Breaking Of Internal Tides Research Articles

Sensitivity of Internal-Tide Generation to Stratification and Its Implication for Deep Overturning Circulations

Abstract The simple scaling relation for internal-tide generation proposed by Jayne and St. Laurent is widely used for parameterizing turbulent mixing induced by breaking of internal tides. Based on the internal-tide generation derived from a 0.1° ocean general circulation model, we show that depending on which stratification is used, this relation produces different vertical distributions of internal-tide generation. When using the buoyancy frequency at the seafloor, which is a common practice, the scaling relation produces, relative to the model, too-strong internal-tide generation in the upper 2000 m and too-weak internal-tide generation in the lower 2000 m. Moreover, the different vertical distributions in the different ocean basins, characterized by a generally decreasing internal tide generation with increasing depth in the Indo-Pacific but not-decreasing or even increasing internal tide generation with increasing depth in the upper 3000 m of the Atlantic, cannot be captured when using bottom stratification. These unsatisfactory features can be easily removed by replacing the buoyancy frequency at the seafloor by a buoyancy frequency averaged over a large part of the water column. To our knowledge, this sensitivity to stratification has not been explicitly quantified for the global ocean. Because of this sensitivity, the scaling relation of Jayne and St. Laurent should be used with an averaged stratification to ensure a more adequate representation of turbulent diffusivity due to tidal mixing and water mass transformation in the deep oceans.

Energy Conversion Rate from Subinertial Surface Tides to Internal Tides

Abstract Subinertial, topographically trapped diurnal internal tides are an important energy source for turbulent mixing in the subarctic oceans. However, their generation may not be estimated by the conventional barotropic-to-baroclinic conversion because their vertical structure is sometimes barotropic, unlike superinertial internal tides that are always baroclinic. Here, a new energy diagram is presented, in which the barotropic mode is decomposed into the surface and topographic modes, with the latter being classified as part of the internal modes together with the baroclinic mode. The energy equation for the newly defined topographic mode is then derived, providing an appropriate formulation of the energy conversion rate from the subinertial surface tides to the topographically trapped internal tides. A series of numerical experiments confirm that the formulation successfully predicts the energy conversion rate for various cases, with the relative contribution of the baroclinic and topographic modes varying significantly depending on the bottom topography and stratification. Furthermore, this surface-to-internal conversion is demonstrated to give a significantly larger estimate than the barotropic-to-baroclinic conversion for subinertial tides. Applying the formulation to the results of a realistic numerical simulation in the Kuril Straits, an area with the strongest mixing due to subinertial diurnal tides, shows that the surface mode is converted into the baroclinic and topographic modes with comparable magnitudes, responsible for most of the energy dissipation in this area. These results indicate the need to reestimate the global distribution of the generation rate of the subinertial internal tides using our new formulation and to clarify their dissipation mechanisms. Significance Statement Diurnal internal tides in mid- to high-latitude oceans are very different from semidiurnal internal tides, in that they are trapped by topographic features and characterized by uniform rotation throughout the water column rather than by vertical oscillations within the water column. Focusing on this character, we formulate for the first time the generation rate of diurnal internal tides trapped over variable bottom topography. A series of idealized numerical experiments and application to the Kuril Straits show the validity and usefulness of this formulation, which provides a significantly larger generation estimate than previous studies. The results of this study are important for accurate global mapping of turbulent mixing induced by the breaking of internal tides.

Dissipation of mesoscale eddies and its contribution to mixing in the northern South China Sea

It is reported that turbulent mixing is enhanced in the South China Sea (SCS), and it is highly variable in both space and time. Generation and breaking of internal tides has been identified as the main process to drive turbulent mixing in the SCS, while the contributions from other processes are not clear enough. Here we investigate the potential contribution from mesoscale eddies to turbulent mixing in the SCS using a high resolution numerical simulation. Our results show that mesoscale eddies in the SCS effectively dissipate over complex rough topography and indicate that the generation of submesoscale motions and lee waves are two pathways for the transfer of mesoscale eddy energy down to small dissipation scales. The energy loss from mesoscale eddies near the Xisha Islands is estimated to be sufficient to sustain turbulent kinetic energy dissipation rate of O (10−8) W/kg. This study suggests an alternative and potentially efficient mechanism to internal tides for the local maintenance of turbulent mixing in the SCS.

