Internal tides and waves near the continental shelf edge

Abstract

The subject is reviewed from the viewpoints of theory, internal tide and wave structure and their implications.

A wider theoretical context suggests scope for further investigation of natural or nearly-trapped forms above the inertial frequency.

Although internal tides in many locations are observed to have first-mode vertical structure, higher modes are seen offshore from shallow shelf-break forcing and for particular Froude numbers, and may be expected locally near generation. Bottom intensification is often observed where the sea floor matches the characteristic slope. Solitons form from internal tides of large amplitude or at large changes of depth.

Internal tides and solitons are observed also at many sills and in straits, and to intensify in canyons.

Non-linear effects of the waves, especially solitons, include the conveyance of water, nutrients, ‘‘mixing potential'’ etc. away from their source to other locations, and the generation of mean currents. The waves transfer energy and possibly heat between the ocean and shelf, may be a source of medium frequency waves on the shelf (periods of minutes) and can contribute to interior mixing and overturning, bottom stirring and sediment movement.     

Wind-forced continental shelf waves from a geographical origin

The response of a barotropic coastal ocean on a step-shaped continental shelf to a traveling sinusoidal wind stress forcing is predicted theoretically using a frictional force proportional to the alongshore current velocity. This theory is compared to a small set of observations from the northeast coast of Australia where a sudden widening of the continental shelf provides a geographical origin. The comparison is accomplished by means of frequency response functions relating alongshore wind stress with alongshore velocity. Amplitudes of the response functions are predicted to increase with alongshore distance equatorward and also to decrease with frequency at any location. These predictions are verified by the measurements. Predicted phase lags are generally less than about 30°, with observations agreeing with theory to within about 20°C. In general, the measurements provide reasonable evidence to support the theory of wind-forced continental shelf waves from a geographical origin.     

Barotropic waves along an eastern continental shelf

Abstract

An analysis is presented of the propagation of barotropic non-divergent oscillations along the western side of an ocean basin along which the persistent circulation in the basin is strongly intensified and laterally sheared. Because the Rossby number of a western boundary current is near unity, the properties of these waves are strongly affected by the steady circulation pattern. It is shown that for relatively long wavelengths, these waves can travel along the shelf in both directions; however, for a small range of short wavelengths they can only propagate northward and are unstable. Along the southeastern coast of North America, the unstable waves have wavelengths of order 150 km and periods of order 10 days. However, these waves can become stable oscillations in the deeper water northeast of Cape Hatteras. These oscillations are a possible explanation of the initiation of Gulf Stream meanders along the continental rise.     

A note on edge waves on a flat shelf

Abstract

A variational approximation to the dispersion relation for trapped waves on a flat shelf of depth h ₁, bounded internally by a vertical coast and externally by a semi-infinite ocean of depth h ₂>h ₁, is obtained through an integral-equation formulation that accounts for all of the non-propagated modes that are excited at the discontinuity in depth (the conventional formulation of the edge-wave problem allows only for the propagated mode on the shelf and the dominant, non-propagated mode in the deep water). Coriolis effects are neglected. The exact result in the limit ω² h ₂/g↓0 (ω = angular frequency) is obtained by conformal mapping and compared with the variational approximation, which proves to be quite accurate over the entire range 1>h ₂/h ₁>x. The effects of the higher-order, non-propagated modes are found to be small for the long waves observed over the Southern California shelf by Snodgrass, Munk and Miller (1962).     

