Internal Tide Generation Research Articles

Numerical Simulation of the Generation and Evolution of Internal Tides and Solitary Waves at Sofala Shelf Break

Numerical Simulation of the Generation and Evolution of Internal Tides and Solitary Waves at Sofala Shelf Break

Energetics of Semidiurnal Internal Tides in the Andaman Sea

AbstractA detailed energetic estimate of the barotropic and baroclinic semidiurnal internal tides over the Andaman Sea is performed by using the three‐dimensional Massachusetts Institute of Technology general circulation model. Model‐simulated currents and density fields are validated using in situ observations with high temporal resolution from a buoy located at 10.5°N, 94°E. The generation and dissipation regions of internal tides and their propagation in the domain are identified by quantifying the distribution of total tidal energy among generation, radiation, and dissipation. The model simulation suggests that the internal tides are mainly generated in the north of Sumatra coast, in the Sombrero channel, south of the Car Nicobar Island, and north of the Andaman Island. From these generation sites, a portion of the energy propagates into the Andaman Sea and the remainder propagates toward the southern Bay of Bengal. The depth‐integrated baroclinic energy fluxes are found to be a maximum of ~30 kW/m at the major generation sites in the domain. The model‐estimated energy dissipation rates suggest that the maximum amount of energy dissipates near the generation sites themselves. In the region north of the Sumatra coast, almost 87% of the barotropic energy is converted into baroclinic energy and 23% (0.91 GW) of the converted baroclinic energy is ultimately radiated out from the generation sites. The barotropic‐to‐baroclinic conversion rate over the whole domain is estimated to be ~23 GW, out of which, a major part ~18 GW (80%) dissipates near the generation sites. This reveals that the local dissipation of baroclinic energy dominates in the Andaman Sea.

Observations of semidiurnal internal tides on the Patagonian Shelf

The Patagonian Shelf in the western South Atlantic is known for strong semidiurnal tides and intense seasonal stratification. Both observations and models reveal substantial cross-isobath tidal energy fluxes at the shelf break between 44 and 41°S. These conditions are potentially favorable for internal wave generation, but global tidal models do not show significant baroclinic energy radiation from this region. A possible explanation for the lack of offshore radiation is explored through analyzing the data from two moorings deployed along the Patagonian shelf break. At both mooring sites, the velocity spectra reveal strong baroclinic oscillations at the semidiurnal frequency with a vertical structure resembling the first mode. Unlike barotropic tides with strong cross-isobath polarization, the baroclinic tidal ellipses are less polarized. Internal tide propagation is delineated by estimating a proxy for the baroclinic energy flux, which is the product of band-passed baroclinic velocity near the bottom and temperature at mid-depth. The proxy vectors show that internal tide propagation is highly sensitive to the strength of the Malvinas Current propagating northward over the continental slope. When the mean current becomes stronger, the proxy vectors turn southward, pointing upstream of the Malvinas Current direction. It is concluded that the presence of an energetic western boundary current reduces the offshore radiation of internal tides, likely due to the wave refraction on the mean current.

Internal Tide Generation at the Vitória‐Trindade Ridge, South Atlantic Ocean

AbstractSea surface height data from multiple satellite altimetric missions are analyzed in order to investigate the surface manifestation of internal tides generated at the Vitória‐Trindade Ridge (VTR), in the western South Atlantic Ocean. The VTR is formed by a sequence of submerged seamounts disposed in a west‐east alignment around 20.5°S, extending for over 1,000 km from the Brazilian continental margin to the Trindade and Martim Vaz islands. Point‐wise harmonic analysis of the along‐track sea surface height data, combined with a two‐dimensional plane wave fitting at selected subregions, depicts well‐organized northbound and southbound wave beams radiating from the VTR, and propagating as far as ~1,000 km from the ridge. Energy convergence is observed at a focal point located circa 300 km south of the VTR, associated with a lens effect due to the arc‐shaped ridge. Wavenumber spectra show highest energy associated with wavelengths of 140 and 70 km, close to the theoretical values expected for the first and second baroclinic modes, respectively. Energy fluxes for the mode 1 principal lunar (M2) constituent reach values of 2 to 3 kW/m for the southward beams and 1 kW/m north of the VTR. Judging from its surface signature, the VTR appears to be the most significant internal tide generation site in the western South Atlantic.

