Search

The solution from linear theory for the barotropic-to-baroclinic tidal energy conversion into vertical modes is validated with numerical simulations and analytical results. The main result is the translation of the traditional critical slope condition into a modewise condition on the topographic height only. Our findings are then used for estimates of the global M2 tidal conversion into the first 10 vertical modes in the open ocean (excluding the continental shelves and slopes). We observe a rapid increase with mode number of the fraction of the World Ocean where linear theory is invalid. In terms of conversion, which is highly variable in space, this corresponds to an even more rapid increase with mode number of the fraction of the converted energy that is strongly affected by nonlinear effects. Out of the 373.6 GW of the globally integrated conversion into modes 1–10, only 241.7 GW occur in locations where linear theory is valid. While it represents 95% for mode 1, this fraction rapidly drops with mode number to reach 27% for mode 10. Moreover, for the conversion into a single mode, we show that capping the linear solution at supercritical topography is inappropriate. Hence, linear theory appears unfit to directly quantify the role played by high-mode internal tides in the internal wave energy budget. [ABSTRACT FROM AUTHOR]

Enhanced diapycnal mixing induced by the near-bottom breaking of internal waves is an essential component of the lower meridional overturning circulation. Despite its crucial role in the ocean circulation, tidally driven internal wave breaking is challenging to observe due to its inherently short spatial and temporal scales. We present detailed moored and shipboard observations that resolve the spatiotemporal variability of the tidal response over a small-scale bump embedded in the continental slope of Tasmania. Cross-shore tidal currents drive a nonlinear trapped response over the steep bottom around the bump. The observations are roughly consistent with two-dimensional high-mode tidal lee-wave theory. However, the alongshore tidal velocities are large, suggesting that the alongshore bathymetric variability modulates the tidal response driven by the cross-shore tidal flow. The semidiurnal tide and energy dissipation rate are correlated at subtidal time scales, but with complex temporal variability. Energy dissipation from a simple scattering model shows that the elevated near-bottom turbulence can be sustained by the impinging mode-1 internal tide, where the dissipation over the bump is O(1%) of the incident depth-integrated energy flux. Despite this small fraction, tidal dissipation is enhanced over the bump due to steep topography at a horizontal scale of O(1) km and may locally drive significant diapycnal mixing. Significance Statement: Near-bottom turbulent mixing is a key element of the global abyssal circulation. We present observations of the spatiotemporal variability of tidally driven turbulent processes over a small-scale topographic bump off Tasmania. The semidiurnal tide generates large-amplitude transient lee waves and hydraulic jumps that are unstable and dissipate the tidal energy. These processes are consistent with the scattering of the incident low-mode internal tide on the continental slope of Tasmania. Despite elevated turbulence over the bump, near-bottom energy dissipation is small relative to the incident wave energy flux. [ABSTRACT FROM AUTHOR]

It is well known that strong low-mode internal tides generated in Luzon Strait propagate westward to impinge continental slopes in the northeastern South China Sea (SCS). The reflection and scattering of these internal tides including diurnal and semidiurnal components on the slopes are quantitatively investigated using two sets of mooring data and a linear internal tide model with realistic topography and stratification. Flux reflections computed from mooring data collected on the continental slopes are consistent with the linear model. Based on the results of the observations and simulations, a map of low-mode internal tide reflection and scattering coefficients along the continental margin in the northeastern SCS is revealed. On average, diurnal internal tides lose 38% of their energy to high modes (≥mode 4) that are assumed to dissipate on the slopes, transmit 28% onto the continental shelf, and reflect 31% back to the deep ocean. On the contrary, most of the semidiurnal energy (89%) transmits onto the continental shelf, and only 11% is scattered to high modes (7%) and reflected back to the deep ocean (4%). For diurnal internal tides, a large fraction of energy that is scattered to high modes and reflected back to the deep sea can be attributed to the critical–supercritical slopes, while the weak reflection for the semidiurnal energy is due to the subcritical slopes. These quantitative descriptions for evolutions of low-mode internal tides incident to the slopes provide an energy budget map on the continental slopes in the northeastern SCS. [ABSTRACT FROM AUTHOR]

