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- Author or Editor: Amy F. Waterhouse x
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Abstract
Internal tides, generated by barotropic tides flowing over rough topography, are a primary source of energy into the internal wave field. As internal tides propagate away from generation sites, they can dephase from the equilibrium tide, becoming nonstationary. Here, we examine how low-frequency quasigeostrophic background flows scatter and dephase internal tides in the Tasman Sea. We demonstrate that a semi-idealized internal tide model [the Coupled-Mode Shallow Water model (CSW)] must include two background flow effects to replicate the in situ internal tide energy fluxes observed during the Tasmanian Internal Tide Beam Experiment (TBeam). The first effect is internal tide advection by the background flow, which strongly depends on the spatial scale of the background flow and is largest at the smaller scales resolved in the background flow model (i.e., 50–400 km). Internal tide advection is also shown to scatter internal tides from vertical mode-1 to mode-2 at a rate of about 1 mW m−2. The second effect is internal tide refraction due to background flow perturbations to the mode-1 eigenspeed. This effect primarily dephases the internal tide, attenuating stationary energy at a rate of up to 5 mW m−2. Detailed analysis of the stationary internal tide momentum and energy balances indicate that background flow effects on the stationary internal tide can be accurately parameterized using an eddy diffusivity derived from a 1D random walk model. In summary, the results identify an efficient way to model the stationary internal tide and quantify its loss of stationarity.
Abstract
Internal tides, generated by barotropic tides flowing over rough topography, are a primary source of energy into the internal wave field. As internal tides propagate away from generation sites, they can dephase from the equilibrium tide, becoming nonstationary. Here, we examine how low-frequency quasigeostrophic background flows scatter and dephase internal tides in the Tasman Sea. We demonstrate that a semi-idealized internal tide model [the Coupled-Mode Shallow Water model (CSW)] must include two background flow effects to replicate the in situ internal tide energy fluxes observed during the Tasmanian Internal Tide Beam Experiment (TBeam). The first effect is internal tide advection by the background flow, which strongly depends on the spatial scale of the background flow and is largest at the smaller scales resolved in the background flow model (i.e., 50–400 km). Internal tide advection is also shown to scatter internal tides from vertical mode-1 to mode-2 at a rate of about 1 mW m−2. The second effect is internal tide refraction due to background flow perturbations to the mode-1 eigenspeed. This effect primarily dephases the internal tide, attenuating stationary energy at a rate of up to 5 mW m−2. Detailed analysis of the stationary internal tide momentum and energy balances indicate that background flow effects on the stationary internal tide can be accurately parameterized using an eddy diffusivity derived from a 1D random walk model. In summary, the results identify an efficient way to model the stationary internal tide and quantify its loss of stationarity.
Abstract
The spatial structure of tidal amplitude and phase in a simplified system of connected estuaries, an idealized version of Florida’s Intracoastal Waterway, is analyzed with a linear analytical model. This model includes friction, the earth’s rotation, and variable bathymetry. It is driven at the connection with the ocean by a co-oscillating tide. Model results compare well with observations of pressure and currents in a section of the Intracoastal Waterway on the east coast of Florida. The comparison suggests that the waterway is highly frictional, causing the amplitude of the water elevation and tidal velocity to decrease away from the inlets to a minimum in the middle of the waterway. The local phase relationship between velocity and water elevation changed nonlinearly from 90° with no friction to 45° with maximum friction. In moderately to highly frictional basins, the phase lag was consistently less than 45°.
Abstract
The spatial structure of tidal amplitude and phase in a simplified system of connected estuaries, an idealized version of Florida’s Intracoastal Waterway, is analyzed with a linear analytical model. This model includes friction, the earth’s rotation, and variable bathymetry. It is driven at the connection with the ocean by a co-oscillating tide. Model results compare well with observations of pressure and currents in a section of the Intracoastal Waterway on the east coast of Florida. The comparison suggests that the waterway is highly frictional, causing the amplitude of the water elevation and tidal velocity to decrease away from the inlets to a minimum in the middle of the waterway. The local phase relationship between velocity and water elevation changed nonlinearly from 90° with no friction to 45° with maximum friction. In moderately to highly frictional basins, the phase lag was consistently less than 45°.
