Internal tide generation due to topographically adjusted barotropic tide

<p>We model internal tides generated by the interaction of a barotropic tide with variable topography. For the barotropic part, an asymptotic solution valid over the variable topography is considered. The resulting non-uniform ambient flow is used as a prescribed barotropic forcing for the baroclinic equations (linearized, non-hydrostatic, Euler equations within the Boussinesq approximation).</p><p>The internal-tide generation problem is reformulated by means of a Coupled-Mode System (CMS) based on the decomposition of the baroclinic stream function in terms of vertical basis functions that consistently satisfy the bottom boundary condition. The proposed CMS is solved numerically with a finite difference scheme and shows good convergence properties, providing efficient calculations of internal tides due to 2D topographies of arbitrary height and slope. We consider several seamounts and shelf profiles and perform calculations for a wide range of heights and slopes. Our results are compared against existing analytical estimates on the far-field energy flux in order to examine the limit of validity of common simplifications (Weak Topography Approximation, Knife edge). For subcritical cases, local extrema of the energy flux exist for different heights. Non-radiating topographies are also identified for some profiles of large enough heights. For supercritical cases, the energy flux is in general an increasing function with increasing height and criticality, and does not compare well against analytical results for very steep idealized topographies. The effect of the adjusted barotropic tide in the energy flux and the local properties of the baroclinic field is investigated through comparisons with other semi-analytical methods based on a uniform barotropic tide (Green’s function approach).  A method for estimating the sea-surface signature of internal tides is also provided.</p>

Implementation of the barotropic tide in oceanic circulation models. Current tests with the NEMO model

<p>This study proposes a new methodology for implementing the barotropic tide in an ocean general circulation model (OGCM). The assumptions underlying this methodology are that the best barotropic tide solutions are computed by specialized models and that the fields that should be accurately reproduced by the OGCM are the transport fields from the specialized tide model. The target/reference solution for the OGCM is thus the projection of the tide model on the OGCM grid, for each tidal harmonic.</p><p>The proposed methodology involves little change of the OGCM modeland yields almost exactly the reference solution, with a cost that is belowmost of the current methodologies. It relies on the modification of the tidepotential, or more accurately, on the replacement of all terms associatedwith the tide (tide potential, self attraction and loading, tide dissipation,  ...) by a general tide forcing term in the barotropic momentum equationwhich is calculated from the –known- reference solution.</p><p>The tide forcing terms can be tricky to calculate as they depend on details of the OGCM numerical schemes (for both temporal and spatial operators). A general procedure, automatically adapting the chosen schemes, is proposed for their calculation, so that the procedure is independent of the model.  </p><p>Tests with academic configurations are first proposed to validate the methodology and its implementation, and the OGCM is chosen to be the NEMO (Nucleus for European Modelling of the Ocean) model.</p><p>A global ¼° configuration with realistic bathymetry and with FES tide solutions (Finite Element Solution) are then performed. Current tests show that when FES solutions are crudely interpolated on the NEMO grid, the methodology exactly reproduces the FES fluxes, but the associates NEMO SSH is very noisy in regions where FES has high resolution. This problem is currently addressed. To get rid of this problem, fluxes must be carefully integrated along each grid cell, so that the reproduced SSH is exactly an average of the FES SSH within the NEMO grid cell. Hopefully, we will be able to present final –clean- solutions at the conference.</p>

The Drag on the Barotropic Tide due to the Generation of Baroclinic Motion

The interaction of a barotropic flow with topography generates baroclinic motion that exerts a stress on the barotropic flow. Here, explicit solutions are calculated for the spatial-mean flow (i.e., the barotropic tide) resulting from a spatially uniform but time-varying body force (i.e., astronomical forcing) acting over rough topography. This approach of prescribing the force contrasts with that of previous authors who have prescribed the barotropic flow. It is found that the topographic stress, and thus the impact on the spatial-mean flow, depend on the nature of the baroclinic motion that is generated. Two types of stress are identified: (i) a “wave drag” force associated with propagating wave motion, which extracts energy from the spatial-mean flow, and (ii) a topographic “spring” force associated with standing motion at the seafloor, including bottom-trapped internal tides and propagating low-mode internal tides, which significantly damps the time-mean kinetic energy of the spatial-mean flow but extracts no energy in the time-mean. The topographic spring force is shown to be analogous to the force exerted by a mechanical spring in a forced-dissipative harmonic oscillator. Expressions for the topographic stresses appropriate for implementation as baroclinic drag parameterizations in global models are presented.

