A numerical model of the internal tide in knight inlet,British Columbia

Abstract

A two‐dimensional, hydrostatic numerical model of the tides in Knight Inlet is compared with observations of velocity and density obtained from three cyclesonde moorings. The observations from a fourth cyclesonde mooring were used to provide boundary data at the open end of the model. The time period in the fjord that the model simulates was a period of high, freshwater runoff, so that the fjord had a distinct, surface layer. The use of high, vertical resolution was avoided by attaching a homogeneous, fresh, surface layer to the top of the model. The density equation was linearized about a mean, fixed density field, and the mixing of density was not allowed.

The model reproduces the semidiurnal (M₂, S₂ and N₂) and diurnal (K₁ and O₁) velocity and density signals in the inlet. The shallow‐water constituents (M₄ and MK₃) are reproduced even though the density equation has been linearized. The fortnightly constituent (MSf) is poorly simulated. When the advection terms in the momentum equation are set to zero, the basic features of the semidiurnal and diurnal constituents are still reproduced, but the shallow‐water constituents are poorly simulated.

The energy flux along the inlet of the M₂ internal tide is insensitive to the advective terms in the momentum equation. The total rate of dissipation of M₂ energy is similar to the energy flux in the M₂ internal tide near the sill, which implies that, according to the model, most of the energy removed from the barotropic tide is fed into the internal tide. The majority of the energy in the M₂ internal tide is dissipated close to the sill of the inlet, but enough of the energy makes its way to the head of the inlet to reflect and set up a recognizable standing wave pattern.     

On tidal resonance in the global ocean and the back‐effect of coastal tides upon open‐ocean tides

Abstract

The resonance of semi‐diurnal tidal elevations is investigated with a forward numerical forced damped global tide model and an analytical model of forced‐damped tides in a deep ocean basin coupled to a shelf. The analytical model contains the classical half‐wavelength and quarter‐wavelength resonances in the deep ocean and shelf, respectively, as well as a forcing‐scale dependence which depends on the ratio of the phase speed of open‐ocean gravity waves to that of the astronomical forcing. In the analytical model, when the deep ocean and shelf resonate separately at the same frequency, the resonance in the coupled system shifts to frequencies slightly higher and lower than the original frequency, such that a ‘double bump’ is seen in plots of elevation amplitude versus frequency. The addition of a shelf to a resonant open ocean tends to reduce open‐ocean tides, especially when the shelf is also near resonance. The magnitude of this ‘back‐effect’ is controlled by shelf friction. A weakly damped resonant shelf has a larger back‐effect on the open‐ocean tide than does a strongly damped shelf. Numerical simulations largely bear out the analytical model predictions, at least qualitatively. Idealized simulations show that continents enhance tides by enabling the half‐wavelength resonance. Simulations with realistic geometry and topography but varying longitudinal structure in the astronomical forcing display an influence of the forcing scale on tidal amplitudes somewhat similar to that seen in the analytical model. A frequency sweep in the semi‐diurnal band in experiments with realistic geometry and topography reveals weakly resonant peaks in the amplitudes of several shelf regions and in the globally averaged open‐ocean amplitudes. Finally, the back‐effect of the shelf upon the open ocean is seen in simulations in which locations of resonant coastal tides are blocked out and open‐ocean tidal elevations are significantly altered (increased, generally) as a result.     

Oceanographic observations on the Scotian Shelf during CASP

Abstract

Winter‐time (1985–86) observations of sea‐level, surface waves, currents, bottom pressure, and water properties were made on the Scotian Shelf as part of the Canadian Atlantic Storms Program (CASP). The purpose of the field program and the locations, instrument systems, and sampling schemes are described.

Statistics on the observed currents are presented, and monthly estimates of the longshore transport of the Nova Scotian Current are given for four months spanning the winter season (December to March). The 1985–86 transports are compared with previous estimates of the baroclinic transport made using the dynamic method.

Cross‐shelf temperature and salinity distributions corresponding to the beginning and end of the field program are described and compared with the climatological means.