ВНУТРЕННИЙ ПРИЛИВ НА ПЛАТО САНТОС

We analyze internal tides over the Santos Plateau in the South Atlantic. The study is based on the measurements of temperature and currents on the line of moorings normal to the South America coast in the latitudinal band between 28°S and 31°S. The moorings were deployed at distances between 25 and 888 km (from the 500 m isobath) southeast of the continental slope. The instruments were set at 900 m. Numerical modeling revealed the properties of internal tides (amplitudes, wavelength, and decay of amplitudes) along the line of their propagation from the continental slope. The amplitudes of internal tide decrease from the continental slope in the direction to the Vema Channel from 36 m to 15 m. The densities of the energy of tidal internal waves were calculated from the semidiurnal tidal components of current and temperature time series taking into account the vertical gradients of temperature and the Brunt-Vaisala frequency. Decay of the energy of internal tide occurs according to an inverse power law. Numerical modeling of the generation and propagation of internal tides reveals that beams of internal tides are formed near the continental slope. The energy decay based on modeling is similar to the measured data.

The Lifecycle of Semidiurnal Internal Tides over the Northern Mid-Atlantic Ridge

AbstractThe life cycle of semidiurnal internal tides over the Mid-Atlantic Ridge (MAR) sector south of the Azores is investigated using in situ, a high-resolution mooring and microstructure profiler, and satellite data, in combination with a theoretical model of barotropic-to-baroclinic tidal energy conversion. The mooring analysis reveals that the internal tide horizontal energy flux is dominated by mode 1 and that energy density is more distributed among modes 1–10. Most modes are compatible with an interpretation in terms of standing internal tides, suggesting that they result from interactions between waves generated over the MAR. Internal tide energy is thus concentrated above the ridge and is eventually available for local diapycnal mixing, as endorsed by the elevated rates of turbulent energy dissipation ε estimated from microstructure measurements. A spring–neap modulation of energy density on the MAR is found to originate from the remote generation and radiation of strong mode-1 internal tides from the Atlantis-Meteor Seamount Complex. Similar fortnightly variability of a factor of 2 is observed in ε, but this signal’s origin cannot be determined unambiguously. A regional tidal energy budget highlights the significance of high-mode generation, with 81% of the energy lost by the barotropic tide being converted into modes >1 and only 9% into mode 1. This has important implications for the fraction (q) of local dissipation to the total energy conversion, which is regionally estimated to be ~0.5. This result is in stark contrast with the Hawaiian Ridge system, where the radiation of mode-1 internal tides accounts for 30% of the regional energy conversion, and q < 0.25.

Changes in Bottom Water Physical Properties Above the Mid‐Atlantic Ridge Flank in the Brazil Basin

AbstractWarming of abyssal waters in recent decades has been widely documented around the global ocean. Here repeat hydrographic data collected in 1997 and 2014 near a deep fracture zone canyon in the eastern Brazil Basin are used to quantify the long‐term change. Significant changes are found in the Antarctic Bottom Water (AABW) within the canyon. The AABW in 2014 was warmer (0.08 ± 0.06 ), saltier (0.01 ± 0.005), and less dense (0.005 ± 0.004 ) than in 1997. In contrast, the change in the North Atlantic Deep Water has complicated spatial structure and is almost indistinguishable from zero at 95% confidence. The resulting divergence in vertical displacement of the isopycnals modifies the local density stratification. At its peak, the local squared buoyancy frequency ( ) near the canyon is reduced by about 20% from 1997 to 2014. Similar reduction is found in the basinwide averaged profiles over the Mid‐Atlantic Ridge flank along 25 W in years 1989, 2005, and 2014. The observed changes in density stratification have important implications for internal tide generation and dissipation.

