high-salinity water to the south, and a weak flow field comprised of relatively fresh BoB water to the north. The front contains a line of high chlorophyll extending from the coastal upwelling zone, often for several hundred kilometers. Elevated turbulent diffusivities ∼10−2 m2 s−1 along with large diapycnal fluxes of heat and salt were found within the front. The formation of the front and vertical transports are linked to local wind stress curl. Large vertical velocities (∼50 m day−1) indicate the importance of ageostrophic, submesoscale processes. To examine these processes, the Ertel potential vorticity (PV) was computed using the observations and numerical model output. The model output shows a ribbon of negative PV along the front between the coastal upwelling zone and two eddies (Sri Lanka Dome and an anticyclonic eddy) typically found in the southern BoB. PV estimates support the view that the flow is susceptible to submesoscale instabilities, which in turn generate high vertical velocities within the front. Frontal upwelling and heightened mixing show that the seasonal front is regionally important to linking the fresh surface water of the BoB with the Arabian Sea.
Significance Statement
Within the ocean, motions span extraordinarily wide ranges of sizes and time scales. In this study we focus on a narrow, intensified feature called a front. This front occurs in the southern Bay of Bengal during the summer monsoon and forms a boundary between fresher water to the north and saltier water to the south. Features such as this are difficult to study, however, by combining observations made from ships and satellites with output from numerical models of the ocean, we are able to better understand the front. This is important because fronts like the one studied here play a role in determining the pathways of heat within the ocean, which, in turn, may feedback into the atmosphere and weather patterns.
Abstract
The formation of a sharp oceanic front located south-southeast of Sri Lanka during the southwest monsoon is examined through in situ and remote observations and high-resolution model output. Remote sensing and model output reveal that the front extends approximately 200 km eastward from the southeast coast of Sri Lanka toward the southern Bay of Bengal (BoB). This annually occurring front is associated with the boundary between the southwest monsoon current with high-salinity water to the south, and a weak flow field comprised of relatively fresh BoB water to the north. The front contains a line of high chlorophyll extending from the coastal upwelling zone, often for several hundred kilometers. Elevated turbulent diffusivities ∼10−2 m2 s−1 along with large diapycnal fluxes of heat and salt were found within the front. The formation of the front and vertical transports are linked to local wind stress curl. Large vertical velocities (∼50 m day−1) indicate the importance of ageostrophic, submesoscale processes. To examine these processes, the Ertel potential vorticity (PV) was computed using the observations and numerical model output. The model output shows a ribbon of negative PV along the front between the coastal upwelling zone and two eddies (Sri Lanka Dome and an anticyclonic eddy) typically found in the southern BoB. PV estimates support the view that the flow is susceptible to submesoscale instabilities, which in turn generate high vertical velocities within the front. Frontal upwelling and heightened mixing show that the seasonal front is regionally important to linking the fresh surface water of the BoB with the Arabian Sea.
Significance Statement
Within the ocean, motions span extraordinarily wide ranges of sizes and time scales. In this study we focus on a narrow, intensified feature called a front. This front occurs in the southern Bay of Bengal during the summer monsoon and forms a boundary between fresher water to the north and saltier water to the south. Features such as this are difficult to study, however, by combining observations made from ships and satellites with output from numerical models of the ocean, we are able to better understand the front. This is important because fronts like the one studied here play a role in determining the pathways of heat within the ocean, which, in turn, may feedback into the atmosphere and weather patterns.
Abstract
Around Hopen Island, the satellite images and experiments with drifting buoys describe the movement of the drifting ice and depict tidally generated trapped motion. An analytical solution is applied to investigate the trapping phenomenon. A general solution is achieved by the superposition of the incident and reflected (scattered) waves for an elliptically shaped island above the critical latitude. The incident wave simulates the tidal wave propagation toward the island and its prominent feature, an amphidromic point located to the southeast from Hopen Island. The analytical solution for the reflected wave is constructed in elliptic coordinates. Tide amplitudes and cophase lines are analyzed in the island’s vicinity and compared to observations and numerical model results. A simulated drift of Lagrangian water particles constructed with the help of analytical solutions reproduces well the observed clockwise trapped motion of the drifting buoy near Hopen Island. Since the resonance may amplify the semidiurnal incident tide, we have also investigated the natural modes of water oscillations near the island. While this paper focuses on the details of the model used at the specific site of Hopen Island, a similar trapping analysis can be applied to circular or elliptic islands that have a small scale relative to the barotropic Rossby deformation radius.