The autospectra of the observed currents exhibit energy concentrations at frequencies of 0.2–0.5, 1.0, 1.4 and 2.0 cycles per day (cpd). Coastal‐trapped wave motions account for significant portions of the energy in the two lowest frequency bands, forced by wind stress and the diurnal tide, respectively. Inertial oscillations generated by wind stress events predominate at 1.4 cpd, and the semidiurnal tide, at 2 cpd. These motions are described separately, and references to more detailed discussions are given.     

Analysis of internal solitary waves observed in Davis Strait

Abstract

Current meters and a thermistor chain deployed in the proximity of a drill‐ship over the continental shelf off Baffin Island revealed the presence of large amplitude internal waves. This paper reviews the properties of the internal waves, observed to propagate away from the coast and to coincide with the local low water phase of the tide at the drill‐ship. The observations are considered in terms of internal solitary wave models. A detailed comparison is presented of wave properties with a long‐wave model incorporating continuous stratification and shear.     

Oceanic tides over the Newfoundland and Scotian Shelves from TOPEX/POSEIDON altimetry

Abstract

A modified response analysis in the form of an orthotide parametrization is used to derive major semi‐diurnal and diurnal tidal constituents over the Newfoundland and Scotian Shelves from TOPEX/POSEIDON altimeter data. The orthotide formulation simultaneously solves for eight major semi‐diurnal and diurnal constituents, and has an accuracy of better than ～1.5 cm for each constituent. Tidal elevations are derived from the altimeter data on the ascending and descending satellite ground tracks, and interpolated using the method of statistical interpolation. The semi‐diurnal constituents (M₂, S₂ and N₂) compare favourably with available in‐situ observations and a numerical model. The diurnals (K₁ and O₁) are not as accurate as the semi‐diurnals, especially in the nearshore environment. The paper demonstrates the ability of TOPEX/POSEIDON altimetry to provide accurate tidal data over a continental shelf.     

The circulation and hydrography of conception bay,Newfoundland

Abstract

The hydrography and circulation of Conception Bay (Newfoundland) are described based on hydrographic, current‐meter and drifter data collected over four years (1988–1991). The seasonal cycles of temperature (‐1.6 to 13–17°C) and salinity (31–32.5) in the bay closely follow those on the adjacent shelf. Exchange of bottom water was observed in April 1989. Deepwater exchange was observed from late fall to early winter of 1989–90. Tidal currents are weak, 1–2 cm s^‐1 for the M₂ and K₁ constituents. Observed Eulerian mean currents (<3 cm s^‐1) are smaller than the standard deviation (1–11 cm s^‐1); however, there is a persistent outflowing current of 10 to 20 cm s^‐1 within 2 km of the shoreline on the eastern side of the outer bay. The Lagrangian correlation length scale is from 4 to 10 km, in agreement with the weak coherence squared (≤0.4) found between the fixed current‐meter sites separated by greater than 4–5 km. The variable currents (up to 20 cm s^‐1) tend to be cyclonic. Cyclonic eddies were observed near the mouth on the eastern side of the bay, adjacent to the outflow. A simplified fractal dispersion model gives residence times of 42 d similar to those obtained from a scaling analysis (30–40 d) and a diagnostic numerical model (30 d).     

On the mean and tidal currents in Hudson strait

Abstract

The vertical structures of the mean and tidal flows in Hudson Strait are described from moored current‐meter data collected during an 8‐week period in August to October of 1982. The residual flow in the strongly stratified waters off Quebec is directed along the Strait to the southeast, is highly baroclinic and is concentrated near shore (within an offshore length scale of approximately an internal Rossby radius). Maximum mean speeds of 0.3 m s^?1 were observed near‐surface (30 m). In the weakly stratified waters on the northern side of the Strait along Baffin Island the mean flow is northwestward. The maximum speeds are 0.1 m s^?1 near‐surface (30 m) and the current amplitudes decrease to 0.05 m s^?1 at 100 m. The mean southeastward transport is estimated to be 0.93 ±0.23 × 10⁶ m³ s^?1 with a northwestward transport of 0.82 ± 0.24 × 10⁶ m³ s^?1. Over most of the Strait the across‐channel residual currents are directed towards the Quebec shore with velocities ranging from 0.02 to 0.1 ms^?1. Current variability is dominated by the tides, the M₂ being the major tidal constituent. In the vicinity of the mooring the M₂ tide is primarily barotropic, progressive in nature, and has along‐channel current amplitudes varying across the Strait from 0.20 to 0.45 m s^?1. Observed differences in tidal sea‐level elevations across the Strait can be accounted for by the cross‐channel variations characteristic of Kelvin waves.     

