Internal Tide Generation Research Articles

Global M2 internal tide and its seasonal variability from high resolution ocean circulation and tide modeling

The present study describes a model simulation, where ocean tide dynamics are simulated simultaneously with the ocean circulation. The model is forced by a lunisolar tidal forcing described by ephemerides and by daily climatological wind stress, heat, and fresh water fluxes. The horizontal resolution is about 0.1° and thus, the model implicitly resolves meso‐scale eddies and internal waves. In this model simulation the globalM2 barotropic to baroclinic tidal energy conversion amounts to 1.2 TW. We show global maps of the surface signature of the M2baroclinic tide and compare it with an estimate obtained from 19 years of satellite altimeter data. Further, the simulated seasonality in the low mode internal tide field is presented and, as an example, the physical mechanisms causing the non‐stationarity of the internal tide generated in Luzon Strait are discussed. In general, this study reveals the impact of inter‐annual changes of the solar radiative forcing and wind forced ocean circulation on the generation and propagation of the low mode internal tides. The model is able to simulate non‐stationary signals in the internal tide field on global scales which have important implications for future satellite altimeter missions.

An evaluation of the barotropic and internal tides in a high‐resolution global ocean circulation model

Global comparisons of barotropic and internal tides generated in an eddy‐resolving ocean circulation model are made with tidal estimates obtained from altimetric sea surface heights and an altimetry‐constrained tide model. As far as we know, our Hybrid Coordinate Ocean Model (HYCOM) simulations shown here and in an earlier paper are the only published high‐resolution global simulations to contain barotropic tides, internal tides, the general circulation, and mesoscale eddies concurrently. Comparing the model barotropic tide with a global data‐assimilative shallow water tide model shows that the global tidal elevation differences are approximately evenly split between discrepancies in tidal amplitude and phase. Both the model and observations show strong generation of internal tides at a limited number of “hot spot” regions with propagation of beams of energy for thousands of kilometers away from the sources. The model internal tidal amplitudes compare well with observations near these energetic tidal regions. Averaged over these regions, the model and observation internal tide amplitude estimates agree to approximately 15% for the four largest semidiurnal constituents and 23% for the four largest diurnal constituents. Away from the hot spots, the comparison between the model and altimetric amplitude is not as good due, in part, to two problems, errors in the model barotropic tides and overestimation of the altimetric tides in regions of strong mesoscale eddy activity. Examining the general energy distribution of the simulated internal tide is an important first step in the evaluation of internal tides in HYCOM.

Diurnal modulation of semidiurnal internal tides in Luzon Strait

A three-dimensional model is applied to the South China Sea to study the generation of internal tides in the Luzon Strait, a mixed diurnal dominant barotropic tidal environment. The computed internal tidal flux is in good agreement with limited observations and with estimates from the barotropic tidal inversion. The diurnal internal tides are simple harmonic oscillations. The semidiurnal internal tides, on the other hand, are highly nonlinear with striking daily amplitude variations. Comparison with an analytical mixed internal tide–lee wave model shows that the diurnal modulation is caused by interaction of barotropic diurnal tidal currents with the linear internal waves. The highly nonlinear semidiurnal internal tides likely is responsible for the observed diurnally modulated nonlinear internal waves in the South China Sea. The semidiurnal internal tides also appears to be the major source for the enormous vertical mixing in the Luzon Strait.

Time‐varying parametric subharmonic instability from repeat CTD surveys in the northwestern Pacific Ocean

Time‐varying diapycnal diffusivity signals are estimated using the fine‐scale parameterization method from high‐resolution CTD data along three repeat sections in the northwestern Pacific Ocean. Indicative of the parametric subharmonic instability (PSI), locally‐elevated diapycnal mixing is detected alongallthree sections within the 25°–29°N band where bottom topography is relatively featureless. Due to their proximity to the semidiurnal internal tide generation sites, the two sections along ∼137°E have a time‐mean diffusivity value 2.5 × 10−5 m2 s−1 in the 300–2,000 m upper ocean. In contrast, it is 1.2 × 10−5 m2 s−1along the 165°E section. The time‐varying diffusivity along both sections is dominated by signals whose vertical structure resembles the local first dynamic normal mode profile. At the 137°E site of 25°–29°N, the local spring‐neap modulated semidiurnal tidal current is found to lead the CTD‐derived diffusivity time series by 6 days and can alter the diffusivity level by 0.24 × 10−5 m2 s−1. Similarly, the concurrent surface wind work is found to modify the diffusivity level by 0.35 × 10−5 m2 s−1. The combined spring‐neap tide and wind work forcing explains 47% of the observed, time‐varying diffusivity signals.