Hydrodynamic modelling of Port Foster, Deception Island, Antarctica

AbstractOver the last decade, the Antarctic continent has been the object of intensive scientific programmes. However, the emphasis of these studies rarely focuses on the Antarctic as a source of potential elements such as mercury. The release of mercury to the environment is known to occur at Deception Island, associated with volcanic activity. In this study, a 3D hydrodynamic model was used to assess the role of water circulation on the dispersion of released mercury. Sea level variation and tidal circulation data were obtained. Residence time was calculated using two different approaches. Internal tide generation in summer and winter were recognized and the barotropic tidal components obtained. Lagrangian tracers were used to depict particle circulation (simulating particulate mercury) in a three month summer simulation for barotropic and baroclinic conditions. The results show that particles accumulate in the northern and western parts of the bay. It is acknowledged that the results of the 3D model are associated with a non-negligible uncertainty, which can only be reduced with an ongoing commitment to monitoring. The findings of this study indicate that mercury accumulation is occurring in Port Foster (Deception Island), which is a potential threat to the local ecosystem.

Propagation of the Semidiurnal Internal Tide: Phase Velocity Versus Group Velocity

AbstractThe superposition of two waves of slightly different wavelengths has long been used to illustrate the distinction between phase velocity and group velocity. The first‐mode M2 and S2 internal tides exemplify such a two‐wave model in the natural ocean. The M2 and S2 tidal frequencies are 1.932 and 2 cycles per day, respectively, and their superposition forms a spring‐neap cycle in the semidiurnal band. The spring‐neap cycle acts like a wave, with its frequency, wave number, and phase being the differences of the M2 and S2 internal tides. The spring‐neap cycle and energy of the semidiurnal internal tide propagate at the group velocity. Long‐range propagation of M2 and S2 internal tides in the North Pacific is observed by satellite altimetry. Along a 3,400 km beam spanning 24°–54°N, the M2 and S2 travel times are 10.9 and 11.2 days, respectively. For comparison, it takes the spring‐neap cycle 21.1 days to travel over this distance. Spatial maps of the M2 phase velocity, the S2 phase velocity, and the group velocity are determined from phase gradients of the corresponding satellite observed internal tide fields. The observed phase and group velocities agree with theoretical values estimated using the World Ocean Atlas 2013 annual‐mean ocean stratification.

SOMAR-LES: A framework for multi-scale modeling of turbulent stratified oceanic flows

A new multi-scale modeling technique, SOMAR-LES, is presented in this paper. Localized grid refinement gives SOMAR (the Stratified Ocean Model with Adaptive Resolution) access to small scales of the flow which are normally inaccessible to general circulation models (GCMs). SOMAR-LES drives a LES (Large Eddy Simulation) on SOMAR’s finest grids, forced with large scale forcing from the coarser grids. Three-dimensional simulations of internal tide generation, propagation and scattering are performed to demonstrate this multi-scale modeling technique. In the case of internal tide generation at a two-dimensional bathymetry, SOMAR-LES is able to balance the baroclinic energy budget and accurately model turbulence losses at only 10% of the computational cost required by a non-adaptive solver running at SOMAR-LES’s fine grid resolution. This relative cost is significantly reduced in situations with intermittent turbulence or where the location of the turbulence is not known a priori because SOMAR-LES does not require persistent, global, high resolution. To illustrate this point, we consider a three-dimensional bathymetry with grids adaptively refined along the tidally generated internal waves to capture remote mixing in regions of wave focusing. The computational cost in this case is found to be nearly 25 times smaller than that of a non-adaptive solver at comparable resolution. In the final test case, we consider the scattering of a mode-1 internal wave at an isolated two-dimensional and three-dimensional topography, and we compare the results with Legg (2014) numerical experiments. We find good agreement with theoretical estimates. SOMAR-LES is less dissipative than the closure scheme employed by Legg (2014) near the bathymetry. Depending on the flow configuration and resolution employed, a reduction of more than an order of magnitude in computational costs is expected, relative to traditional existing solvers.

Climate Process Team on Internal Wave-Driven Ocean Mixing.

Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatio-temporal patterns of mixing are largely driven by the geography of generation, propagation and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last five years and under the auspices of US CLIVAR, a NSF- and NOAA-supported Climate Process Team has been engaged in developing, implementing and testing dynamics-based parameterizations for internal-wave driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here we review recent progress, describe the tools developed, and discuss future directions.