Significance Statement
This study aims to understand how the semidiurnal tide propagates and generates strong currents near Hopen Island in the Barents Sea. The trapping of the semidiurnal (M2) tide around Hopen Island leads to an organized dipole structure in sea level, which rotates clockwise. The dipole generates maximum amplitudes of water surface elevation and the strong current near the south and north tips of the island. The abrupt sea level change induced by the dipole sets up often violent currents, which, together with drifting ice, can be dangerous for navigation. The strong tidal currents generate permanent clockwise circulation around the islands, which is essential for biological life and waste disposal as material disposed of near the islands will be trapped for an extended time. Our investigation elucidates the role of dipoles in the local enhancement of tides around the islands.
Abstract
Around Hopen Island, the satellite images and experiments with drifting buoys describe the movement of the drifting ice and depict tidally generated trapped motion. An analytical solution is applied to investigate the trapping phenomenon. A general solution is achieved by the superposition of the incident and reflected (scattered) waves for an elliptically shaped island above the critical latitude. The incident wave simulates the tidal wave propagation toward the island and its prominent feature, an amphidromic point located to the southeast from Hopen Island. The analytical solution for the reflected wave is constructed in elliptic coordinates. Tide amplitudes and cophase lines are analyzed in the island’s vicinity and compared to observations and numerical model results. A simulated drift of Lagrangian water particles constructed with the help of analytical solutions reproduces well the observed clockwise trapped motion of the drifting buoy near Hopen Island. Since the resonance may amplify the semidiurnal incident tide, we have also investigated the natural modes of water oscillations near the island. While this paper focuses on the details of the model used at the specific site of Hopen Island, a similar trapping analysis can be applied to circular or elliptic islands that have a small scale relative to the barotropic Rossby deformation radius.
Significance Statement
This study aims to understand how the semidiurnal tide propagates and generates strong currents near Hopen Island in the Barents Sea. The trapping of the semidiurnal (M2) tide around Hopen Island leads to an organized dipole structure in sea level, which rotates clockwise. The dipole generates maximum amplitudes of water surface elevation and the strong current near the south and north tips of the island. The abrupt sea level change induced by the dipole sets up often violent currents, which, together with drifting ice, can be dangerous for navigation. The strong tidal currents generate permanent clockwise circulation around the islands, which is essential for biological life and waste disposal as material disposed of near the islands will be trapped for an extended time. Our investigation elucidates the role of dipoles in the local enhancement of tides around the islands.
Abstract
Recent work has shown that, when nontraditional (NT) effects associated with the horizontal component of the Coriolis parameter are taken into account, equatorial waves (EWs) experience critical reflection when they reflect off the seafloor at the latitude where their frequency is equal to the inertial frequency. As a result, the vertical shear associated with the wave is strongly enhanced locally and results in bottom-intensified mixing. Using an off-the-shelf parameterization for mixing, these studies have shown that this process could play an important role in driving diapycnal upwelling in the abyssal ocean, but the specific mechanisms generating the mixing have not been studied yet. In this work, we address this limitation by running two-dimensional, high-resolution, nonhydrostatic simulations of the critical reflection of internal waves modified by NT effects. These simulations can resolve the instabilities triggered when the wave reflects off the bottom, allowing us to characterize the energy cascade to smaller scales and to estimate the mixing it generates. We find that shear instabilities drive elevated turbulent diffusivities between 10−1 and −10−3 m2 s−1 over a critical layer of 100–300 m thick. The shear instabilities result directly from the enhancement of kinetic energy in the reflected wave that is confined against the seafloor during the critical reflection process. Simultaneously, higher harmonics are generated and flux energy upward in the water column. These higher harmonics are unstable to parametric subharmonic instability, which absorbs their energy and drive enhanced dissipation above the critical layer, to a height of O(1000) m off the bottom. We show how these results depend on key elements of the EWs and of the medium and discuss the implementation of a parameterization of these effects in global ocean models.