Propagation and dissipation of internal tides in the Oslofjord

Abstract. Observations of velocity, pressure, temperature and salinity in the inner Oslofjord have been analysed to provide new information about the relationships between internal tides generated by tidal currents across the Drøbak Sill and dissipation and diffusivity in the fjord. The most energetic vertical displacement of density surfaces inside the sill is associated with the first internal mode that has maximum amplitude around sill depth. The amplitude of the vertical displacement around sill depth correlates with the amplitude of the surface elevation, and, at a distance of 1 km inside the sill, the ratio between the amplitudes is 38, decreasing to 11 at a distance of 10 km. The greatest vertical displacements inside the sill, however, are found at 40 m depth. These latter internal waves are not associated with a first-mode internal tide, but are rather associated with higher internal modes controlled by stratification. The energy flux of the internal wave propagating from the Drøbak Sill into the inner fjord on the east side of the Håøya Island is estimated to vary in the range 155–430 kW. This is the same order of magnitude as the estimated barotropic energy loss over the Drøbak Sill (250 kW), but only 4–10% of the total barotropic flux. Approximately 40–70% of the internal energy flux is lost within a distance of 10 km from the sill. The mean diffusivity below 90 m depth in this area (~20 cm2 s−1) is more than four times higher than in the rest of the fjord (~5 cm2 s−1 or less).

Sensitivity of internal tide generation in Hawaii

Energy from the barotropic tide is transferred into the baroclinic tide over topographic gradients, which provides a mechanism for the ocean boundaries to communicate with the deep ocean, to close energy budgets, and as a source of flux affecting nutrient supply and larval transport. Understanding the temporal variability of the conversion from barotropic to baroclinic tides is critical to our understanding of these processes. Using a numerical model and its adjoint, we examine the sensitivity of tidal conversion at Kaena Ridge in Hawaii. We find a sensitivity to changes in the upper ocean due to a phase difference between the pressure anomaly and tidal velocity caused by internal waves generated on the opposite slope of the ridge; however, we also find that conversion is equally as sensitive to local, deep stratification changes.

Absence of internal tidal beams due to non-uniform stratification

A linear internal-tide generation model is applied to the Faeroe–Shetland Channel, using observed profiles of stratification. Several degrees of simplification are considered: 1) uniform, i.e. constant N; 2) vertically varying N (z); 3) the full N(x, z) and associated geostrophic background flows. It is shown that clearly identifiable internal tidal beams and internal-wave attractors occur in the first case, but not in the other cases where the pattern is patchy due to internal reflections from the strong inhomogeneities in the medium. Given the general occurrence of pycnoclines and geostrophic background flows in the ocean, it is argued that this internal scattering can be expected to be a widespread phenomenon.

Analysis of four‐dimensional variational state estimation of the Hawaiian waters

In this study, we evaluate results from an incremental strong constraint four‐dimensional variational data assimilation (IS4D‐Var) experiment applied to the circulation around the Hawaiian Islands using the Regional Ocean Modeling System (ROMS). Assimilated observations include (1) satellite‐derived high‐resolution swath radiometer sea surface temperatures (SST) and along‐track altimetric sea surface heights (SSH) and (2) in situ temperature and salinity profiles from Argo floats, autonomous Seagliders, and shipboard conductivity‐temperature‐depth. Two assimilation configurations are compared: adjusting initial conditions versus adjusting both initial conditions along with atmospheric forcing. In the latter case, we compare two separate forcing products. For all experiments, we investigate how the assimilation alters the tidal, inertial, and mesoscale variability. Significant improvements in the observation‐model fit are found for SST and salinity regardless of assimilation configuration or atmospheric forcing; however, significant change to the subsurface temperature is made when adjusting only initial conditions. Baroclinic tides are altered during the assimilation because of changes in the density field in regions of strong internal tide generation. Spurious inertial oscillations are found in assimilation circulations that are associated with the IS4D‐Var increment when using either SST or SSH observations; however, this increase in the inertial energy had minimal effect on the mesoscale variability.

