Numerical and experimental modelling of the internal tide near a continental shelf (original) (raw)
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Along-slope generation as an explanation for some unusually large internal tides
Deep Sea Research Part I: Oceanographic Research Papers, 2002
Why are the internal waves observed on the Portuguese shelf at 411N (which have thermocline displacements of up to 45 m) many times larger than expected from 2D shelf edge internal tide generation theory? Barotropic tidal forcing is too small to create them, either at the local shelf edge or from the nearby Oporto seamount. Using wave refraction techniques it is demonstrated that they must be created by the interaction between tidal currents and a major westward projection of the shelf edge about 50 km to the south. The off-shelf propagating internal tidal energy thus generated is subsequently refracted back onto the shelf in the form of non-linear internal wave packets. Refraction explains not only how the energy reaches the shelf, but also the orientation of the waves relative to the shelf edge and details of their appearance in a synthetic aperture radar image. The result demonstrates that shelf edge internal tide generation can be more complex than is suggested by the 2D approach, and that global shelf edge internal tide energy must be larger than previously thought. r
Interactions of internal tides with a heterogeneous and rotational ocean
2021
We consider the interactions of internal tides (ITs) with a dynamic, rotational and heterogeneous ocean, and spatially varying topography. The IT fields are expanded using vertical modal basis functions, whose amplitudes vary horizontally and temporally. We obtain the evolution equations of modal amplitudes and energy including simultaneous three-way interactions with the mean flow, buoyancy and topography. We apply these equations to a set of idealized and two realistic data-assimilative primitive equation simulations. These simulations reveal that significant interactions of ITs with the background fields occur at topographic features and strong currents, in particular when the scales of the background and ITs are similar. In local hot spots, the new three-way interaction terms, when compared to the total modal conversion, are found to reach up to 10 %–30 % at steep topography and approximately 50 % in the Gulf Stream. We provide a dimensional analysis to guide the diagnosis of su...
From Tides to Mixing Along the
The cascade from tides to turbulence has been hypothesized to serve as a major energy pathway for ocean mixing. We investigated this cascade along the Hawaiian Ridge using observations and numerical models. A divergence of internal tidal energy flux observed at the ridge agrees with the predictions of internal tide models. Large internal tidal waves with peak-to-peak amplitudes of up to 300 meters occur on the ridge. Internal-wave energy is enhanced, and turbulent dissipation in the region near the ridge is 10 times larger than open-ocean values. Given these major elements in the tides-to-turbulence cascade, an energy budget approaches closure.
Journal of Geophysical Research, 1999
An analytical model has been developed to describe the generation of a linear interfacial wave over a steep ocean margin by a barotropic tide propagating toward the shelf break with a variable angle of incidence. The stratification is reduced to a two-layer system, and the model uses step-like shelf geometry. In both shallow and deep regions an open boundary is assumed (this implies particularly that there is no reflection at the coast). The model is forced with the amplitude and direction of an incident barotropic Poincar6 wave propagating toward the shelf break. With this forcing, the model gives the amplitude, direction of propagation, and wavenumber of both barotropic and baroclinic Poincar6 waves transmitted onto the shelf and reflected into the deep region in the vicinity of the shelf break. After comparison with Baines' [1973] model, our model is compared with internal tide observations made in July 1996 on the Malin Shelf within the U.K. Land Ocean Interaction Study-Shelf Edge Study program. The observations are from moored thermistor chains and acoustic Doppler current profilers sited at two locations, one near the shelf break and the other 47.5 km onto the shelf. Observations at this latter mooring are not described by the generation model because of nonlinear changes and damping as the internal wave propagates through shallow water. Baroclinic displacements of the thermocline of 8 m amplitude were observed close to the shelf break, and total baroclinic energy was estimated at 2.4 J/m 3 during neap tide and 3 J/m 3 during spring tide. Both amplitude and energy of the shoreward propagating internal tide waves are compared with the model. Using a barotropic forcing taken from bibliographical data, good agreement with observations is found during neap tide (when the density structure is close to being two-layer) for an incident barotropic tide of 1 m amplitude and propagation direction on a bearing of 23øT (T means from True North in a clockwise sense).
