Shelf Waves Research Articles

Tides and tidal currents along the Okhotsk coast of Hokkaido

The development and propagation of the diurnal tidal currents along the Okhotsk coast of Hokkaido is made clear using newly obtained data. the diurnal currents are generated at the Soya Strait by the difference of the tidal amplitude and phase between the Sea of Okhotsk and the Japan Sea, and propagate as the shelf waves trapped along the coast. As a result, the amplitude in the coast becomes small and the phase is advanced for 1∼2 hours compared to those in the offshore area. For the semidiurnal tides, the influence of the difference of the tides between both seas is restricted near the strait because they are quickly dispersed as the Poincare wave.

The diffraction of coastally trapped waves into and from a strait

Abstract For the idealised geometry in Figure 2, the results of Buchwald and Kachoyan (1987) for a barotropic ocean are extended to include the diffraction of shelf waves by a strait. Assuming a known flux through the strait together with an independent incident shelf wave, the amplitudes of the scattered shelf wave modes are calculated by the adoption of a modal expansion in the strait. The boundary condition at the strait mouth is then satisfied by the use of a Galerkin technique. The results show that higher mode amplitudes are underestimated by Buchwald and Kachoyan (1987). These results are extended to the case of a strait of finite length joining two semi-infinite oceans. An incident shelf wave in one ocean gives rise to a pressure gradient along the strait, and strait oscillations ensue. For a range of geometries and frequencies, calculations show that up to half the incident energy is diffracted through the strait, with some transfer into higher modes. The generation of oscillations in the strait by a periodic wind-stress along the strait is also considered. For parameters relevant to the Bass Strait and the ACE observations the results indicate that incident shelf waves on the south coast are the more likely source of the waves observed on the east coast of Australia.

Diurnal tides in the Arctic Ocean

A two‐dimensional numerical model with a space grid of about 14 km is applied to calculate diurnal tidal constituents K1 and O1 in the Arctic Ocean. Calculated corange and cotidal charts show that along the continental slope, local regions of increased sea level amplitude, highly variable phase and enhanced currents occur. It is shown that in these local regions, shelf waves (topographic waves) of tidal origin are generated. In the Arctic Ocean and Northern Atlantic Ocean more than 30 regions of enhanced currents are identified. To prove the near‐resonant interaction of the diurnal tides with the local bottom topography, the natural periods of oscillations for all regions have been calculated. The flux of energy averaged over the tidal period depicts the gyres of semitrapped energy, suggesting that the shelf waves are partially trapped over the irregularities of the bottom topography. It is shown that the occurrence of near‐resonance phenomenon changes the energy flow in the tidal waves. First, the flux of energy from the astronomical sources is amplified in the shelf wave regions, and afterwards the tidal energy is strongly dissipated in the same regions.

Generation mechanism of higher mode nondispersive shelf waves by wind forcing

The higher mode predominance in the current velocity fields associated with wind-induced shelf waves in the nondispersive regime is studied with a special attention to the effect of the geographical boundary, e.g. wide strait or wide bank areas. The effect of such large topographic change is represented by wind forcing with a finite dimension near the geographical boundary. The time development processes of the wind-induced shelf waves is examined in the context of an initial-value problem, where a spatially finite wind stress is applied att=0. Various modes of shelf waves excited at the boundary start propagating simultaneously and develop monotonically within the forcing region. After the passage of such wave, the energy of wind is used to maintain the attained equilibrium condition, i.e. the steady shelf circulation. The current evolution of the lower mode is restricted to the earlier stage because of the large propagation speed. In contrast, the higher mode waves can travel slowly within the forcing region so that the kinetic energy is supplied from wind stress for a long time before the equilibrium condition is established. Consequently, the observation at the fixed point near the geographical boundary would show that the higher mode waves gradually dominate as time goes on, i.e. for the long-term forcing.

Sea-bottom temperature, salinity and dissolved oxygen on the continental margin off south-western Africa

From a historical data base of temperature, salinity and dissolved oxygen for the Benguela shelf between Cape Agulhas and Cape Frio, average bottom patterns for each of these parameters are presented along with statistical justifications. Some physical interpretation is given for various features and variances, involving the poleward undercurrent, wind and upwelling, continental shelf waves and internal tides at the shelf edge and, in the case of oxygen, sediment-exchange chemistry.