Abstract
We describe the spatiotemporal variability and vertical structure of turbulent Reynolds stresses (RSs) in a stratified inner shelf with an energetic internal wave climate. The RSs are estimated from direct measurements of velocity variance derived from bottom-mounted acoustic Doppler current profilers. We link the RSs to different physical processes, namely, internal bores, midwater shear instabilities within vertical shear events related to wind-driven subtidal along-shelf currents, and nonturbulent stresses related to incoming nonlinear internal wave (NLIW) trains. The typical RS magnitudes are O(0.01) Pa for background conditions, with diurnal pulses of O(0.1–1) Pa, and O(1) Pa for the NLIW stresses. A NLIW train is observed to produce a depth-averaged vertical stress divergence sufficient to accelerate water 20 cm s−1 in 1 h, suggesting NLIWs may also be important contributors to the depth-averaged momentum budget. The subtidal stresses show significant periodic variability and are O(0.1) Pa. Conditionally averaged velocity and RS profiles for northward/southward flow provide evidence for downgradient turbulent momentum fluxes, but also indicate departures from this expected regime. Estimates of the terms in the depth-averaged momentum equation suggest that the vertical divergence of the RSs are important terms in both the cross-shelf and along-shelf directions, with geostrophy also present at leading-order in the cross-shelf momentum balance. Among other conclusions, the results highlight that internal bores and shoaling NLIWs may also be important dynamical players in other inner shelves with energetic internal waves.
Abstract
We describe the spatiotemporal variability and vertical structure of turbulent Reynolds stresses (RSs) in a stratified inner shelf with an energetic internal wave climate. The RSs are estimated from direct measurements of velocity variance derived from bottom-mounted acoustic Doppler current profilers. We link the RSs to different physical processes, namely, internal bores, midwater shear instabilities within vertical shear events related to wind-driven subtidal along-shelf currents, and nonturbulent stresses related to incoming nonlinear internal wave (NLIW) trains. The typical RS magnitudes are O(0.01) Pa for background conditions, with diurnal pulses of O(0.1–1) Pa, and O(1) Pa for the NLIW stresses. A NLIW train is observed to produce a depth-averaged vertical stress divergence sufficient to accelerate water 20 cm s−1 in 1 h, suggesting NLIWs may also be important contributors to the depth-averaged momentum budget. The subtidal stresses show significant periodic variability and are O(0.1) Pa. Conditionally averaged velocity and RS profiles for northward/southward flow provide evidence for downgradient turbulent momentum fluxes, but also indicate departures from this expected regime. Estimates of the terms in the depth-averaged momentum equation suggest that the vertical divergence of the RSs are important terms in both the cross-shelf and along-shelf directions, with geostrophy also present at leading-order in the cross-shelf momentum balance. Among other conclusions, the results highlight that internal bores and shoaling NLIWs may also be important dynamical players in other inner shelves with energetic internal waves.
Abstract
Finescale methods are currently being applied to estimate the mean turbulent dissipation rate and diffusivity on regional and global scales. This study evaluates finescale estimates derived from isopycnal strain by comparing them with average microstructure profiles from six diverse environments including the equator, above ridges, near seamounts, and in strong currents. The finescale strain estimates are derived from at least 10 nearby Argo profiles (generally <60 km distant) with no temporal restrictions, including measurements separated by seasons or decades. The absence of temporal limits is reasonable in these cases, since the authors find the dissipation rate is steady over seasonal time scales at the latitudes being considered (0°–30° and 40°–50°). In contrast, a seasonal cycle of a factor of 2–5 in the upper 1000 m is found under storm tracks (30°–40°) in both hemispheres. Agreement between the mean dissipation rate calculated using Argo profiles and mean from microstructure profiles is within a factor of 2–3 for 96% of the comparisons. This is both congruous with the physical scaling underlying the finescale parameterization and indicates that the method is effective for estimating the regional mean dissipation rates in the open ocean.
Abstract
Finescale methods are currently being applied to estimate the mean turbulent dissipation rate and diffusivity on regional and global scales. This study evaluates finescale estimates derived from isopycnal strain by comparing them with average microstructure profiles from six diverse environments including the equator, above ridges, near seamounts, and in strong currents. The finescale strain estimates are derived from at least 10 nearby Argo profiles (generally <60 km distant) with no temporal restrictions, including measurements separated by seasons or decades. The absence of temporal limits is reasonable in these cases, since the authors find the dissipation rate is steady over seasonal time scales at the latitudes being considered (0°–30° and 40°–50°). In contrast, a seasonal cycle of a factor of 2–5 in the upper 1000 m is found under storm tracks (30°–40°) in both hemispheres. Agreement between the mean dissipation rate calculated using Argo profiles and mean from microstructure profiles is within a factor of 2–3 for 96% of the comparisons. This is both congruous with the physical scaling underlying the finescale parameterization and indicates that the method is effective for estimating the regional mean dissipation rates in the open ocean.