Internal tides in a dendritic submarine canyon

Submarine canyons are a common geomorphological feature along continental slopes worldwide and often found to be ‘hotspots’ of internal tide activity. However, the majority of well-studied submarine canyons are simple linear incisions or have meandering morphology; internal tide energetics in branching (dendritic) canyons has not previously been investigated. Here we present a high-resolution (500-m) numerical modelling study of the internal tide within Whittard Canyon, a large, dendritic submarine canyon system that incises the Celtic Sea continental slope. A modified version of the Princeton Ocean Model is used to simulate the M2 (semidiurnal) internal tide in the Whittard Canyon region, verified against a hydrographic dataset collected by an autonomous ocean glider. Much of the internal tide energy entering Whittard Canyon originates to the southeast, along the Celtic Sea shelf break. Internal tide generation also occurs within the canyon itself, but is in part compensated by areas of negative energy conversion. Depth-integrated internal tide energy fluxes exceed 8kWm−1 in the eastern limb of the canyon. The internal tide is topographically steered through the major limbs and along-canyon energy flux is bottom intensified, suggesting topographic focusing. The down canyon extent of bottom intensification closely corresponds to the point that along-canyon slope becomes near-critical to the semidiurnal internal tide. Energetically, the multiple limbs of Whittard Canyon behave differently, some are net sources of internal tide energy whilst others are net sinks. Internal tide energy dissipation also varies between the canyon limbs; bulk dissipation rates are 2.1-7.7×10-8Wkg-1. In addition, the effect of bathymetric resolution on internal tide generation and propagation is investigated by progressively smoothing the model domain. Decreasing the bathymetric resolution reduces internal tide generation and energy dissipation in both Whittard Canyon and the model domain as a whole, however, internal tide energy flux into the canyon is not consistently changed. At least 1.5-km resolution bathymetry is required to adequately resolve the semidiurnal internal tide field in this region of complex topography.

Diurnal Critical Latitude and the Latitude Dependence of Internal Tides, Internal Waves, and Mixing Based on Barcoo Seamount

AbstractVertical mixing is a key issue in ocean circulation modeling today. Mixing, particularly tidal mixing, is poorly represented in ocean and climate models, which generally ignore critical latitude effects. Critical latitude is the latitude where the inertial frequency equals the tidal frequency and differs for each tidal constituent. Critical latitudes strongly influence generation and propagation of internal tides. Using a model, latitude effects on tidal interactions with a seamount were examined by varying the latitude from 20° to 38°, through the range of the diurnal critical latitudes. The diurnal critical latitudes were found to strongly influence propagation of the diurnal internal tides, the magnitude of the semidiurnal tides, the energy in the harmonic and higher frequencies, the barotropic mean flow, and the diffusivities. The strongest effects occurred between the K1 and O1 critical latitudes. Here the semidiurnal tides, harmonics, and high frequencies were enhanced, barotropic mean velocities weakened, energy at the harmonics and higher frequencies increased, and diffusivities increased. Spectral techniques indicate that most of these impacts are the result of nonlinear wave‐wave interactions and resonant phenomena with the prominent mechanism harmonic transfers. There was no evidence of parametric subharmonic instabilities. The semidiurnal tides indicated a resonant response at 20°S, which is near the latitude for the combined M2 and K1 tidal period, ∼19°S.

An asymptotic model for the propagation of oceanic internal tides through quasi-geostrophic flow

We derive a time-averaged ‘hydrostatic wave equation’ from the hydrostatic Boussinesq equations that describes the propagation of inertia–gravity internal waves through quasi-geostrophic flow. The derivation uses a multiple-scale asymptotic method to isolate wave field evolution over intervals much longer than a wave period, assumes the wave field has a well-defined non-inertial frequency such as that of the mid-latitude semi-diurnal lunar tide, assumes that the wave field and quasi-geostrophic flow have comparable spatial scales and neglects nonlinear wave–wave dynamics. As a result the hydrostatic wave equation is a reduced model applicable to the propagation of large-scale internal tides through the inhomogeneous and moving ocean. A numerical comparison with the linearized and hydrostatic Boussinesq equations demonstrates the validity of the hydrostatic wave equation model and illustrates how the model fails when the quasi-geostrophic flow is too strong and the wave frequency is too close to inertial. The hydrostatic wave equation provides a first step toward a coupled model for energy transfer between oceanic internal tides and quasi-geostrophic eddies and currents.