Abstract
Recent work has shown that, when nontraditional (NT) effects associated with the horizontal component of the Coriolis parameter are taken into account, equatorial waves (EWs) experience critical reflection when they reflect off the seafloor at the latitude where their frequency is equal to the inertial frequency. As a result, the vertical shear associated with the wave is strongly enhanced locally and results in bottom-intensified mixing. Using an off-the-shelf parameterization for mixing, these studies have shown that this process could play an important role in driving diapycnal upwelling in the abyssal ocean, but the specific mechanisms generating the mixing have not been studied yet. In this work, we address this limitation by running two-dimensional, high-resolution, nonhydrostatic simulations of the critical reflection of internal waves modified by NT effects. These simulations can resolve the instabilities triggered when the wave reflects off the bottom, allowing us to characterize the energy cascade to smaller scales and to estimate the mixing it generates. We find that shear instabilities drive elevated turbulent diffusivities between 10−1 and −10−3 m2 s−1 over a critical layer of 100–300 m thick. The shear instabilities result directly from the enhancement of kinetic energy in the reflected wave that is confined against the seafloor during the critical reflection process. Simultaneously, higher harmonics are generated and flux energy upward in the water column. These higher harmonics are unstable to parametric subharmonic instability, which absorbs their energy and drive enhanced dissipation above the critical layer, to a height of O(1000) m off the bottom. We show how these results depend on key elements of the EWs and of the medium and discuss the implementation of a parameterization of these effects in global ocean models.
Abstract
The Gulf Stream (GS) is one of the strongest ocean currents on the planet. Eddy-rich resolution models are needed to properly represent the dynamics of the GS; however, kinetic energy (KE) can be in excess in these models if not dissipated efficiently. The question of how and how much energy is dissipated and in particular how it flows through ocean scales thus remains an important and largely unanswered question. Using a high-resolution (∼2 km) ocean model [Coastal and Regional Ocean Community (CROCO)], we characterize the spatial and temporal distribution of turbulent cascades in the GS based on a coarse-grained method. We show that the balanced flow is associated with an inverse cascade while the forward cascade is explained by ageostrophic advection associated with frontogenesis. Downscale fluxes are dominant at scales smaller than about 20 km near the surface and most intense at the GS North Wall. There is also strong seasonal variability in KE flux, with the forward cascade intensifying in winter and the inverse cascade later in spring. The forward cascade, which represents an interior route to dissipation, is compared with both numerical and boundary dissipation processes. The contribution of interior dissipation is an order of magnitude smaller than that of the other energy sinks. We thus evaluate the sensitivity of horizontal momentum advection schemes on energy dissipation and show that the decrease in numerical dissipation in a high-order scheme leads to an increase in dissipation at the boundaries, not in the downscale flux.
Abstract
The Gulf Stream (GS) is one of the strongest ocean currents on the planet. Eddy-rich resolution models are needed to properly represent the dynamics of the GS; however, kinetic energy (KE) can be in excess in these models if not dissipated efficiently. The question of how and how much energy is dissipated and in particular how it flows through ocean scales thus remains an important and largely unanswered question. Using a high-resolution (∼2 km) ocean model [Coastal and Regional Ocean Community (CROCO)], we characterize the spatial and temporal distribution of turbulent cascades in the GS based on a coarse-grained method. We show that the balanced flow is associated with an inverse cascade while the forward cascade is explained by ageostrophic advection associated with frontogenesis. Downscale fluxes are dominant at scales smaller than about 20 km near the surface and most intense at the GS North Wall. There is also strong seasonal variability in KE flux, with the forward cascade intensifying in winter and the inverse cascade later in spring. The forward cascade, which represents an interior route to dissipation, is compared with both numerical and boundary dissipation processes. The contribution of interior dissipation is an order of magnitude smaller than that of the other energy sinks. We thus evaluate the sensitivity of horizontal momentum advection schemes on energy dissipation and show that the decrease in numerical dissipation in a high-order scheme leads to an increase in dissipation at the boundaries, not in the downscale flux.
Abstract
Long waves play an important role in coastal inundation and shoreline and dune erosion, requiring a detailed understanding of their evolution in nearshore regions and interaction with shorelines. While their generation and dissipation mechanisms are relatively well understood, there are fewer studies describing how reflection processes govern their propagation in the nearshore. We propose a new approach, accounting for partial reflections, which leads to an analytical solution to the free wave linear shallow-water equations at the wave-group scale over general varying bathymetry. The approach, supported by numerical modeling, agrees with the classic Bessel standing solution for a plane sloping beach but extends the solution to arbitrary alongshore uniform bathymetry profiles and decomposes it into incoming and outgoing wave components, which are a combination of successively partially reflected waves lagging each other. The phase lags introduced by partial reflections modify the wave amplitude and explain why Green’s law, which describes the wave growth of free waves with decreasing depth, breaks down in very shallow water. This reveals that the wave amplitude at the shoreline is highly dependent on partial reflections. Consistent with laboratory and field observations, our analytical model predicts a reflection coefficient that increases and is highly correlated with the normalized bed slope (bed slope relative to wave frequency). Our approach shows that partial reflections occurring due to depth variations in the nearshore are responsible for the relationship between the normalized bed slope and the amplitude of long waves in the nearshore, with direct implications for determining long-wave amplitudes at the shoreline and wave runup.