Deep Sea Currents Driven by Breaking Internal Tides on the Continental Slope

AbstractMooring data collected on the continental slope of the South China Sea show that along‐slope deep sea bottom currents are generated when large spring internal tides (internal waves with tidal frequency) are observed, with the maximum velocity amplitude exceeding 0.15 m/s. The observations are consistent with predictions that near‐bottom breaking of internal waves can result in generation of along‐slope flows when these waves obliquely approach the slope. A linear internal tide model in one horizontal dimension with realistic topography and stratification is used to show that the breaking of internal tides is likely due to near‐critical reflection on the slope. Combining the mooring observations and the model simulation, an along‐slope near‐bottom transport of ~0.5 Sv is estimated. Along‐slope bottom flows caused by breaking internal waves potentially provide a significant way to deform continental slopes and affect deep water exchange between the marginal sea and open ocean.

Dynamics of an Abyssal Circulation Driven by Bottom-Intensified Mixing on Slopes

AbstractThe large-scale circulation of the abyssal ocean is enabled by small-scale diapycnal mixing, which observations suggest is strongly enhanced toward the ocean bottom, where the breaking of internal tides and lee waves is most vigorous. As discussed recently, bottom-intensified mixing induces a pattern of near-bottom up- and downwelling that is quite different from the traditionally assumed widespread upwelling. Here the consequences of bottom-intensified mixing for the horizontal circulation of the abyssal ocean are explored by considering planetary geostrophic dynamics in an idealized “bathtub geometry.” Up- and downwelling layers develop on bottom slopes as expected, and these layers are well described by boundary layer theory. The basin-scale circulation is driven by flows in and out of these boundary layers at the base of the sloping topography, which creates primarily zonal currents in the interior and a net meridional exchange along western boundaries. The rate of the net overturning is controlled by the up- and downslope transports in boundary layers on slopes and can be predicted with boundary layer theory.

Nonhydrostatic Simulations of Tide‐Induced Mixing in the Halmahera Sea: A Possible Role in the Transformation of the Indonesian Throughflow Waters

AbstractThe Indonesian Throughflow (ITF) waters are significantly transformed within the Indonesian Archipelago and consequently influence the large‐scale ocean circulation such as Agulhas and Leeuwin Currents. Existing ocean general circulation models (OGCMs) are, however, incapable of reproducing the transformation of the ITF waters, since tidal forcing is neglected in such models. In the present study, we first conduct high‐resolution nonhydrostatic three‐dimensional numerical experiments focusing on the transformation of the ITF waters in the Halmahera Sea which is thought to be the most important bottleneck in simulating the ITF water mass properties. It is shown that intensive vertical mixing induced by breaking of internal tides in the shallow regions in the Halmahera Sea dilutes the ITF waters, significantly reducing model biases found in the existing OGCMs. We next evaluate quantitatively the effect of tide‐induced vertical mixing on the transformation of the ITF waters. It is shown that tide‐induced vertical mixing dominates the transformation of the ITF waters, although some supplementary processes such as horizontal mixing associated with the submesoscale eddies resulting from tidal interaction with land configurations cannot be ignored.

A three-dimensional map of tidal dissipation over abyssal hills

The breaking of internal tides is believed to provide a large part of the power needed to mix the abyssal ocean and sustain the meridional overturning circulation. Both the fraction of internal tide energy that is dissipated locally and the resulting vertical mixing distribution are crucial for the ocean state, but remain poorly quantified. Here we present a first worldwide estimate of mixing due to internal tides generated at small-scale abyssal hills. Our estimate is based on linear wave theory, a nonlinear parameterization for wave breaking and uses quasi-global small-scale abyssal hill bathymetry, stratification, and tidal data. We show that a large fraction of abyssal-hill generated internal tide energy is locally dissipated over mid-ocean ridges in the Southern Hemisphere. Significant dissipation occurs above ridge crests, and, upon rescaling by the local stratification, follows a monotonic exponential decay with height off the bottom, with a nonuniform decay scale. We however show that a substantial part of the dissipation occurs over the smoother flanks of mid-ocean ridges, and exhibits a middepth maximum due to the interplay of wave amplitude with stratification. We link the three-dimensional map of dissipation to abyssal hills characteristics, ocean stratification, and tidal forcing, and discuss its potential implementation in time-evolving parameterizations for global climate models. Current tidal parameterizations only account for waves generated at large-scale satellite-resolved bathymetry. Our results suggest that the presence of small-scale, mostly unresolved abyssal hills could significantly enhance the spatial inhomogeneity of tidal mixing, particularly above mid-ocean ridges in the Southern Hemisphere.