Energetics of Barotropic and Baroclinic Tides in the Monterey Bay Area

Abstract A detailed energy analysis of the barotropic and baroclinic M2 tides in the Monterey Bay area is performed. The authors first derive a theoretical framework for analyzing internal tide energetics based on the complete form of the barotropic and baroclinic energy equations, which include the full nonlinear and nonhydrostatic energy flux contributions as well as an improved evaluation of the available potential energy. This approach is implemented in the Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS). Results from three-dimensional, high-resolution SUNTANS simulations are analyzed to estimate the tidal energy partitioning among generation, radiation, and dissipation. A 200 km × 230 km domain including all typical topographic features in this region is used to represent the Monterey Bay area. Of the 152-MW energy lost from the barotropic tide, approximately 133 MW (88%) is converted into baroclinic energy through internal tide generation, and 42% (56 MW) of this baroclinic energy radiates away into the open ocean. The tidal energy partitioning depends greatly on the topographic features. The Davidson Seamount is most efficient at baroclinic energy generation and radiation, whereas the Monterey Submarine Canyon acts as an energy sink. Energy flux contributions from nonlinear and nonhydrostatic effects are also examined. In the Monterey Bay area, the nonlinear and nonhydrostatic contributions are quite small. Moreover, the authors investigate the character of internal tide generation and find that in the Monterey Bay area the generated baroclinic tides are mainly linear and in the form of internal tidal beams. Comparison of the modeled tidal conversion to previous theoretical estimates shows that they are consistent with one another.

The Cascade of Tidal Energy from Low to High Modes on a Continental Slope

Abstract 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 conversion 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.

Incoherent Nature of M2 Internal Tides at the Hawaiian Ridge

Abstract Moored current, temperature, and conductivity measurements are used to study the temporal variability of M2 internal tide generation above the Kaena Ridge, between the Hawaiian islands of Oahu and Kauai. The energy conversion from the barotropic to baroclinic tide measured near the ridge crest varies by a factor of 2 over the 6-month mooring deployment (0.5–1.1 W m−2). The energy flux measured just off the ridge undergoes a similar modulation as the ridge conversion. The energy conversion varies largely because of changes in the phase of the perturbation pressure, suggesting variable work done on remotely generated internal tides. During the mooring deployment, low-frequency current and stratification fluctuations occur on and off the ridge. Model simulations suggest that these variations are due to two mesoscale eddies that passed through the region. The impact of these eddies on low-mode internal tide propagation over the ridge crest is considered. It appears that eddy-related changes in stratification and perhaps cross-ridge current speed contribute to the observed phase variations in perturbation pressure and hence the variable conversion over the ridge.

Spatial and Temporal Variability of the M2 Internal Tide Generation and Propagation on the Oregon Shelf

Abstract A 1-km-horizontal-resolution model based on the Regional Ocean Modeling System is implemented along the Oregon coast to study average characteristics and intermittency of the M2 internal tide during summer upwelling. Wind-driven and tidally driven flows are simulated in combination, using realistic bathymetry, atmospheric forcing, and boundary conditions. The study period is April through August 2002, when mooring velocities are available for comparison. Modeled subtidal and tidal variability on the shelf are in good quantitative agreement with moored velocity time series observations. Depth-integrated baroclinic tidal energy flux (EF), its divergence, and topographic energy conversion (TEC) from the barotropic to baroclinic tide are computed from high-pass-filtered, harmonically analyzed model results in a series of 16-day time windows. Model results reveal several “hot spots” of intensive TEC on the slope. At these locations, TEC is well balanced by EF divergence. Changes in background stratification and currents associated with wind-driven upwelling and downwelling do not appreciably affect TEC hot spot locations but may affect intensity of internal tide generation at those locations. Relatively little internal tide is generated on the shelf. Areas of supercritical slope near the shelf break partially reflect baroclinic tidal energy to deeper water, contributing to spatial variability in seasonally averaged on-shelf EF. Despite significant temporal and spatial variability in the internal tide, the alongshore-integrated flux of internal tide energy onto the Oregon shelf, where it is dissipated, does not vary much with time. Approximately 65% of the M2 baroclinic tidal energy generated on the slope is dissipated there, and the rest is radiated toward the shelf and interior ocean in roughly equal proportions. An experiment with smoother bathymetry reveals that slope-integrated TEC is more sensitive to bathymetric roughness than on-shelf EF.