Tidal circulation and buoyancy effects in the St. Lawrence Estuary

Abstract

The action of tides on density‐driven circulation, internal gravity waves, and mixing was investigated in the St. Lawrence Estuary between Rimouski and Québec City. Time‐varying fields of water level, currents and density were computed under typical summer conditions using a three‐dimensional hydrostatic coastal ocean model that incorporates a second order turbulence closure submodel. These results are compared with current meter records and other observations. The model and the observations reveal buoyancy effects produced by tidal forcing. The semi‐diurnal tide raises the isopycnals over the sills at the head of the Laurentian Trough and English Bank, producing internal tides radiating seaward. Relatively dense intermediate waters rise from below 75‐m depth to the near surface over the sills, setting up gravity currents on the inner slopes. Internal hydraulic controls develop over the outer sills; during flood, surface flow separation occurs at the entrances of the Saguenay Fjord and the upper estuary west of Ilet Rouge Bank. Early during ebb flow (restratification), the surface layer deepens to encompass the tops of the sills. As the ebb current intensifies, the model predicts the formation of seaward internal jumps over the outer sills, which were confirmed from acoustic reflection observations. As the internal Froude number increases further, flow separation migrates up to sill height. As a result of these transitions, internal bores emanate from the head region one to two hours before low water. We find that the mixing of oceanic and surface waters near the sills is driven by the vertical shear produced during ebb in the channel south of Ilet Rouge, the shear produced in the bottom gravity flood currents, and, to a lesser extent, the processes over the sills.     

Baroclinic oscillations of tidal frequency at ocean weather station P

Abstract

We analyse time series records of isopleth depths derived from two extended sequences of hourly and bi‐hourly sampled profiles taken at Ocean Weather Station P during the summers of 1961 and 1969. Vertical displacements to 240‐m depth are mainly of semidiurnal frequency with r.m.s. amplitudes of 1–4 m. Displacements at diurnal and near‐inertial frequencies are typically less than a metre and have little statistical significance. Within the semidiurnal band, motions appear to be predominantly at the principal solar (S₂) rather than the principal lunar (M₂) semidiurnal frequency. The phase of the M₂ baroclinic tide is roughly equal to that of the M₂ barotropic tide (as extrapolated from coastal and seamount observations); phases of other constituents differ appreciably from barotropic values.     

A simulation of sea‐ice motion and distribution off Newfoundland during LIMEX,March 1987

Abstract

A coupled ice‐ocean dynamical model is applied to the simulation of sea‐ice motion and distribution off Newfoundland during the Labrador Ice Margin Experiment (LIMEX), March 1987. In the model, the ice is coupled to a barotropic ocean through an Ekman layer that deepens with increasing wind speed. A 6‐hourly gridded wind dataset was used as input to drive the ice and the ocean. The results show that ice velocities with ice‐ocean coupling are appreciably higher than those without coupling because of the generation of wind‐driven coastal currents. This suggests that coupled ice‐ocean dynamics should always be considered in short‐term sea‐ice models. The model gives reasonable agreement with the observed ice edge except in the southern boundary where ice‐melt has a strong influence on the ice‐edge position. Ocean currents, sea level and ice velocities computed from the model are in qualitative agreement with limited current‐meter, tide‐gauge, and ice drifter trajectory data.     