Comparison of calculated energy flux of internal tides with microstructure measurements

Vertical mixing caused by breaking of internal tides plays a major role in maintaining the deep-ocean stratification. This study compares observations of dissipation from microstructure measurements to calculations of the vertical energy flux from barotropic to internal tides, taking into account the temporal variation due to the spring-neap tidal cycle. The dissipation data originate from two surveys in the Brazil Basin Tracer Release Experiment (BBTRE), and one over the LArval Dispersal along the Deep East Pacific Rise (LADDER3), supplemented with a few stations above the North-Atlantic Ridge (GRAVILUCK) and in the western Pacific (IZU). A good correlation is found between logarithmic values of energy flux and local dissipation in BBTRE, suggesting that the theory is able to predict energy fluxes. For the LADDER3, the local dissipation is much smaller than the calculated energy flux, which is very likely due to the different topographic features of BBTRE and LADDER3. The East Pacific Rise consists of a few isolated seamounts, so that most of the internal wave energy can radiate away from the generation site, whereas the Brazil Basin is characterised by extended rough bathymetry, leading to a more local dissipation. The results from all four field surveys support the general conclusion that the fraction of the internal-tide energy flux that is dissipated locally is very different in different regions.

Sensitivity of the Ocean State to the Vertical Distribution of Internal-Tide-Driven Mixing

Abstract The ocean interior stratification and meridional overturning circulation are largely sustained by diapycnal mixing. The breaking of internal tides is a major source of diapycnal mixing. Many recent climate models parameterize internal-tide breaking using the scheme of St. Laurent et al. While this parameterization dynamically accounts for internal-tide generation, the vertical distribution of the resultant mixing is ad hoc, prescribing energy dissipation to decay exponentially above the ocean bottom with a fixed-length scale. Recently, Polzin formulated a dynamically based parameterization, in which the vertical profile of dissipation decays algebraically with a varying decay scale, accounting for variable stratification using Wentzel–Kramers–Brillouin (WKB) stretching. This study compares two simulations using the St. Laurent and Polzin formulations in the Climate Model, version 2G (CM2G), ocean–ice–atmosphere coupled model, with the same formulation for internal-tide energy input. Focusing mainly on the Pacific Ocean, where the deep low-frequency variability is relatively small, the authors show that the ocean state shows modest but robust and significant sensitivity to the vertical profile of internal-tide-driven mixing. Therefore, not only the energy input to the internal tides matters, but also where in the vertical it is dissipated.

Internal Bores and Breaking Internal Tides on the Oregon Continental Slope

AbstractObservations 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.

Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Application to the Southern Ocean

Abstract Recent estimates from observations and inverse models indicate that turbulent mixing associated with internal wave breaking is enhanced above rough topography in the Southern Ocean. In most regions of the ocean, abyssal mixing has been primarily associated with radiation and breaking of internal tides. In this study, it is shown that abyssal mixing in the Southern Ocean can be sustained by internal waves generated by geostrophic motions that dominate abyssal flows in this region. Theory and fully nonlinear numerical simulations are used to estimate the internal wave radiation and dissipation from lowered acoustic Doppler current profiler (LADCP), CTD, and topography data from two regions in the Southern Ocean: Drake Passage and the southeast Pacific. The results show that radiation and dissipation of internal waves generated by geostrophic motions reproduce the magnitude and distribution of dissipation previously inferred from finescale measurements in the region, suggesting that it is one of the primary drivers of abyssal mixing in the Southern Ocean.

Numerical study of the bottom‐intensified tidal mixing using an “eikonal approach”

Locally enhanced turbulent mixing above abyssal rough bottom bathymetry is one of the candidates that might make up for the lack of diapycnal diffusivity in maintaining the global overturning circulation. In the present study, we carry out a series of numerical experiments using an eikonal approach to examine the vertical distribution of energy dissipation rates caused by breaking of the semidiurnal internal tide. Special attention is directed to the physical parameters that control the magnitude and vertical decay scale of the bottom‐intensified mixing. It is shown that breaking of internal tides with horizontal scales much less than 1 km is responsible for bottom‐intensified mixing. There is an inevitable trade‐off between the magnitude and the vertical decay scale of bottom‐intensified mixing so that tidal interactions with abyssal rough bottom bathymetry are unlikely to create mixing hot spots intensive enough to affect the global overturning circulation.