Impact of a Mean Current on the Internal Tide Energy Dissipation at the Critical Latitude

AbstractPrevious numerical studies of the dissipation of internal tides in idealized settings suggest the existence of a critical latitude (~29°) where dissipation is enhanced. But observations only indicate a modest enhancement at this latitude. To resolve this difference between observational and numerical results, the authors study the latitudinal dependence of internal tides’ dissipation in more realistic conditions. In particular, the ocean is not a quiescent medium; the presence of large-scale currents or mesoscale eddies can impact the propagation and dissipation of internal tides. This paper investigates the impact of a weak background mean current in numerical simulations. The authors focus on the local dissipation of high spatial mode internal waves near their generation site. The vertical profile of dissipation and its variation with latitude without the mean current are consistent with earlier studies. But adding a weak mean current has a major impact on the latitudinal distribution of dissipation. The peak at the critical latitude disappears, and the dissipation is closer to a constant, albeit with two weak peaks at ~25° and ~35° latitude. This disappearance results from the Doppler shift of the internal tides’ frequency, which hinders the nonlinear transfer of energy to small-scale secondary waves via the parametric subharmonic instability (PSI). The new two weak peaks correspond to the Doppler-shifted critical latitudes of the left- and right-propagating waves. The results are confirmed in simulations with simple sinusoidal topography. Thus, although nonlinear transfers via PSI are efficient at dissipating internal tides, the exact location of the dissipation is sensitive to large-scale oceanic conditions.

Coastal‐trapped behavior of the diurnal internal tide at O'ahu, Hawai'i

AbstractThe influence of rotation on the structure and propagation of internal tides around O'ahu, Hawai'i is investigated using in situ observations and a tidally forced, primitive equation model with realistic bathymetry and stratification. Particular attention is given to the diurnal internal tide, which largely has been de‐emphasized in previous studies of the region because of the dominance of the semidiurnal internal tide but has been determined by recent studies to be a significant contributor to baroclinic variability. Though both diurnal and semidiurnal internal tides are generated primarily over Ka'ena Ridge to the northwest of the island, the diurnal internal tide propagates clockwise around the island as an imperfectly trapped wave, while the semidiurnal internal tide propagates away from the ridge, unaffected by rotation. The diurnal and semidiurnal internal tides fall into the superinertial frequency range; however, the diurnal frequency apparently is sufficiently close to inertial (∼ 1.4f) for rotation to affect internal tide propagation. The in situ observations support the model finding that diurnal trapping provides the primary source of baroclinic variability along the eastern coast of the island, a stretch of coastline otherwise sheltered from the internal tide energy generated over the Hawaiian Ridge. The findings in Hawai'i suggest that coastal trapping of superinertial internal tides may be a significant source of variability and mixing in other nearshore systems around the world.

Profiling measurement of internal tide in the Bali Strait by reciprocal sound transmission

A reciprocal sound transmission experiment was carried out from 10 to 12 June 2015 along one-crossed-strait line in the Bali Strait with strong tidal current to measure the vertical section structures of range-averaged current and temperature at a 3 minutes interval. The five-layer structures of those parameters in the vertical sections were reconstructed by the regularized of travel time data for 2 rays. The hourly mean current showed a generation of nonlinear internal tide with amplitudes of (1.0—1.5)m/s and period of 6 hours, superimposed on semi-diurnal internal tide with amplitudes, decreasing from the upper to lower layer. The hourly mean temperature was characterized by variation with amplitude of (1.0-1.5) and period of 6 and 8 hours. Current variation revealed an out of phase relation between the upper and lower layer while temperature varied in phase for all five layers. The 2-day average current formed a stratified structure, varying from -0.6 to -0.1m/s and from 23.8 to 28, respectively. The five-layer current and temperature were significantly over the inversion errors. It is suggested that thermal stratification in the Bali strait was caused by intrusion of dense cold water from the Indian Ocean due to coastal upwelling.