Abstract
Long waves play an important role in coastal inundation and shoreline and dune erosion, requiring a detailed understanding of their evolution in nearshore regions and interaction with shorelines. While their generation and dissipation mechanisms are relatively well understood, there are fewer studies describing how reflection processes govern their propagation in the nearshore. We propose a new approach, accounting for partial reflections, which leads to an analytical solution to the free wave linear shallow-water equations at the wave-group scale over general varying bathymetry. The approach, supported by numerical modeling, agrees with the classic Bessel standing solution for a plane sloping beach but extends the solution to arbitrary alongshore uniform bathymetry profiles and decomposes it into incoming and outgoing wave components, which are a combination of successively partially reflected waves lagging each other. The phase lags introduced by partial reflections modify the wave amplitude and explain why Green’s law, which describes the wave growth of free waves with decreasing depth, breaks down in very shallow water. This reveals that the wave amplitude at the shoreline is highly dependent on partial reflections. Consistent with laboratory and field observations, our analytical model predicts a reflection coefficient that increases and is highly correlated with the normalized bed slope (bed slope relative to wave frequency). Our approach shows that partial reflections occurring due to depth variations in the nearshore are responsible for the relationship between the normalized bed slope and the amplitude of long waves in the nearshore, with direct implications for determining long-wave amplitudes at the shoreline and wave runup.
Abstract
Mixing along sloping isopycnals plays a key role in the transport and uptake of heat and carbon by the ocean. This mixing is quantified by a lateral diffusivity, which can be measured by tracking the lateral spreading of point release tracer patches. We present a definition for the area of a tracer patch, the time derivative of which provides the lateral diffusivity. To accurately estimate the diffusivity, an ensemble mean concentration field of many tracer release experiments is required. We use numerical experiments to quantify how accurately the “true” lateral diffusivity (obtained from the ensemble mean concentration field) can be estimated from a single tracer release experiment (one ensemble member). To simulate observational campaigns, we also estimate the diffusivity from a single tracer release that is spatially and/or temporally subsampled, quantifying how the error between the estimated diffusivity and the true diffusivity grows as this sampling resolution worsens. We perform these numerical experiments in a two-layer quasigeostrophic model of turbulent flow on a β plane, using an ensemble of 50 passive tracer release experiments, each initialized as a 2D Gaussian but with differing realizations of the turbulent flow. We find that the diffusivity estimates from the single tracer releases have a relative root-mean-square error (RMSE) of 1.43% from the true diffusivity. Subsampling a single tracer release experiment every 956 km increases the relative RMSE from the true diffusivity to 3.1%; also subsampling every 277 days raises this figure to 6.5%.
Abstract
Mixing along sloping isopycnals plays a key role in the transport and uptake of heat and carbon by the ocean. This mixing is quantified by a lateral diffusivity, which can be measured by tracking the lateral spreading of point release tracer patches. We present a definition for the area of a tracer patch, the time derivative of which provides the lateral diffusivity. To accurately estimate the diffusivity, an ensemble mean concentration field of many tracer release experiments is required. We use numerical experiments to quantify how accurately the “true” lateral diffusivity (obtained from the ensemble mean concentration field) can be estimated from a single tracer release experiment (one ensemble member). To simulate observational campaigns, we also estimate the diffusivity from a single tracer release that is spatially and/or temporally subsampled, quantifying how the error between the estimated diffusivity and the true diffusivity grows as this sampling resolution worsens. We perform these numerical experiments in a two-layer quasigeostrophic model of turbulent flow on a β plane, using an ensemble of 50 passive tracer release experiments, each initialized as a 2D Gaussian but with differing realizations of the turbulent flow. We find that the diffusivity estimates from the single tracer releases have a relative root-mean-square error (RMSE) of 1.43% from the true diffusivity. Subsampling a single tracer release experiment every 956 km increases the relative RMSE from the true diffusivity to 3.1%; also subsampling every 277 days raises this figure to 6.5%.