Modelling the barotropic tide along the West-Iberian margin

The present work explores the use of a numerical model to predict the barotropic tide along the West-Iberian region, extending from the Gulf of Cadiz to the Bay of Biscay and from the shelf to nearby seamounts (Gorringe and Galicia banks). The model is used, in a single isopycnal layer, to simulate the 2D propagation of the following eight principal tidal constituents: M2, S2, N2, K2, K1, O1, P1 and Q1. Astronomical tide-raising force is introduced into the equations of motion in order to improve model results. Recently updated global tide solutions are optimally combined to force a polychromatic tidal spectrum at the open boundaries. New bathymetry is built from hydrographic databases and used to increase the accuracy of the model, especially over the Portuguese continental shelf. Data from several tide gauges and acoustic Doppler current profilers are used to validate the numerical solution. Tidal amplitude and tidal current velocity solutions are evaluated by classical harmonic analysis of in situ and simulated time-series. Model outputs demonstrate the improvement of the regional hydrodynamic tide solution from earlier references. The harmonic solutions highlight small-scale variability over the shelf, and over nearby seamounts, due to the generation of diurnal continental shelf waves and topographic modulation of the semi-diurnal tidal ellipses. The barotropic forcing term is calculated over the study region and the main internal tide generation “hotspots” are revealed.

Numerical study of M2 internal tide generation and propagation in the Luzon Strait

Based on the z-coordinate ocean model HAMSOM, we introduced the internal-tide viscosity term and applied the model to numerically investigate the M2 internal tide generation and propagation in the Luzon Strait (LS). The results show that (1) in the upper 250 m depth, at the thermocline, the maximum amplitude of the generated internal tides in the LS can reach 40 m; (2) the major internal tides are generated to the northwest of Itbayat Island, the southwest of Batan Island and the northwest of the Babuyan Islands; (3) during the propagation the baroclinic energy scattering and reflection is obvious, which exists under the effect of the specific topography in the South China Sea (SCS); (4) the westward-propagating internal tides are divided into two branches entering the SCS. While passing through 118°E, the major branch is divided into two branches again. The strongest internal tides in the LS are generated to the northwest of Itbayat Island and propagate northeastward to the Pacific. However, to the east of 122°E, most of the internal tides propagate southeastward to the Pacific as a beam.

A Theory of Vertical Modes in Multilayer Stratified Fluids

AbstractA theory of vertical modes in multilayer stratified fluids is proposed. A matrix notation is introduced to generalize the theory to an arbitrary number of layers. The properties of vertical modes including their orthogonality are derived. The linearized shallow-water equations and total energy equation are then decomposed into vertical modal components in the presence of large horizontal variations in bottom elevation and stratification, which induce linear interactions among vertical modes. The theory is applied to the derivation of vertical modes in three-layer stratified fluids and an internal tide generation problem under two-layer stratification. It is shown that the proposed theory correctly approaches the continuous counterpart as the number of layers increases.

Topographies lacking tidal conversion

AbstractThe consensus is that in a stratified sea a classical model of tidal flow over irregular but smooth topography necessarily leads to the generation of internal tides, regardless of the shape of the topography. This is referred to as tidal conversion. Here it is shown, however, that there exists a large class of topographies for which there is neither tidal conversion nor any scattering of incident internal waves. This result is obtained in a uniformly stratified, rigid-lid sea using a barotropic tide that, owing to its large horizontal scale, is supposed to be simply a mass-conserving, periodic back-and-forth flow. The baroclinic response at the tidal frequency is, upon non-dimensionalizing and stretching of coordinates, determined by a standard hyperbolic boundary value problem (BVP). We here solve this hyperbolic BVP by mapping a domain of complicated, yet a priori unknown shape, onto a uniform-depth channel for which the same hyperbolic problem is known to display neither conversion of the barotropic tide nor scattering of internal wave modes. The map achieving this is required to satisfy hyperbolic Cauchy–Riemann equations, defined as analogues of the Cauchy–Riemann equations that are used in solving elliptic problems. Mapping the rigid-lid surface in the original Cartesian frame onto a rigid-lid surface in the transformed frame, this map is solved in terms of one arbitrary function. Each particular function defines a new topographic shape that can be computed a posteriori. The map is unique provided the Jacobian of transformation does not vanish, which is guaranteed for subcritical bottom topography, whose slope is everywhere less than that of the characteristics. For topographies that can thus be mapped onto a channel, tidal conversion and scattering are absent. Examples discussed include the (classical) wedge, a (near-Gaussian) ridge, a continental slope and (near) sinusoidal topographies.