Diurnal shelf waves off Hamada on San'in Coast

The tidal current data observed off Hamada on San'in coast have shown the diurnal tidal currents to be larger than the semidiurnal ones by a factor of 5–8, although the ratio (K1+O1)/(M2+S2) for the tidal heights at Hamada is 1.3. Furthermore, the diurnal currents are found to be more remarkable on the shelf slope than on the shelf. We consider such diurnal current features as being due to the vortical mode waves, and show that the broad shelf and steep shelf slope off San'in coast allow 1st-mode interior shelf waves (ISWs) at a diurnal-period. Using a simple shelf model, it is shown that ISWs occur in response to the seaward component of diurnal tidal oscillations on the shelf and their propagation originates from the western entrance of the Tsushima Straits.

Observations of coastal jets in the Southern Baltic

Hydrographic and moored current meter observations have been performed in the southern Arkona basin in both periods of summer and winter stratification between July 1988 and February 1990. The coastal boundary layer north of the islands Rügen and Hiddensee is characterized by strong coastal jets with velocities of up to 1 m s −1 and a time scale of 2–3 days. The jets possess a strong harotropic component, are nearly independent of stratification, and have a coherent longshore structure over a distance of at least 40 km. Both a forced mode and a freely propagating mode with an eastward directed phase velocity of about 0.8 m s −1 have been observed. The eastward directed jet is associated with an Ekman-onshore transport and downwelling. In the case of a westward directed jet the cross-shore circulation is reversed. The correlation between the east component of the wind and the longshore component of the current in the coastal boundary layer is significant. The wind fluctuations lead the current fluctuations by about 6 h. Parameters of the first mode of a barotropic shelf wave for the southern Arkona basin have been calculated and are in good agreement with the observed parameters of the free motion.

Hydrographic observations during the Tasman boundary experiment off the west coast of South Island, New Zealand

Abstract Hydrographic observations over the west coast shelf during the Tasman Boundary Experiment (TASBEX) in 1986/87 are presented. Temperature dianges over the shelf were related to mixed‐layer development, shelf waves, and seasonal changes, with wind‐driven upwelling being important close to the coast. During upwelling, a surface coastal current was observed and at times a weak undercurrent or countercurrent developed. Changes in freshwater inflow resulted in changes in the depth of the low‐salinity surface layer. In the north, flows were generally weaker than in the south, where the shelf is narrow and the Southland Current dominates. Changes in the position and strength of the Southland Current were observed and on one occasion the response to a wind change event was a relaxation of the flow to a coastal Southland Current regime.

Propagation of coastal‐trapped waves under an ice cover in Hudson Bay*

Abstract Three arrays of current‐meter moorings were deployed under landfast sea ice in southeast Hudson Bay for eight weeks in spring 1986. Spectral analysis shows low‐frequency signals with periods of 3 to 11 days. These signals are interpreted as being due to coastal‐trapped waves propagating cyclonically in Hudson Bay; their theoretical dispersion relations and corresponding modal structures are presented for winter stratification and are compared with observations. At a period of 3 days both the modified external Kelvin wave and higher mode continental shelf waves may be important in describing the observed low‐frequency variability, whereas at a period of 10 days the Kelvin wave appears to be the dominant mode. The generation mechanisms for these coastal trapped waves are also investigated. Two sources have been studied: the longshore atmospheric pressure gradient and the average atmospheric pressure over the ice cover in Hudson Bay. Coherence and phase analyses performed with time series of longsho...

The resonant generation of shelf waves by a moving cyclone

The resonant generation of shelf waves by the local atmospheric disturbance displacing longshore is considered. The model, which is more precise compared with that in refs 3 and 4 owing to the consideration of dispersion of the trapped waves, was applied to the analysis. It is shown that comparatively low-frequency waves are generated most effectively when the cyclone displacement rate is close to the maximum phase velocity of a single shelf mode.