Semi‐diurnal internal wave diffraction caused by Dixon Entrance,British Columbia

Abstract

To develop an understanding of the complex internal tidal phenomena observed near and inside Dixon Entrance, an idealized numerical model was developed for the area, which explores the influence of various topographic features on the scattering of internal tides. The model uses a non‐linear, two‐layered, frictionless finite difference formulation of the shallow water equations and is forced by a barotropic wave over simplified topography. It was found that the main bathymetric features responsible for the generation of semi‐diurnal internal tides are the steep continental slope together with the orientation of Dixon Entrance. The prevalent baroclinic wave pattern, which is similar to the one found by Buchwald (1971), suggests that the western end of Dixon Entrance can be considered as an internal tide generation region for the open ocean. Use of the simple model allows easy identification of the generated waves. When the model is run with a non‐flat channel it reproduces features observed inside Dixon Entrance.     

Skew eddy fluxes as signatures of non‐linear tidal current interactions,with application to Georges Bank

Abstract

The eddy flux of a conservative scalar in a time‐dependent rotary velocity field may have a component that is normal to the scalar gradient. This component is the “skew flux”, which consists of the scalar transport by the Stokes velocity and a part that is always non‐divergent (and hence does not affect scalar evolution). Since tidal velocity fields usually have rotary features, tidal‐band eddy scalar fluxes may include a skew component that can be useful in indicating the occurrence of non‐linear current interactions.

The skew temperature flux associated with the semidiurnal tide in a continental shelf region is demonstrated using simple models, and moored current and temperature observations from Georges Bank. The observed fluxes on the Bank are largely directed along isobaths, with apparent contributions from the topographic rectification of the barotropic tidal current over the Bank's side and from the rotary tidal ellipses in a frontal region. Simple models indicate that the weaker cross‐isobath fluxes can arise through the influence of frictionally induced vertical structure on topographic tidal rectification, a baroclinic tidal current interaction, or the interaction of baroclinic and barotropic tidal currents. In some cases, the simple models show qualitative agreement with the observed fluxes and currents but, in general, more realistic models and better estimates of the background mean temperature field are required to obtain quantitative estimates of the relative importance of these interactions and other processes. Nevertheless, the observations and models suggest that non‐linear interactions involving both barotropic and baroclinic tidal currents are occurring on Georges Bank.     

Airborne measurements of the ocean's Ku‐band radar cross‐section at low incidence angles

Abstract

Ocean backscatter data obtained with a K_u‐band airborne radar are presented along with coincident altimeter and directional wave spectral estimates. These data were collected using one sensor, NASA's radar ocean wave spectrometer (ROWS). The measurements are compared with an electromagnetic scattering model for perfectly conducting Gaussian random surfaces. The normalized radar cross‐section (NRCS) data cover those incidence angles (0–20°) where both quasi‐specular and Bragg scattering mechanisms are expected. Under certain conditions, identification and separation of these two mechanisms is possible. The scanning radar allows observations of the azimuthal variations in NRCS that are at times indicative of short‐scale wave generation in the wind direction.     

Modelling stratification and baroclinic flow in the estuarine transition zone of the St. Lawrence estuary

Abstract

This paper presents a hydrodynamic study of the St. Lawrence Estuary's estuarine transition zone, a 100 km region where fresh water from the river mixes with salt water from the estuary. The circulation of the estuarine transition zone is driven by strong tides, a large river flow, and well‐defined salinity gradients. For this study, a three‐dimensional hydrodynamic model was applied to the estuarine transition zone of the St. Lawrence Estuary and used to examine stratification and density‐driven baroclinic flow. The model was calibrated to field observations and subsequently predicted water level elevations, along‐channel currents, and salinity with mean errors of less than 9%, 11%, and 17%, respectively. The baroclinic density‐driven currents were distinguished from the tidal barotropic currents by using principal component analysis. Stratification and baroclinic flow were observed to vary throughout the estuarine transition zone on tidal and subtidal spring‐neap time scales. On a semidiurnal tidal time scale, stratification was periodic, and baroclinic flow was represented by pulses of sheared exchange flow, suggesting that neither buoyancy forcing nor turbulent mixing is dominant at this scale. On a subtidal spring‐neap time scale, stratification and baroclinic flow varied inversely with tidal energy, increasing on weak neap tides and decreasing on strong spring tides.     