Breaking internal tides contribute substantially to small-scale turbulent mixing in the ocean interior and hence to maintaining the large-scale overturning circulation. How much internal tide energy is available for ocean mixing can be estimated by using semianalytical methods based on linear theory. Until recently, a method resolving the horizontal direction of the internal waves generated by conversion of the barotropic tide was lacking. We here present the first global application of such a method to the first vertical mode of the principal lunar semidiurnal internal tide. We also show that the effect of supercritical slopes on the modally decomposed internal tides is different than previously suggested. To deal with this the continental shelf and the shelf slope are masked in the global computation. The global energy conversion obtained agrees roughly with the previous results by Falahat et al. if the mask is applied to their result, which decreases their energy conversion by half. Thus, around half of the energy conversion obtained by their linear calculations occurs at continental slopes and shelves, where linear theory tends to break down. The barotropic-to-baroclinic energy flux at subcritical slopes away from the continental margins is shown to vary substantially with direction depending on the shape and orientation of topographic obstacles and the direction of the local tidal currents. Taking this additional information into account in tidal mixing parameterizations could have important ramifications for vertical mixing and water mass properties in global numerical simulations. [ABSTRACT FROM AUTHOR]

Coastal trapped waves (CTWs) transport energy along coastlines and drive coastal currents and upwelling. CTW modes are nonorthogonal when frequency is treated as the eigenvalue, preventing the separation of modal energy fluxes and quantification of longshore topographic scattering. Here, CTW modes are shown to be orthogonal with respect to energy flux (but not energy) when the longshore wavenumber is the eigenvalue. The modal evolution equation is a simple harmonic oscillator forced by longshore bathymetric variability, where downstream distance is treated like time. The energy equation includes an expression for modal topographic scattering. The eigenvalue problem is carefully discretized to produce numerically orthogonal modes, allowing CTW amplitudes, energy fluxes, and generation to be precisely quantified in numerical simulations. First, a spatially uniform K1 longshore velocity is applied to a continental slope with a Gaussian bump in the coastline. Mode-1 CTW generation increases quadratically with the amplitude of the bump and is maximum when the bump's length of coastline matches the natural wavelength of the CTW mode, as predicted by theory. Next, a realistic K1 barotropic tide is applied to the Oregon coast. The forcing generates mode-1 and mode-2 CTWs with energy fluxes of 6 and 2 MW, respectively, which are much smaller than the 80 MW of M2 internal-tide generation in this region. CTWs also produce 1-cm sea surface displacements along the coast, potentially complicating the interpretation of future satellite altimetry. Prospects and challenges for quantifying the global geography of CTWs are discussed. [ABSTRACT FROM AUTHOR]

On the basis of measurements from an observing mooring system, the observational evidence of parametric subharmonic instability (PSI) that transfers energy from semidiurnal internal tides (ITs) to the subharmonic waves at the East China Sea continental shelf slope is presented for the first time. Although the mooring station is very close to the energetic semidiurnal IT generation site, about 76% of the observed shear variance is contained in the near-inertial band, which is found to have comparable upward- and downward-propagating energy components. Bispectra and bicoherence estimates further confirm the occurrence of PSI transferring energy from the low-mode M2 ITs (vertical wavelength of ~1000 m) to high-mode subharmonic waves (vertical wavelength of ~200 m). The calculated energy transfer rate g reveals an averaged net value of ~5 × 10−9 W kg−1. Strong temporal variation of g is found that is not exactly in phase with the semidiurnal energy flux. After looking into the local vorticity fields, it is strongly suggested that the varying background relative vorticity associated with the evolving Kuroshio has modified the efficiency of PSI at the mooring location through changing the local effective inertial frequency. [ABSTRACT FROM AUTHOR]

All exchanges between the open ocean and the Antarctic continental shelf must cross the Antarctic Slope Current (ASC). Previous studies indicate that these exchanges are strongly influenced by mesoscale and tidal variability, yet the mechanisms responsible for setting the ASC's transport and structure have received relatively little attention. In this study the roles of winds, eddies, and tides in accelerating the ASC are investigated using a global ocean–sea ice simulation with very high resolution (1/48° grid spacing). It is found that the circulation along the continental slope is accelerated both by surface stresses, ultimately sourced from the easterly winds, and by mesoscale eddy vorticity fluxes. At the continental shelf break, the ASC exhibits a narrow (~30–50 km), swift (>0.2 m s−1) jet, consistent with in situ observations. In this jet the surface stress is substantially reduced, and may even vanish or be directed eastward, because the ocean surface speed matches or exceeds that of the sea ice. The shelfbreak jet is shown to be accelerated by tidal momentum advection, consistent with the phenomenon of tidal rectification. Consequently, the shoreward Ekman transport vanishes and thus the mean overturning circulation that steepens the Antarctic Slope Front (ASF) is primarily due to tidal acceleration. These findings imply that the circulation and mean overturning of the ASC are not only determined by near-Antarctic winds, but also depend crucially on sea ice cover, regionally-dependent mesoscale eddy activity over the continental slope, and the amplitude of tidal flows across the continental shelf break. [ABSTRACT FROM AUTHOR]