Flow convergence over a broad,flat continental shelf

The broad (～500 km) southeastern Bering Sea continental shelf contains three fronts; outer (shelf break, ～170-m depth), middle (～100-m depth), and inner (～50-m depth). The shelf break and inner fronts appear to be analogous to similar fronts reported from other mid-latitude continental shelves; extensively studied examples are from the mid-Atlantic bight, off Nova Scotia, and around the British Isles. The middle front may have counterparts on the broad North Sea and East China Sea shelves.One-month current and temperature records from either side of the middle front, ～150 km landward from the shelf break, showed convergence in the layers deeper than 30 m in both the cross-shelf flow field and heat flux. The convergence was ～3 cm s^?1, so an average upwelling at ～1 × 10^?3cm s^?1 and divergence in the surface layer were required to maintain continuity. Variations in the degree of convergence arose primarily from 1 to 5-day fluctuations in sub-tidal flow across the outer shelf domain seaward of the front.Diffusive landward heat flux was dominated by tidal scales. Horizontal eddy conductivities describing the flux were ～1 ? 10⁶ on the landward side and ～5 × 10⁶cm² s^?1 on the seaward side, and were less in the layers above the bottom layer. Advective flux by the mean flow was the same order as diffusive flux, but landward in the bottom layer and seaward in the mid-water column layers, in agreement with deductions from water mass analyses. Frontal effects reduced the net cross-shelf heat flux beneath ～30 m by about 50%. The observation of a flow convergence in the middle of a broad, flat continental shelf poses an important question of dynamics.     

Critical levels for forced Rossby and continental shelf waves

The generation of waves on a geostrophic shear flow by a travelling forcing pattern is considered. The model describes both atmospheric Rossby waves on a zonal shear flow and continental shelf waves on a boundary current. By means of the Laplace transform technique, the development of the solution in time is studied, starting from some initial instant when the forcing starts. The asymptotic form of the forced solution is shown to depend crucially upon whether the speed of the travelling forcing lies inside the range of the current or not. The possible application of the results to the Florida current is discussed.     

Long period edge waves off Southern Africa

Long gravity wave height oscillations of up to 60 cm with periods between 12 min and 1 h have been observed on tide gauge recordings from the southern coast of South Africa. Short period (30 min to 1 h), small height (3 mb) air pressure pulses were recorded at stations along the same coastline. Two separate events of contrasting nature are described in detail. The simple model of Snodgrass et al. (1962, Journal of Marine Research, 20, 3–30) is used to explain the sea waves as resonant, coastally trapped, edge waves on the Agulhas Bank forced by the atmospheric pulses.     

Generation of baroclinic topographic waves by a tropical cyclone impacting a low-latitude continental shelf

Numerical model experiments have been performed to analyze the low-latitude baroclinic continental shelf response to a tropical cyclone. The theory of coastally trapped waves suggests that, provided appropriate slope, latitude, stratification and wind stress, bottom-intensified topographic Rossby waves can be generated by the storm. Based on a scale analysis, the Nicaragua Shelf is chosen to study propagating topographic waves excited by a storm, and a model domain is configured with simplified but similar geometry. The model is forced with wind stress representative of a hurricane translating slowly over the region at 6 km h⁻¹. Scale analysis leads to the assumption that baroclinic Kelvin wave modes have minimal effect on the low-frequency wave motions along the slope, and coastal-trapped waves are restricted to topographic Rossby waves. Analysis of the simulated motions suggests that the shallow part of the continental slope is under the influence of barotropic topographic wave motions and at the deeper part of the slope baroclinic topographic Rossby waves dominate the low-frequency motions. Numerical solutions are in a good agreement with theoretical scale analysis. Characteristics of the simulated baroclinic waves are calculated based on linear theory of bottom-intensified topographic Rossby waves. Simulated waves have periods ranging from 153 to 203 h. The length scale of the waves is from 59 to 87 km. Analysis of energy fluxes for a fixed volume on the slope reveals predominantly along-isobath energy propagation in the direction of the group velocity of a topographic Rossby wave. Another model experiment forced with a faster translating hurricane demonstrates that fast moving tropical cyclones do not excite energetic baroclinic topographic Rossby waves. Instead, robust inertial oscillations are identified over the slope.     

Low frequency edge waves over a trench-ridge topography adjoining a straight coastline

Abstract

The possible interaction of trapped midoceanic boundary waves with a nearby coastline is examined by considering a step trench-ridge topography adjoining a semi-infinite straight coastline. The full dispersion equation, including the effect of the earth's rotation, is derived for long waves over this topography. It is shown that the presence of the coastline begins to have a significant effect on the behaviour of quasigeostrophic ridge waves whenever the wave length is greater than three times the ridge coastline separation.