The Generation and Evolution of Nonlinear Internal Waves in the Deep Basin of the South China Sea

Abstract Time series observations of nonlinear internal waves in the deep basin of the South China Sea are used to evaluate mechanisms for their generation and evolution. Internal tides are generated by tidal currents over ridges in Luzon Strait and steepen as they travel west, subsequently generating high-frequency nonlinear waves. Although nonlinear internal waves appear repeatedly on the western slopes of the South China Sea, their appearance in the deep basin is intermittent and more closely related to the amplitude of the semidiurnal than the predominant diurnal tidal current in Luzon Strait. As the internal tide propagates westward, it evolves under the influence of nonlinearity, rotation, and nonhydrostatic dispersion. The interaction between nonlinearity and rotation transforms the internal tide into a parabolic or corner shape. A fully nonlinear two-layer internal wave model explains the observed characteristics of internal tide evolution in the deep basin for different representative forcing conditions and allows assessment of differences between the fully and weakly nonlinear descriptions. Matching this model to a wave generation solution for representative topography in Luzon Strait leads to predictions in the deep basin consistent with observations. Separation of the eastern and western ridges is close to the internal semidiurnal tidal wavelength, contributing to intensification of the westward propagating semidiurnal component. Doppler effects of internal tide generation, when combined with a steady background flow, suggest an explanation for the apparent suppression of nonlinear wave generation during periods of westward intrusion of the Kuroshio.

Direct and large-eddy simulations of internal tide generation at a near-critical slope

A numerical study is performed to investigate nonlinear processes during internal wave generation by the oscillation of a background barotropic tide over a sloping bottom. The focus is on the near-critical case where the slope angle is equal to the natural internal wave propagation angle and, consequently, there is a resonant wave response that leads to an intense boundary flow. The resonant wave undergoes both convective and shear instabilities that lead to turbulence with a broad range of scales over the entire slope. A thermal bore is found during upslope flow. Spectra of the baroclinic velocity, both inside the boundary layer and in the external region with free wave propagation, exhibit discrete peaks at the fundamental tidal frequency, higher harmonics of the fundamental, subharmonics and inter-harmonics in addition to a significant continuous part. The internal wave flux and its distribution between the fundamental and harmonics is obtained. Turbulence statistics in the boundary layer including turbulent kinetic energy and dissipation rate are quantified. The slope length is varied with the smaller lengths examined by direct numerical simulation (DNS) and the larger with large-eddy simulation (LES). The peak value of the near-bottom velocity increases with the length of the critical region of the topography. The scaling law that is observed to link the near-bottom peak velocity to slope length is explained by an analytical boundary-layer solution that incorporates an empirically obtained turbulent viscosity. The slope length is also found to have a strong impact on quantities such as the wave energy flux, wave energy spectra, turbulent kinetic energy, turbulent production and turbulent dissipation.

Experimental mixing parameterization due to multiphase fluid–structure interactions

Experimental estimates of the rate at which energy is extracted from the barotropic tide at corrugated sloping topography are presented. To this end, a series of experimental simulations of the process of generation of internal tides (i.e., internal waves of the tidal frequency) over a corrugated slope in stratified fluid were performed. An oceanic interior is modeled as four-layer stratified fluid. The main focus in these studies was to obtain the relation for the potential energy available for mixing as a function of a slope of a corrugated slope. The available potential energy available for partial mixing to the topographic slope was compared with the available potential energy sufficient for complete mixing of the four layers. The experimental data were compared with the analytic results of a linear theory and found in agreement with a recent theoretically predicted scenario showing that the dominant contribution of the energy distribution in internal wave field resides in waves of the lowest allowed frequency.

A Mechanism for Local Dissipation of Internal Tides Generated at Rough Topography

Abstract Fine- and micro-structure observations indicate that turbulent mixing is enhanced within O(1) km above rough topography. Enhanced mixing is associated with internal wave breaking and, in many regions of the ocean, has been linked to the breaking and dissipation of internal tides. The generation and dissipation of internal tides are explored in this study using a high-resolution two-dimensional nonhydrostatic numerical model, which explicitly resolves the instabilities leading to wave breaking, configured in an idealized domain with a realistic multiscale topography and flow characteristics. The control simulation, chosen to represent the Brazil Basin region, produces a vertical profile of energy dissipation and temporal characteristics of finescale motions that are consistent with observations. Results suggest that a significant fraction of mixing in the bottom O(1) km of the ocean is sustained by the transfer of energy from the large-scale internal tides to smaller-scale internal waves by nonlinear wave–wave interactions. The time scale of the energy transfer to the smaller scales is estimated to be on the order of a few days. A suite of sensitivity experiments is carried out to examine the dependence of the energy transfer time scale and energy dissipation on topographic roughness, tidal amplitude, and Coriolis frequency parameters. Implications for tidal mixing parameterizations are discussed.