Current meter observations from the Labrador and Newfoundland shelves and comparisons with barotropic model predictions and IIP surface currents

Abstract

Recent current measurements from the southern Labrador and northeastern Newfoundland shelves confirm the presence of inshore and offshore branches of the Labrador Current with high mean currents and low standard deviations. At mid‐shelf weaker and more variable currents occur over the banks, and cross‐shelf flows are found to be associated with the shelf topography. An annual cycle of the inshore branch, in phase with wind forcing, is significant on the NE Newfoundland Shelf but not detectable on Hamilton Bank. The phase of the annual cycle in the offshore branch is consistent with buoyancy, not wind forcing. The observations compare reasonably well with results from a barotropic model for the region and the International Ice Patrol (IIP) surface current map. Differences occur particularly in regions of high bathymetrie curvature or an ill‐defined shelf break. The model location of the Labrador Current lies inshore of that indicated by the data, suggesting the need for better definition of the northern inflow boundary condition and the inclusion of baroclinicity. The HP surface current map agrees well with observations offshore, but shows an unrealistic, broad inshore branch, especially on the Grand Bank These differences have important implications for the drift models.     

The California tsunami of 15 June 2005 along the coast of North America

Abstract

An M_w = 7.2 earthquake occurred on 15 June 2005 (utc) seaward of northern California off the west coast of North America. Based on the earthquake location and source parameters, the West Coast and Alaska Tsunami Warning Center issued a tsunami warning for the region extending from the California‐Mexico border to northern Vancouver Island, British Columbia (the first tsunami warning for this region since the 1994 M_w = 8.2 Shikotan earthquake). Six tide gauges on the west coast recorded tsunami waves from this event, with a maximum trough‐to‐crest wave height of 27.7 cm observed at Crescent City, California. Waves of 2.5 to 6.5 cm were measured at the five other sites: Port Orford (Oregon), North Spit and Arena Cove (California), and Tofino and Bamfield (British Columbia). The open‐ocean Deep‐ocean Assessment and Reporting of Tsunami (DART) buoys, 46404 and 46405, recorded tsunami waves of 0.5 and 1.5 cm, respectively, closely matching wave heights derived from numerical models. Incoming tsunami wave energy was mainly at periods of 10 to 40 min. The observed tsunami wave field is interpreted in terms of edge (trapped) and leaky (non‐trapped) waves and a “trapping coefficient” is introduced to estimate the relative contribution of these two wave types. Due to the high (3000 m) water depth in the source area, approximately two‐thirds of the total tsunami energy went to leaky wave modes and only one‐third to edge wave modes. The improved response to and preparedness for the 2005 California tsunami compared to the 1994 Shikotan tsunami is attributable, in part, to the operational capability provided by the open‐ocean bottom‐pressure recorder (DART) system, higher quality coastal tide gauges, and the effective use of numerical models to simulate real‐time tsunamis.     

Current Observations of Internal Tides and Parametric Subharmonic Instability in Luzon Strait

Acoustic Doppler Current Profiler (ADCP) measurements of the velocity structure in the thermocline in Luzon Strait are presented. The statistics for current, vertical variation of the inertia-gravity waveband, parametric subharmonic instability (PSI), and current shear are analyzed. It was found that 1) barotropic flow primarily consists of a nearly circular mixed tide. Diurnal tides are strongest and show smooth variance with a fortnightly spring-neap cycle, indicative of the astronomical tide-generating force. However, the semi-diurnal band power exhibits a high-frequency oscillation as a result of non-linear interactions. The high-frequency band power with high values during the spring tide oscillates with the tidal cycle. Near-inertial wave motions showing random variance may be caused by changes in the wind forcing at the sea surface or by random forcing. 2) Baroclinic velocities exhibit strong shear structure. The observed large changes in the amplitude of the baroclinic velocity and the limited vertical extent of the high-velocity cores may be interpreted as internal wave beams that pass through the observed water column. Semi-diurnal tides are dominant in the baroclinic velocity. Kinetic energy spectra also revealed that additional peaks were centred at sum-tidal-inertial interaction frequencies (such as M₂ ?+?f) and difference-interaction frequencies (such as M₂ ???f). The spectral exponent of the baroclinic velocity is ω^?α (1?<?α?<?3). 3) Strong non-linear interactions among internal waves exist, and the semi-diurnal (M₂) component plays a key role in these interactions. Bicoherence analysis showed that M₂/2 waves were non-linearly coupled with the dominant M ₂ internal tide. 4) The polarization relations were used to diagnose observational internal tidal motions. Diurnal waves propagate to the east-northeast, and the semi-diurnal–diurnal waves propagate westward. In the case of diurnal tides, the minor to major axis ratio is different from the expected value of f/ω_{K 1} because of the deviation of inclinations, whereas, for semi-diurnal tides, it is close to the expected value of f/ω _M2 at depths from 30 to 150 m.