Internal tide generation at sloping topography is nominally determined by the local slope geometry, density stratification, and tidal forcing. Recent global ocean models have revealed that remotely generated internal tides (RITS) can also influence locally generated internal tides (LITs). Field measurements with through-the-water column moorings on the southern portion of the Australian North West Shelf (NWS) suggested that RITs led to local regions with either positive or negative barotropic to baroclinic energy conversion. Three-dimensional numerical simulations were used to examine the role of RITs on local internal tide climatology on the inner slope and shelf portion of the NWS. The model demonstrated the principle remote generation site was the western portion of the offshore Exmouth Plateau. Extending the model domain to include this offshore plateau region increased the local net energy conversion on the inner shelf by 13.5% and on the slope by 8%. Simulations using an idealized 2D model configuration aligned along the principal direction of RIT propagation demonstrated that the sign and magnitude of the local energy conversion was dependent on the distance between the remote and local generation sites, the phase difference between the local barotropic tide and the RIT, and the amplitude of both the local barotropic tide and the RIT. For RITs with a low-wave Froude number (Fr < 0.05), where Fr is the ratio of the internal wave baroclinic velocity to the linear wave speed, the conversion rates were consistent with kinematic predictions based on the phase difference only. For stronger flows with Fr > 0.05, the conversion rates showed a nonlinear dependence on Fr. [ABSTRACT FROM AUTHOR]

A series of laboratory experiments are performed to investigate the scattering of low-mode internal tides at a continental shelf by varying the criticality parameter and normalized topographic height independently. A wide-range synchronized particle image velocimetery (PIV) measures the velocity fields of the internal tides. Beams radiate from both the shelf break and the bottom of the slope, indicating that energy transfers from low modes to higher modes, which is verified by the modal decomposition. Energy is also transferred to higher harmonics, whose amplitude is less than a quarter of that of the first harmonic. The fraction of energy transmitted onshore and dissipated on the topography is determined by both the criticality parameter and the normalized topographic height, while the fraction of energy reflected offshore is dependent only on the criticality parameter. Mean flow with a shear structure induced by internal tides is observed along the continental slope, with horizontal velocity generally half of the amplitude of the incident waves. A net onshore transport along the slope is caused by the onshore current with larger thickness. The strength of the mean flow is dependent on both the criticality parameter and the normalized topographic height, and a linear relationship between the energy of the mean flow and the vertical shear of internal tides is revealed. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

The reflection of a low-mode internal tide on the Tasman continental slope is investigated using simulations of realistic and simplified topographies. The slope is supercritical to the internal tide, which should predict a large fraction of the energy reflected. However, the response to the slope is complicated by a number of factors: the incoming beam is confined laterally, it impacts the slope at an angle, there is a roughly cylindrical rise directly offshore of the slope, and a leaky slope-mode wave is excited. These effects are isolated in simulations that simplify the topography. To separate the incident from the reflected signal, a response without the reflector is subtracted from the total response to arrive at a reflected signal. The real slope reflects approximately 65% of the mode-1 internal tide as mode 1, less than two-dimensional linear calculations predict, because of the three-dimensional concavity of the topography. It is also less than recent glider estimates, likely as a result of along-slope inhomogeneity. The inhomogeneity of the response comes from the Tasman Rise that diffracts the incoming tidal beam into two beams: one focused along beam and one diffracted to the north. Along-slope inhomogeneity is enhanced by a partially trapped, superinertial slope wave that propagates along the continental slope, locally removing energy from the deep-water internal tide and reradiating it into the deep water farther north. This wave is present even in a simplified, straight slope topography; its character can be predicted from linear resonance theory, and it represents up to 30% of the local energy budget. [ABSTRACT FROM AUTHOR]

Observations of breaking internal tides on the Oregon continental slope during a 40-day deployment of 5 moorings along 43°12′N are presented. Remotely generated internal tides shoal onto the slope, steepen, break, and form turbulent bores that propagate upslope independently of the internal tide. A high-resolution snapshot of a single bore is captured from lowered acoustic Doppler current profilers (LADCP)/CTD profiles in a 25-h time series at 1200 m. The bore is cold, salty, over 100 m tall, and has a turbulent head where instantaneous dissipation rates are enhanced ( ε > 10−6 W kg−1) and sediment is resuspended. At the two deepest slope moorings (1452 and 1780 m), similar borelike phenomena are observed in near-bottom high-resolution temperature time series. Mean dissipation rates and diapycnal diffusivities increase by a factor of 2 when bores are present ( W kg−1 and m s−1) and observed internal tides are energetic enough to drive these enhanced dissipation rates. Globally, the authors estimate an average of 1.3 kW m−1 of internal tide energy flux is directed onto continental slopes. On the Oregon slope, internal tide fluxes are smaller, suggesting that it is a relatively weak internal tide sink. Mixing associated with the breaking of internal tides is therefore likely to be larger on other continental slopes. [ABSTRACT FROM AUTHOR]