As an example, the dispersion curves are presented for the topography of the Heceta Bank off the coast of Oregon and it is conjectured that the presence of this off-shore ridge may provide an explanation for the anomalous direction of propagation of the 0.1 c.p.d. shelf wave reported by Mooers and Smith (1968).     

Internal waves,baroclinic energy fluxes and mixing at the European shelf edge

The energy flux in internal waves generated at the Celtic Sea shelf break was estimated by (i) applying perturbation theory to a week-long dataset from a mooring at 200 m depth, and (ii) using a 2D non-hydrostatic circulation model over the shelf break. The dataset consisted of high resolution time-series of currents and vertical stratification together with two 25-h sets of vertical profiles of the dissipation of turbulent kinetic energy. The observations indicated an average energy flux of 139 W m⁻¹, travelling along the shelf break towards the northwest. The average energy flux across the shelf break at the mooring was only 8 W m⁻¹. However, the waves propagating onshelf transported up to 200 W m⁻¹, but they were only present 51% of the time. A comparison between the divergence of the baroclinic energy flux and observed dissipation within the seasonal thermocline at the mooring showed that the dissipation was at least one order of magnitude larger. Results from a 2D model along a transect perpendicular to the shelf break showed a time-averaged onshelf energy flux of 153–425 W m⁻¹, depending on the magnitude of the barotropic forcing. A divergence zone of the energy flux was found a few kilometre offshore of the location of the observations in the model results, and fluxes on the order of several kW m⁻¹ were present in the deep waters further offshelf from the divergence zone. The modelled fluxes exhibited qualitative agreements with the phase and hourly onshelf magnitudes of the observed energy fluxes. Both the observations and the model results show an intermittent onshelf energy flux of 100–200 W m⁻¹, but these waves could only propagate ∼20–30 km onshore before dissipating. This conclusion was supported by a 25-h dataset sampled some 180 km onto the shelf, where a weak wave energy flux was found going towards the shelf break. We therefore conclude that shelf break generated internal waves are unlikely to be the main source of energy for mixing on the inner part of the shelf.     

Internal waves over the shelf in the western Bay of Bengal: a case study

Generation and propagation of internal waves (IWs) in the coastal waters of the extended shelf of the western Bay of Bengal are investigated for late winter by using the Massachusetts Institute of Technology General Circulation Model (MITgcm). The model is forced with astronomical tides and daily winds. Monthly climatological temperature and salinity fields are used as initial conditions. The simulations are compared with time series observations of temperature and currents from acoustic Doppler current profiler (ADCP) and conductivity-temperature-depth (CTD) moored at three locations south of Gopalpur: two at a local depth of 100 m and another at 400-m depth during 19–21 February 2012. The comparison of the spectral estimates for the time series of temperature from the model and observations are in reasonable agreement for the near-tidal frequency waves. The peak of temperature spectra is always found near the shelf break region which steadily lost its intensity over the continental shelf. The calculation of Richardson number reflected the presence of local mixing due to density overturning in the shelf region. To understand further the generation and propagation of internal tides in the region, energy flux and conversion of barotropic-to-baroclinic M₂ tidal energy are examined. The model simulations suggest that the internal tide is generated all along the shelf slope. The energy flux analysis shows that the internal tides propagate to either side of the generation sites.     

Production and transport of phytoplankton biomass over the continental shelf of the new york bight