RÉSUMÉ?[Traduit par la rédaction] Nous présentons les mesures de la structure des vitesses dans la thermocline faites par profileur de courant à effet Doppler (ADCP) dans le détroit de Luçon. Nous analysons les statistiques sur le courant, la variation verticale de la gamme d'ondes d'inertie-gravité, l'instabilité subharmonique paramétrique (PSI) et le cisaillement du courant. Il ressort que 1) l’écoulement barotrope consiste principalement en une marée mixte presque circulaire. Les marées diurnes sont les plus fortes et présentent une variance régulière dans un cycle vives-eaux mortes-eaux de deux semaines qui révèle la nature astronomique de la force qui produit les marées. Cependant, la puissance de bande semi-diurne affiche une oscillation de haute fréquence causée par des interactions non linéaires. La puissance de bande de haute fréquence avec des valeurs élevées durant les vives-eaux oscille avec le cycle des marées. Les mouvements des ondes quasi inertielles affichant une variance aléatoire peuvent être dus à des variations dans le forçage par le vent à la surface de la mer ou à un forçage aléatoire. 2) Les vitesses baroclines exhibent une structure fortement cisaillée. Les changements marqués observés dans l'amplitude des vitesses baroclines et l'extension verticale limitée des c?urs de vitesse élevée peuvent être interprétés comme des faisceaux d'ondes internes qui traversent la colonne d'eau observée. Les marées semi-diurnes sont dominantes dans les vitesses baroclines. Les spectres d’énergie cinétique ont aussi révélé que des crêtes additionnelles étaient centrées aux fréquences d'interaction cumulative marée-inertie (comme à M₂ ?+?f) et aux fréquences d'interaction différentielle (comme à M₂ ???f). L'exposant spectral de la vitesse barocline est ω^?α (1?<?α?<?3). 3) Il existe de fortes interactions non linéaires entre les ondes internes et la semi-diurne (M₂) joue un rôle clé dans ces interactions. L'analyse de bicohérence a montré que les ondes M₂/2 étaient non-linéairement couplées avec la marée interne dominante M₂ . 4) Nous avons utilisé les relations de polarisation pour diagnostiquer les mouvements de marée internes déduits des observations. Les ondes diurnes se propagent vers l'est-nord-est et les ondes semi-diurnes se propagent vers l'ouest. Dans le cas des marées diurnes, le rapport de l'axe secondaire à l'axe principal diffère de la valeur attendue (f/ω_{K 1} ) à cause de l’écart des inclinaisons alors que pour les marées semi-diurnes, il est proche de la valeur attendue (f/ω _M2 ) à des profondeurs de 30 à 150 m.     

Frequency and directional evaluation of the ocean data gathering program (ODGP) wave spectra at Hibernia

Abstract

The frequency and directional wave‐modelling capability of the Ocean Data Gathering Program (ODGP) deep water spectral wave model is assessed through comparison with WAVEC data gathered at Hibernia. Both qualitative and quantitative analyses indicate better agreement with observations during storms and with the wind‐driven component of the wave spectra. There is statistically poor modelling of the swell. A coherence analysis on derived wave vectors indicates that the ODGP model does not simulate geophysical variability with time‐scales less than about 30 h for overall spectral energy and less than 24 h for wave energy of frequency greater than 0.6 rad s^?1 (0.095 Hz). The signals associated with swell waves are incoherent at nearly all time‐scales.