The linear transfer of tidal energy from large to small scales is quantified for small tidal excursion over a near-critical continental slope. A theoretical framework for low-wavenumber energy transfer is derived from "flat bottom" vertical modes and evaluated with observations from the Oregon continental slope. To better understand the observations, local tidal dynamics are modeled with a superposition of two idealized numerical simulations, one forced by local surface-tide velocities and the other by an obliquely incident internal tide generated at the Mendocino Escarpment 315 km southwest of the study site. The simulations reproduce many aspects of the observed internal tide and verify the modal-energy balances. Observed transfer of tidal energy into high-mode internal tides is quantitatively consistent with observed turbulent kinetic energy (TKE) dissipation. Locally generated and incident simulated internal tides are superposed with varying phase shifts to mimic the effects of the temporally varying mesoscale. Altering the phase of the incident internal tide alters (i) internal-tide energy flux, (ii) internal-tide generation, and (iii) energy con-version to high modes, suggesting that tidally driven TKE dissipation may vary between 0 and 500 watts per meter of coastline on 3-5-day time scales. Comparison of observed in situ internal-tide generation and satellite-derived estimates of surface-tide energy loss is inconclusive. [ABSTRACT FROM AUTHOR]

Two year-long (2004-05 and 2005-06) records of currents from two moorings deployed at the continental slope of the Laptev Sea (78°26′N, 125°40′E) are used in order to define the properties of tidal currents in the upper ~200-m ocean layer. Harmonic and spectral analyses of currents showed that the semidiurnal tidal constituent S2 dominates over the semidiurnal M2 and diurnal constituents. This dominance of the S2 constituent in the tidal currents is due to resonant interaction of the superinertial wave with sloping bottom topography. In contrast to the tidal currents, sea level changes are dominated by the M2 constituent, as seen from a tidal model by L. Padman and S. Erofeeva, using assimilation of observational data. Strong anticorrelation (−0.73 ± 0.05) was found between the upper 50-m S2 current amplitudes and local sea ice concentration, with fourfold (from ~2.0 to 8.5 cm s−1) amplification of tidal currents under ice-free conditions. This is probably due to a change of local resonance conditions for the S2 tidal current. These findings may be important for understanding the increasing role of tides in a seasonally ice-free Arctic Ocean. [ABSTRACT FROM AUTHOR]

A complex superposition of locally forced and shoaling remotely generated semidiurnal internal tides occurs on the Oregon continental slope. Presented here are observations from a zonal line of five profiling moorings deployed across the continental slope from 500 to 3000 m, a 24-h expendable current profiler (XCP) survey, and five 15-48-h lowered ADCP (LADCP)/CTD stations. The 40-day moored deployment spans three spring and two neap tides, during which the proportions of the locally and remotely forced internal tides vary. Baroclinic signals are strong throughout spring and neap tides, with 4-5-day-long bursts of strong cross-slope baroclinic semidiurnal velocity and vertical displacement . Energy fluxes exhibit complex spatial and temporal patterns throughout both tidal periods. During spring tides, local barotropic forcing is strongest and energy flux over the slope is predominantly offshore (westward). During neap tides, shoaling remotely generated internal tides dominate and energy flux is predominantly onshore (eastward). Shoaling internal tides do not exhibit a strong spring-neap cycle and are also observed during the first spring tide, indicating that they originate from multiple sources. The bulk of the remotely generated internal tide is hypothesized to be generated from south of the array (e.g., Mendocino Escarpment), because energy fluxes at the deep mooring 100 km offshore are always directed northward. However, fluxes on the slope suggest that the northbound internal tide is turned onshore, most likely by reflection from large-scale bathymetry. This is verified with a simple three-dimensional model of mode-1 internal tides propagating obliquely onto a near-critical slope, whose output conforms fairly well to observations, in spite of its simplicity. [ABSTRACT FROM AUTHOR]