Seasonal and event scale variations in the distribution and growth of phytoplankton in different hydrographic regions of the continental shelf are compared and evaluated in terms of floristic composition and the evolution of density and nutrient structure across the shelf. Annual cycles of phytoplankton biomass inshore of the 1000-m isobath are characterized by a March maximum and a July minimum. Cross-shelf biomass gradients usually increase in an offshore direction, a phenomenon that is most pronounced during March and April when biomass is high, diatoms dominate, and growth rate is light limited. This is a consequence of the combined effects of growth along the stratified side of the shelf-break front and offshore transport of biomass produced nearshore. We estimate that about 90% of the diatom biomass produced during the February to April bloom period (35% of annual production) is exported from shelf to slope water. Similar but less-pronounced gradients develop during summer due to the development of a chlorophyll maximum layer below the pycnocline where growth rate is also light limited. Production and loss are more tightly coupled under these conditions and about 9% of the biomass produced during May to October appears to be exported (5% of annual production). Export during the diatom bloom period is balanced mainly by nitrate inputs from the Gulf of Maine and adjacent slope water while summer export may be balanced by anthropogenic nitrogen input. The latter could be coupled with biomass export by ammonium remineralization and nitrification in the cold pool of the mid-shelf region. In general, export is greatest when diatoms dominate, growth is light limited, and biomass distributions are physically forced. Export is lowest when nanoplankton dominate, growth is nitrogen limited, and biomass distributions are controlled by grazing.The shelf-break front plays a key role, influencing patterns of phytoplankton growth, biomass distributions, and shelf export. During the diatom bloom period, the development of stratification in nutrient-rich offshore water between storm events results in high growth rates and biomass near the surface on the shelf side of the front. Under these conditions, biomass accumulates in the mid-shelf region on a time scale of days to weeks. Export occurs during wind events with net export from the shelf occurring on a time scale of weeks to months. Blooms also develop along the shelf side of the front during summer but below the pycnocline. Most of the summer export of biomass probably takes place here with accumulation and export occurring on a time scale of hours to days. While this export is small compared to export during the diatom bloom period, it may be critical to the prevention of anoxic events such as that of 1976.     

Apparent palaeomagnetic low-inclination excursion in a pre-consolidated continental shelf sediment

The presence of an almost exact 180° change in declination in a piston-core from the continental margin off the west coast of Norway is associated with two distributions of positive inclination of the remanent directions which could have been interpreted to represent an excursion of the geomagnetic field. The over-consolidated top section, defined by anomalously low-inclination directions, reveals a magnetic fabric typical of slurries or deposits affected by water currents, as opposed to an anomalous fabric in the lower section associated with magnetic directions coinciding with the present geomagnetic field. The sampling area reveals seismic features indicative of slumping, erosion and redeposition, which are also reflected by micropalaeontological evidence. It is concluded that the pre-consolidated top-section has been transported by slumping, the anomalously low-dipping directions resulting from processes acting during the initial consolidation.     

Impacts of climate changes on ocean surface gravity waves over the eastern Canadian shelf

A numerical study is conducted to investigate the impact of climate changes on ocean surface gravity waves over the eastern Canadian shelf (ECS). The “business-as-usual” climate scenario known as Representative Concentration Pathway RCP8.5 is considered in this study. Changes in the ocean surface gravity waves over the study region for the period 1979–2100 are examined based on 3 hourly ocean waves simulated by the third-generation ocean wave model known as WAVEWATCHIII. The wave model is driven by surface winds and ice conditions produced by the Canadian Regional Climate Model (CanRCM4). The whole study period is divided into the present (1979–2008), near future (2021–2050) and far future (2071–2100) periods to quantify possible future changes of ocean waves over the ECS. In comparison with the present ocean wave conditions, the time-mean significant wave heights (H _s ) are expected to increase over most of the ECS in the near future and decrease over this region in the far future period. The time-means of the annual 5% largest H _s are projected to increase over the ECS in both near and far future periods due mainly to the changes in surface winds. The future changes in the time-means of the annual 5% largest H _s and 10-m wind speeds are projected to be twice as strong as the changes in annual means. An analysis of inverse wave ages suggests that the occurrence of wind seas is projected to increase over the southern Labrador and central Newfoundland Shelves in the near future period, and occurrence of swells is projected to increase over other areas of the ECS in both the near and far future periods.     

Secondary upwelling over a smooth shelf break

An unsteady model of secondary upwelling over the break at the edge of the continental shelf is described for bottom topography with a smooth but distinct shelf break. Numerical solutions are determined for examples using (i) a simple spin-up wind to illustrate the circulation and (ii) a moving pulse of wind to generate continental shelf waves.