Abstract
The La Jolla Canyon System (LJCS) is a small, steep, shelf-incising canyon offshore of San Diego, California. Observations conducted in the fall of 2016 capture the dynamics of internal tides and turbulence patterns. Semidiurnal (D2) energy flux was oriented up-canyon; 62% ± 20% of the signal was contained in mode 1 at the offshore mooring. The observed mode-1 D2 tide was partly standing based on the ratio of group speed times energy cgE and energy flux F. Enhanced dissipation occurred near the canyon head at middepths associated with elevated strain arising from the standing wave pattern. Modes 2–5 were progressive, and energy fluxes associated with these modes were oriented down-canyon, suggesting that incident mode-1 waves were back-reflected and scattered. Flux integrated over all modes across a given canyon cross section was always onshore and generally decreased moving shoreward (from 240 ± 15 to 5 ± 0.3 kW), with a 50-kW increase in flux occurring on a section inshore of the canyon’s major bend, possibly due to reflection of incident waves from the supercritical sidewalls of the bend. Flux convergence from canyon mouth to head was balanced by the volume-integrated dissipation observed. By comparing energy budgets from a global compendium of canyons with sufficient observations (six in total), a similar balance was found. One exception was Juan de Fuca Canyon, where such a balance was not found, likely due to its nontidal flows. These results suggest that internal tides incident at the mouth of a canyon system are dissipated therein rather than leaking over the sidewalls or siphoning energy to other wave frequencies.
Abstract
The La Jolla Canyon System (LJCS) is a small, steep, shelf-incising canyon offshore of San Diego, California. Observations conducted in the fall of 2016 capture the dynamics of internal tides and turbulence patterns. Semidiurnal (D2) energy flux was oriented up-canyon; 62% ± 20% of the signal was contained in mode 1 at the offshore mooring. The observed mode-1 D2 tide was partly standing based on the ratio of group speed times energy cgE and energy flux F. Enhanced dissipation occurred near the canyon head at middepths associated with elevated strain arising from the standing wave pattern. Modes 2–5 were progressive, and energy fluxes associated with these modes were oriented down-canyon, suggesting that incident mode-1 waves were back-reflected and scattered. Flux integrated over all modes across a given canyon cross section was always onshore and generally decreased moving shoreward (from 240 ± 15 to 5 ± 0.3 kW), with a 50-kW increase in flux occurring on a section inshore of the canyon’s major bend, possibly due to reflection of incident waves from the supercritical sidewalls of the bend. Flux convergence from canyon mouth to head was balanced by the volume-integrated dissipation observed. By comparing energy budgets from a global compendium of canyons with sufficient observations (six in total), a similar balance was found. One exception was Juan de Fuca Canyon, where such a balance was not found, likely due to its nontidal flows. These results suggest that internal tides incident at the mouth of a canyon system are dissipated therein rather than leaking over the sidewalls or siphoning energy to other wave frequencies.
Abstract
Observations from Eel Canyon, located on the north coast of California, show that elevated turbulence in the full water column arises from the convergence of remotely generated internal wave energy. The incoming semidiurnal and bottom-trapped diurnal internal tides generate complex interference patterns. The semidiurnal internal tide sets up a partly standing wave within the canyon due to reflection at the canyon head, dissipating all of its energy within the canyon. Dissipation in the near bottom is associated with the diurnal trapped tide, while midwater isopycnal shear and strain is associated with the semidiurnal tide. Dissipation is elevated up to 600 m off the bottom, in contrast to observations over the flat continental shelf where dissipation occurs closer to the topography. Slope canyons are sinks for internal wave energy and may have important influences on the global distribution of tidally driven mixing.
Abstract
Observations from Eel Canyon, located on the north coast of California, show that elevated turbulence in the full water column arises from the convergence of remotely generated internal wave energy. The incoming semidiurnal and bottom-trapped diurnal internal tides generate complex interference patterns. The semidiurnal internal tide sets up a partly standing wave within the canyon due to reflection at the canyon head, dissipating all of its energy within the canyon. Dissipation in the near bottom is associated with the diurnal trapped tide, while midwater isopycnal shear and strain is associated with the semidiurnal tide. Dissipation is elevated up to 600 m off the bottom, in contrast to observations over the flat continental shelf where dissipation occurs closer to the topography. Slope canyons are sinks for internal wave energy and may have important influences on the global distribution of tidally driven mixing.