Tides in subsurface oceans with meridional varying thickness
Icarus, 2020
Tidal heating can play an important role in the formation and evolution of subsurface oceans of outer-planet moons. Up until now tidal heating has only been studied in subsurface oceans of spatially uniform thickness. We develop a numerical model to consider oceans of spatially variable thickness. We use the Laplace Tidal Equations for the ocean and model the ice shell using membrane theory. The problem is solved using the commercial Finite Element software Comsol Multiphysics®. We use this new model to study the tidal response of Enceladus' ocean with a twofold objective: to understand how ocean thickness variations modify the tidal response of a subsurface ocean and to assess if tidal dissipation in an Enceladan ocean with varying ocean thickness can explain the high heat flux emanating from Enceladus' South Polar Terrain and the perdurance of a subsurface ocean. We consider the effect of meridional ocean thickness changes of spherical harmonic degree two and three as suggested by topography and gravimetry data. We observe that an ocean with degree two topography responds with the same eigenmodes as an ocean of constant thickness but resonances occur for thicker oceans. However, resonant ocean thicknesses are still thin compared to current estimates for Enceladus ocean thickness. Rossby-Haurwitz waves, excited by the obliquity tide for thick oceans of constant thickness, are not excited at the tidal frequency when oceans of variable thickness are considered. This result implies that the role of the obliquity tide in ocean tidal-dissipation might have been overestimated for Enceladus and other icy worlds. An antisymmetric, degree-three ocean thickness variation mixes the ocean modes excited in a constant thickness ocean by the eccentricity and obliquity tide.
Internal tide generation in nonuniformly stratified deep oceans
We present numerical and experimental studies of the conversion of tidal motions of an exponentially stratified fluid over two-dimensional knife edge, Gaussian, and complex bottom topography to radiated internal waves in a model of the deep ocean. We compare the radiated internal wave power for cases of strong stratification, where the buoyancy frequency profile N(z) (proportional to the square root of the density gradient) is much larger than the tidal frequency x, to the power radiated for weak stratifications. We consider particularly internal wave generation for topography below a turning depth z td , where Nðz td Þ5x; for z < z td , internal waves are evanescent. We find that topography below a turning depth does generate internal waves that propagate for z > z td , although the radiated power in these waves is much weaker than in cases without turning depths. The radiated power is predicted well by prior analytical theory if the nonuniform stratification is averaged over depths spanning from the bottom boundary up to an effective height z eff . In the absence of a turning depth, we find z eff is approximately equal to the height of the topography, indicating that only the stratification for depths spanned by the topography is relevant. However, in the presence of a turning depth, the vertical scale of the internal tide becomes larger, and z eff increases approximately linearly with the turning depth height toward values comparable to the total fluid depth.
Tides near a shelf-slope front
Continental Shelf Research, 1988
A two-layer model is used to examine the tides near a shelf-slope front that intersects both the bottom and the sea surface. Because of the presence of super-inertial eigenmodes in such a front, the semidiurnal tide is preferentially amplified (relative to the diurnal tide) by the generation of the baroclinic tide. Over the Mid-Atlantic Bight where the stratification is typically weak (i.e. the baroclinic radius of deformation is small compared with the width of the frontal zone), the baroclinic tide only slightly modifies the barotropic tide, it nevertheless causes a surface (bottom) intensification of the cross-shelf flow at the diurnal (semidiurnal) frequency. The model results compare favorably with observations and their implications on the tidal mixing in the frontal zone are discussed.
Resolving the horizontal direction of internal tide generation
Journal of Fluid Mechanics, 2019
The mixing induced by breaking internal gravity waves is an important contributor to the ocean’s energy budget, shaping, inter alia, nutrient supply, water mass transformation and the large-scale overturning circulation. Much of the energy input into the internal wave field is supplied by the conversion of barotropic tides at rough bottom topography, which hence needs to be described realistically in internal gravity wave models and mixing parametrisations based thereon. A new semi-analytical method to describe this internal wave forcing, calculating not only the total conversion but also the direction of this energy flux, is presented. It is based on linear theory for variable stratification and finite depth, that is, it computes the energy flux into the different vertical modes for two-dimensional, subcritical, small-amplitude topography and small tidal excursion. A practical advantage over earlier semi-analytical approaches is that the new one gives a positive definite conversion...