A strong internal tide is generated in the Luzon Strait that radiates westward to impact the continental shelf of the South China Sea. Mooring data in 1500-m depth on the continental slope show a fortnightly averaged incoming tidal flux of 12 kW m−−1, and a mooring on a broad plateau on the slope finds a similar flux as an upper bound. Of this, 5.5 kW m−−1 is in the diurnal tide and 3.5 kW m−−1 is in the semidiurnal tide, with the remainder in higher-frequency motions. Turbulence dissipation may be as high as 3 kW m−−1. Local generation is estimated from a linear model to be less than 1 kW m−−1. The continental slope is supercritical with respect to the diurnal tide, implying that there may be significant back reflection into the basin. Comparing the low-mode energy of a horizontal standing wave at the mooring to the energy flux indicates that perhaps one-third of the incoming diurnal tidal energy is reflected. Conversely, the slope is subcritical with respect to the semidiurnal tide, and the observed reflection is very weak. A surprising observation is that, despite significant diurnal vertical-mode-2 incident energy flux, this energy did not reflect; most of the reflection was in mode 1. The observations are consistent with a linear scattering model for supercritical topography. Large fractions of incoming energy can reflect depending on both the geometry of the shelfbreak and the phase between the modal components of the incoming flux. If the incident mode-1 and mode-2 waves are in phase at the shelf break, there is substantial transmission onto the shelf; if they are out of phase, there is almost 100%% reflection. The observations of the diurnal tide at the site are consistent with the first case: weak reflection, with most of it in mode 1 and almost no reflection in mode 2. The sensitivity of the reflection on the phase between incident components significantly complicates the prediction of reflections from continental shelves. Finally, a somewhat incidental observation is that the shape of the continental slope has large regions that are near critical to the dominant diurnal tide. This implicates the internal tide in shaping of the continental slope. [ABSTRACT FROM AUTHOR]

Stratified flow over topography is studied, with oceanic applications in mind. A model is developed for a fluid with arbitrary vertical stratification and a free surface, flowing over three-dimensional topography of arbitrary size and steepness, with background rotation, in the linear hydrostatic regime. The model uses an expansion of the flow fields in terms of a set of basis functions, which efficiently capture the vertical dependence of the flow. The horizontal structure may then be found by solving a set of coupled partial differential equations in two horizontal directions and time, subject to simple boundary conditions. In some cases, these equations may be solved analytically, but, in general, simple numerical procedures are required. Using this formulation, the internal tide generated by a time-periodic barotropic tidal flow over a continental shelf and slope is calculated in various idealized configurations. The topography and fluid motion are taken to be independent of one coordinate direction and the fluid to be either two-layer or uniformly stratified. For the two-layer case, expressions for the shoreward and oceanward energy fluxes associated with the internal tide are derived. For the uniformly stratified case, it is studied numerically how the accuracy of the solutions depends upon the number of basis functions used, and it is shown that good solutions and energy flux estimates can often be obtained with only a few basis functions. In both cases, the results show that the position of the coastline, through its effect on the form of the barotropic tide, significantly influences the strength of the internal tide generation. [ABSTRACT FROM AUTHOR]

Recent measurements in a region of continental slope characterized by ridges and valleys running up and down the slope reveal interesting high mode structure in the tidal band velocity signals, with enhanced mixing above the corrugations. In order to understand these observations, numerical simulations of the internal tide generation in this region of topography were performed. Here the focus is on the response of the flow to along;chslope barotropic tidal forcing. For small-amplitude barotropic forcing, internal waves are generated over the continental slope that propagate toward the ocean surface and toward shallower water. When higher-amplitude forcing is combined with large-amplitude corrugations, the flow is locally supercritical downstream of ridges, and transient internal hydraulic jumps result. As the flow relaxes each half tidal period, these jumps are released as internal wave packets, which propagate up into the thermocline. The internal hydraulic jumps are a source of mixing in the valleys, while the small-scale shears associated with the internal waves could lead to mixing higher up the water column. Over the forcing range considered, the response is dominated by slightly higher harmonics of the tidal forcing frequency than predicted by existing analytic theories. [ABSTRACT FROM AUTHOR]

Recent measurements in a region of continental slope characterized by ridges and valleys running up and down the slope reveal interesting high-mode structure in the tidal band velocity signals and enhanced mixing over the corrugations. To deduce the processes responsible for the observed phenomena, numerical simulations of the internal tide generation in this region of topography were performed, focused on the response of the flow to cross-slope barotropic tidal forcing. The flow response is characterized by an internal tide generated at the shelf break that subsequently reflects from the corrugated slope. Above the corrugated slope, a high-mode structure may be created, but only if the Coriolis force is included. It is proposed that interference between the primary internal tide and secondary internal waves forced by the Coriolis-driven along-slope component of primary wave flow field is the cause of the high-mode structure in the simulations. Under suitable conditions of forcing, topography, and stratification, the shear generated by the interference may lead to local mixing. Hence complex topography may be an important contributor to boundary mixing in the ocean. [ABSTRACT FROM AUTHOR]