Abstract
Low-mode internal tides, a dominant part of the internal wave spectrum, carry energy over large distances, yet the ultimate fate of this energy is unknown. Internal tides in the Tasman Sea are generated at Macquarie Ridge, south of New Zealand, and propagate northwest as a focused beam before impinging on the Tasmanian continental slope. In situ observations from the Tasman Sea capture synoptic measurements of the incident semidiurnal mode-1 internal-tide, which has an observed wavelength of 183 km and surface displacement of approximately 1 cm. Plane-wave fits to in situ and altimetric estimates of surface displacement agree to within a measurement uncertainty of 0.3 cm, which is the same order of magnitude as the nonstationary (not phase locked) mode-1 tide observed over a 40-day mooring deployment. Stationary energy flux, estimated from a plane-wave fit to the in situ observations, is directed toward Tasmania with a magnitude of 3.4 ± 1.4 kW m−1, consistent with a satellite estimate of 3.9 ± 2.2 kW m−1. Approximately 90% of the time-mean energy flux is due to the stationary tide. However, nonstationary velocity and pressure, which are typically 1/4 the amplitude of the stationary components, sometimes lead to instantaneous energy fluxes that are double or half of the stationary energy flux, overwhelming any spring–neap variability. Despite strong winds and intermittent near-inertial currents, the parameterized turbulent-kinetic-energy dissipation rate is small (i.e., 10−10 W kg−1) below the near surface and observations of mode-1 internal tide energy-flux convergence are indistinguishable from zero (i.e., the confidence intervals include zero), indicating little decay of the mode-1 internal tide within the Tasman Sea.
Abstract
Low-mode internal tides, a dominant part of the internal wave spectrum, carry energy over large distances, yet the ultimate fate of this energy is unknown. Internal tides in the Tasman Sea are generated at Macquarie Ridge, south of New Zealand, and propagate northwest as a focused beam before impinging on the Tasmanian continental slope. In situ observations from the Tasman Sea capture synoptic measurements of the incident semidiurnal mode-1 internal-tide, which has an observed wavelength of 183 km and surface displacement of approximately 1 cm. Plane-wave fits to in situ and altimetric estimates of surface displacement agree to within a measurement uncertainty of 0.3 cm, which is the same order of magnitude as the nonstationary (not phase locked) mode-1 tide observed over a 40-day mooring deployment. Stationary energy flux, estimated from a plane-wave fit to the in situ observations, is directed toward Tasmania with a magnitude of 3.4 ± 1.4 kW m−1, consistent with a satellite estimate of 3.9 ± 2.2 kW m−1. Approximately 90% of the time-mean energy flux is due to the stationary tide. However, nonstationary velocity and pressure, which are typically 1/4 the amplitude of the stationary components, sometimes lead to instantaneous energy fluxes that are double or half of the stationary energy flux, overwhelming any spring–neap variability. Despite strong winds and intermittent near-inertial currents, the parameterized turbulent-kinetic-energy dissipation rate is small (i.e., 10−10 W kg−1) below the near surface and observations of mode-1 internal tide energy-flux convergence are indistinguishable from zero (i.e., the confidence intervals include zero), indicating little decay of the mode-1 internal tide within the Tasman Sea.
Abstract
Lateral submesoscale processes and their influence on vertical stratification at shallow salinity fronts in the central Bay of Bengal during the winter monsoon are explored using high-resolution data from a cruise in November 2013. The observations are from a radiator survey centered at a salinity-controlled density front, embedded in a zone of moderate mesoscale strain (0.15 times the Coriolis parameter) and forced by winds with a downfront orientation. Below a thin mixed layer, often ≤10 m, the analysis shows several dynamical signatures indicative of submesoscale processes: (i) negative Ertel potential vorticity (PV); (ii) low-PV anomalies with O(1–10) km lateral extent, where the vorticity estimated on isopycnals and the isopycnal thickness are tightly coupled, varying in lockstep to yield low PV; (iii) flow conditions susceptible to forced symmetric instability (FSI) or bearing the imprint of earlier FSI events; (iv) negative lateral gradients in the absolute momentum field (inertial instability); and (v) strong contribution from differential sheared advection at O(1) km scales to the growth rate of the depth-averaged stratification. The findings here show one-dimensional vertical processes alone cannot explain the vertical stratification and its lateral variability over O(1–10) km scales at the radiator survey.