Low-Mode Internal Tide Propagation in a Turbulent Eddy Field

AbstractUnderstanding and predicting how internal tides distort and lose coherence as they propagate through the ocean has been identified as a key issue for interpreting data from the upcoming wide-swath altimeter mission Surface Water and Ocean Topography (SWOT). This study addresses the issue through the analysis of numerical experiments where a low-mode internal tide propagates through a quasigeostrophic turbulent jet. Equations of motion linearized around the slower turbulent field are projected onto vertical modes and assumed to describe the dynamics of the low-mode internal tide propagation. Diagnostics of the terms responsible for the interaction between the wave and the slow circulation are computed from the numerical outputs. The large-scale change of stratification, on top of eddies and jet meanders, contributes significantly to these interaction terms, which is shown to be consistent with an independent scaling analysis. The sensitivity of interaction terms to a degradation of the slow field spatial and temporal resolution indicates that present-day observing systems (Argo network, altimetry) may lack the spatial resolution necessary to correctly predict internal tide evolution. The upcoming SWOT satellite mission may improve upon this situation. The number of vertical modes required to properly estimate interaction terms is discussed. These results advocate development of a simplified model based on solving a modest number of the linearized equations subject to a prescribed mesoscale field and internal tide sources.

Tidal Energy Loss, Internal Tide Radiation, and Local Dissipation for Two-Layer Tidal Flow over a Sill

AbstractA simple analytical model for tidal energy loss at fjord sills and its partitioning into local dissipation and radiated internal tides is presented. The analytical model builds on a two-layer assumption with quasi-steady nonlinear flow over the sill and wave radiation in the far field. When the interface is situated above sill level, upstream- and downstream-propagating internal waves are generated as the bottom-layer flow becomes partially blocked because of a hydraulic control over the sill. When this control sets in, energy is lost in the transition from supercritical flow over the sill to subcritical flow downstream of the sill. The analytical model is compared with observations at the Drøbak sill in the Oslo Fjord and with idealized numerical simulations with a nonhydrostatic primitive equation model. The overall good agreement between observations, analytical model, and numerical model results indicates that the hydraulic control over the sill is a key player for both the generation of internal tides and the local energy loss. The tidal energy loss decreases with increasing height of the interface above the sill. At the same time, the fraction of energy dissipated locally increases from about 20% for the interface situated at sill level to >50% when the upper-layer thickness is less than about 80% of the sill depth. These results correspond well with the observations in the Oslo Fjord where more energy is dissipated near the sill than is radiated away.

A Coupled-Mode Shallow-Water Model for Tidal Analysis: Internal Tide Reflection and Refraction by the Gulf Stream

AbstractA hydrostatic, coupled-mode, shallow-water model (CSW) is described and used to diagnose and simulate tidal dynamics in the greater Mid-Atlantic Bight region. The reduced-physics model incorporates realistic stratification and topography, internal tide forcing from a priori estimates of the surface tide, and advection terms that describe first-order interactions of internal tides with slowly varying mean flow and mean buoyancy fields and their respective shear. The model is validated via comparisons with semianalytic models and nonlinear primitive equation models in several idealized and realistic simulations that include internal tide interactions with topography and mean flows. Then, 24 simulations of internal tide generation and propagation in the greater Mid-Atlantic Bight region are used to diagnose significant internal tide interactions with the Gulf Stream. The simulations indicate that locally generated mode-one internal tides refract and/or reflect at the Gulf Stream. The redirected internal tides often reappear at the shelf break, where their onshore energy fluxes are intermittent (i.e., noncoherent with surface tide) because meanders in the Gulf Stream alter their precise location, phase, and amplitude. These results provide an explanation for anomalous onshore energy fluxes that were previously observed at the New Jersey shelf break and linked to the irregular generation of nonlinear internal waves.