Turbulent mixing and internal tides in Gaoping (Kaoping) Submarine Canyon, Taiwan

Turbulent overturning on scales greater than 10 m is observed near the bottom and in mid-depth layers within the Gaoping (formerly spelled Kaoping) Submarine Canyon (KPSC) in southern Taiwan. Bursts of strong turbulence coexist with bursts of strong sediment concentrations in mid-depth layers. The turbulence kinetic energy dissipation rate in some turbulence bursts exceeds 10 − 4 W kg − 1 , and the eddy diffusivity exceeds 10 − 1 m 2 s − 1 . Within the canyon, the depth averaged turbulence kinetic energy dissipation rate is ~ 7 × 10 − 6 W kg − 1 , and the depth averaged eddy diffusivity is ~ 10 − 2 m 2 s − 1 . These are more than two orders of magnitude greater than typical values in the open ocean, and are much larger than those found in the Monterey Canyon where the strong turbulent mixing has also been. The interaction of tidal currents with the complex topography in Gaoping Submarine Canyon is presumably responsible for the observed turbulent overturning via shear instability and the breaking of internal tides and internal waves at critical frequencies. Strong 1st-mode internal tides exist in KPSC. The depth averaged internal tidal energy near the canyon mouth is ~ 0.17 m 2 s − 2 . The depth integrated internal tidal energy flux at the mouth of the canyon is ~ 14 kW m − 1 , propagating along the axis of the canyon toward the canyon head. The internal tidal energy flux in the canyon is 3–7 times greater than that found in Monterey Canyon, presumably due to the more than 10 times larger barotropic tide in the canyon. Simple energy budget calculations conclude that internal tides alone may provide energy sufficient to explain the turbulent mixing estimated within the canyon. Further experiments are needed in order to quantify the seasonal and geographical distributions of internal tides in Gaoping Submarine Canyon and their effects on the sediment flux in the canyon.

Observations of turbulence in a tidal beam and across a coastal ridge

During a microstructure survey off California in Monterey Bay, we found a midwater beam of strong turbulence emanating from the shelf break along the ray path of the semidiurnal M2 internal tide. Within the 50‐m‐thick beam the turbulence kinetic energy dissipation rate ε exceeded 10−6 W kg−1, and the diapycnal eddy diffusivity Kρ was >0.01 m2 s−1. The beam extended 4 km off the shelf break. Several factors suggest that this beam of strong turbulence resulted from the breaking of semidiurnal internal tides: the beam appeared to originate from the shelf break, which is a potential generation site for semidiurnal internal tides; the beam closely followed the ray path of the semidiurnal internal tide; the average ε off the shelf break varied by a factor of 100 with a semidiurnal tidal periodicity; the isopycnal displacement confirmed the presence of semidiurnal internal tides. Processes associated with the breaking of internal tides are intermittent and sporadic. At the same location we also observed equally intense turbulence in a ∼100‐m‐thick layer of stratified water across the ridge of a sea fan. This layer of strong turbulence was separated from the bottom and was clearly not generated by bottom friction. Although less well resolved in time, the strong turbulence above the bottom seemed to vary with the semidiurnal tide and existed at the lee of the ridge, where the isopycnal surface dipped and rebounded in a pattern resembling that of internal hydraulic jumps. On the basis of the behavior of the density field, we believe that the deep mixing was most likely produced by the across‐ridge current of internal tides. The breaking of internal tides at middepth, where the Richardson number is close to the critical value, is likely due to shear instability. The presence of the coastal ridge provides an alternative pathway for converting energy from internal tides to turbulence via internal hydraulics. Multiplying the average ε in the midwater beam by the length of the global coastline gives 31 GW, only a small fraction of the estimated 360 GW dissipated globally by M2 internal tides. Our observations suggest that either most internal tides are generated away from shelf breaks or most internal tides generated at shelf breaks propagate away from their generation sites, rather than dissipate locally, and eventually contribute to pelagic mixing.