Abstract
Lateral submesoscale processes and their influence on vertical stratification at shallow salinity fronts in the central Bay of Bengal during the winter monsoon are explored using high-resolution data from a cruise in November 2013. The observations are from a radiator survey centered at a salinity-controlled density front, embedded in a zone of moderate mesoscale strain (0.15 times the Coriolis parameter) and forced by winds with a downfront orientation. Below a thin mixed layer, often ≤10 m, the analysis shows several dynamical signatures indicative of submesoscale processes: (i) negative Ertel potential vorticity (PV); (ii) low-PV anomalies with O(1–10) km lateral extent, where the vorticity estimated on isopycnals and the isopycnal thickness are tightly coupled, varying in lockstep to yield low PV; (iii) flow conditions susceptible to forced symmetric instability (FSI) or bearing the imprint of earlier FSI events; (iv) negative lateral gradients in the absolute momentum field (inertial instability); and (v) strong contribution from differential sheared advection at O(1) km scales to the growth rate of the depth-averaged stratification. The findings here show one-dimensional vertical processes alone cannot explain the vertical stratification and its lateral variability over O(1–10) km scales at the radiator survey.
Abstract
Internal waves are predominantly generated by winds, tide–topography interactions, and balanced flow–topography interactions. Observations of vertical shear of horizontal velocity (uz
, υz
) from lowered acoustic Doppler current profilers (LADCP) profiles conducted during GO-SHIP hydrographic surveys, as well as vessel-mounted sonars, are used to interpret these signals. Vertical directionality of intermediate-wavenumber [
Abstract
Internal waves are predominantly generated by winds, tide–topography interactions, and balanced flow–topography interactions. Observations of vertical shear of horizontal velocity (uz
, υz
) from lowered acoustic Doppler current profilers (LADCP) profiles conducted during GO-SHIP hydrographic surveys, as well as vessel-mounted sonars, are used to interpret these signals. Vertical directionality of intermediate-wavenumber [
Abstract
Here, we develop a framework for understanding the observations presented in Part I. In this framework, the internal tide saturates as it shoals as a result of amplitude limitation with decreasing water depth H. From this framework evolves estimates of averaged energetics of the internal tide; specifically, energy ⟨APE⟩, energy flux ⟨F E ⟩, and energy flux divergence ∂ x ⟨F E ⟩. Since we observe that dissipation ⟨D⟩ ≈ ∂ x ⟨F E ⟩, we also interpret our estimate of ∂ x ⟨F E ⟩ as ⟨D⟩. These estimates represent a parameterization of the energy in the internal tide as it saturates over the inner continental shelf. The parameterization depends solely on depth-mean stratification and bathymetry. A summary result is that the cross-shelf depth dependencies of ⟨APE⟩, ⟨F E ⟩, and ∂ x ⟨F E ⟩ are analogous to those for shoaling surface gravity waves in the surf zone, suggesting that the inner shelf is the surf zone for the internal tide. A test of our simple parameterization against a range of datasets suggests that it is broadly applicable.
Abstract
Here, we develop a framework for understanding the observations presented in Part I. In this framework, the internal tide saturates as it shoals as a result of amplitude limitation with decreasing water depth H. From this framework evolves estimates of averaged energetics of the internal tide; specifically, energy ⟨APE⟩, energy flux ⟨F E ⟩, and energy flux divergence ∂ x ⟨F E ⟩. Since we observe that dissipation ⟨D⟩ ≈ ∂ x ⟨F E ⟩, we also interpret our estimate of ∂ x ⟨F E ⟩ as ⟨D⟩. These estimates represent a parameterization of the energy in the internal tide as it saturates over the inner continental shelf. The parameterization depends solely on depth-mean stratification and bathymetry. A summary result is that the cross-shelf depth dependencies of ⟨APE⟩, ⟨F E ⟩, and ∂ x ⟨F E ⟩ are analogous to those for shoaling surface gravity waves in the surf zone, suggesting that the inner shelf is the surf zone for the internal tide. A test of our simple parameterization against a range of datasets suggests that it is broadly applicable.