Interdependence of Internal Tide and Lee Wave Generation at Abyssal Hills: Global Calculations

The generation of internal waves at abyssal hills has been proposed as an important source of bottom-intensified mixing and a sink of geostrophic momentum. Using the theory of Bell, previous authors have calculated either the generation of lee waves by geostrophic flow or the generation of the internal tide by the barotropic tide, but never both together. However, the Bell theory shows that the two are interdependent: that is, the presence of a barotropic tide modifies the generation of lee waves, and the presence of a geostrophic (time mean) flow modifies the generation of the internal tide. Here we extend the theory of Bell to incorporate multiple tidal constituents. Using this extended theory, we recalculate global wave fluxes of energy and momentum using the abyssal-hill spectra, model-derived abyssal ocean stratification and geostrophic flow estimates, and the TPX08 tidal velocities for the eight major constituents. The energy flux into lee waves is suppressed by 13%–19% as a result of the inclusion of tides. The generated wave flux is dominated by the principal lunar semidiurnal tide (M2), and its harmonics and combinations, with the strongest fluxes occurring along midocean ridges. The internal tide generation is strongly asymmetric because of Doppler shifting by the geostrophic abyssal flow, with 55%–63% of the wave energy flux (and stress) directed upstream, against the geostrophic flow. As a consequence, there is a net wave stress associated with generation of the internal tide that reaches magnitudes of 0.01–0.1 N m−2 in the vicinity of midocean ridges.

The Effects of Remote Internal Tides on Continental Slope Internal Tide Generation

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.

The Influence of Subinertial Internal Tides on Near-Topographic Turbulence at the Mendocino Ridge: Observations and Modeling

Shipboard measurements of velocity and density were obtained in the vicinity of a small channel in the Mendocino Ridge, where flows were predominantly tidal. Measured daily inequalities in transport are much greater than those predicted by a barotropic tide model, with the strongest transport associated with full depth flows and the weakest with shallow, surface-confined flows. A regional numerical model of the area finds that the subinertial K1 (diurnal) tidal constituent generates topographically trapped waves that propagate anticyclonically around the ridge and are associated with enhanced near-topographic K1 transports. The interaction of the baroclinic trapped waves with the surface tide produces a tidal flow whose northward transports alternate between being surface confined and full depth. Full depth flows are associated with the generation of a large-amplitude tidal lee wave on the northward face of the ridge, while surface-confined flows are largely nonturbulent. The regional model demonstrates that, consistent with field observations, near-topographic dissipation over the entire ridge is diurnally modulated, despite the semidiurnal tidal constituent having larger barotropic velocities. It is concluded that at this location it is the bottom-trapped subinertial internal tide that governs near-topographic dissipation and mixing. The effect of the trapped wave on regional energetics is to increase the fraction of converted barotropic–baroclinic tidal energy that dissipates locally.

Tidally Driven Processes Leading to Near-Field Turbulence in a Channel at the Crest of the Mendocino Escarpment

In situ observations of tidally driven turbulence were obtained in a small channel that transects the crest of the Mendocino Ridge, a site of mixed (diurnal and semidiurnal) tides. Diurnal tides are subinertial at this latitude, and once per day a trapped tide leads to large flows through the channel giving rise to tidal excursion lengths comparable to the width of the ridge crest. During these times, energetic turbulence is observed in the channel, with overturns spanning almost half of the full water depth. A high-resolution, nonhydrostatic, 2.5-dimensional simulation is used to interpret the observations in terms of the advection of a breaking tidal lee wave that extends from the ridge crest to the surface and the subsequent development of a hydraulic jump on the flanks of the ridge. Modeled dissipation rates show that turbulence is strongest on the flanks of the ridge and that local dissipation accounts for 28% of the energy converted from the barotropic tide into baroclinic motion.

Stratified tidal flow over a tall ridge above and below the turning latitude

The interaction of the barotropic tide with a tall, two-dimensional ridge is examined analytically and numerically at latitudes where the tide is subinertial, and contrasted to when the tide is superinertial. When the tide is subinertial, the energy density associated with the response grows with latitude as both the oscillatory along-ridge flow and near-ridge isopycnal displacement become large. Where $f\neq 0$, nonlinear processes lead to the formation of along-ridge jets, which become faster at high latitudes. Dissipation and mixing is larger, and peaks later in the tidal cycle when the tide is subinertial compared with when the tide is superinertial. Mixing occurs mainly on the flanks of the topography in both cases, though a superinertial tide may additionally generate mixing above topography arising from convective breaking of radiating waves.

Tidal effects on ichthyoplankton aggregation and dispersion in the Southern Gulf of Mexico

The role of vertical barotropic and baroclinic tidal forcing in the aggregation and dispersion of ichthyoplankton in the Southern Gulf of Mexico was analyzed in this study. Samplings of ichthyoplankton and the determination of hydrographic parameters were performed during September 1992 at a single point of 180 m depth, near the shelf break (19º32'N - 92º38.5'W). A 24 h CTD yo-yoing casting and biological samples were taken every 2 h and these measurements were combined with water velocity and density simulations from the Regional Ocean Model System (ROMS). One thermocline and two haloclines were depicted. The Froude number increased with a 2 h lag with respect to the maximal barotropic tide, suggesting the existence of a baroclinic tide. Aggregation and dispersion of the ichthyoplankton showed vertical oscillations in the abundance and the numbers of taxa and larvae with a 5 h lag with respect to the maximal barotropic tide and were in phase with the thermocline oscillation. The vertical oscillation was attributed to a hydraulic control forced by the internal tide.