Diurnal tides near the Yermak Plateau

Recent current measurements obtained from drifting platforms over the Yermak Plateau in the eastern Arctic Ocean confirm that the plateau is a region of greatly enhanced diurnal tidal currents. Modulation of the diurnal currents is clearly related to the plateau topography, as has been previously proposed. We show, however, that temporal variability due to spring‐neap modulation must also be considered in interpreting records from drifting platforms. We review simple models of tidal current amplification in this region and find that the previous assumption of near‐resonant, barotropic shelf waves propagating around the plateau's entire perimeter is inconsistent with the true topography. Instead, we propose that the diurnal variability is due to topographic shelf waves at the K1 and O1 tidal frequencies that are generated at points on the plateau's perimeter where the waves' group velocities are near zero. Observed cross‐slope variations in ellipticity, orientation, and magnitude of tidal oscillations are consistent with the presence of topographic waves generated in this manner. The topographic enhancement of the diurnal tide near the Yermak Plateau has important consequences for the sea ice cover, hydrography, and general circulation of this region. For example, the stress divergence applied by the tidal currents at the ice base greatly exceeds the typical divergence of the surface wind stress, and tides may therefore be important to local ice deformation. The strong cross‐slope tidal currents also appear to be responsible for the production of high‐frequency internal wave packets, which are associated with energetic diapycnal mixing in the pycnocline. We also consider the possibility that tidal rectification is responsible for a mean current transporting Atlantic Water clockwise around the plateau.

Scattering of Long Divergent Shelf Waves by a Thin Barrier Parallel to the Coast

Abstract The barotropic shallow-water equations and exponential topography are used to investigate the low-frequency scattering of an incident shelf wave by a thin barrier located parallel to the coast by means of eigenfunction matching techniques, following Hsieh and Buchwald. In this model, however, the nondivergent (rigid-lid) approximation is relaxed, and hence, we are able to compute the energy in the Kelvin modes. In order for the problem to be well posed, we consider a barrier of finite 1ength in an infinite channel with a rigid wall at the shelf edge. The wall supports a reflected Kelvin wave traveling in the direction opposite to the incident shelf wave. The problem is then formulated in term of the unknown amplitude of this reflected Kelvin wave and solved using the radiation condition that no energy is incident on the barrier from the downstream side of the channel. Energy flux computations show that a large fraction of the energy in an incident mode 1 is transferred to the Kelvin mode in the r...

Equatorward wind and atmospheric pressure spectra as metrics for primary productivity in the Benguela system

Through its connection with upwelling, averaged longshore wind displacement is often invoked as a metric linearly related to productivity on timespans of months to seasons. In this paper, the linearity of such a relationship is questioned by analysing Ekman divergence against the modifying influence of freely propagating continental shelf waves. Both arise from common synoptic forcing events. Also considered is how the periodicity of the wind can be a more important factor in estimates of productivity than the integrated strength and duration of longshore wind. A suitable phase relationship between remotely generated coastal-trapped waves and local wind is a requirement for efficient upwelling. The theoretical concept of a metric for productivity, using a representation in an n-dimensional frequency space, is proposed.

Linear systems analysis of momentum on the continental shelf and slope of the central Great Barrier Reef

Current meter records from a mooring transect deployed across the continental shelf and slope of the central Great Barrier Reef, Australia during 1985 have been analyzed in a study of the subtidal momentum balance. In the 3–20 day wave band, a single‐input linear systems model of the subtidal along‐shelf flow, driven by across‐shelf pressure gradient (i.e., assuming semi‐geostrophic balance), explained over 70% of the variance on the shelf, but only 30% at the shelf break and upper slope. A two‐input model driven by along‐shelf horizontal pressure gradient and wind stress, and incorporating along‐shelf acceleration and bottom stress, explained approximately 60% of the variance on both the shelf and upper slope. The model responses evidently combine local wind‐driven circulation and freely‐propagating continental shelf waves. Linear resistance coefficients estimated from the two‐input model averaged 0.07 cm s−1, but were higher (0.09) within the reef matrix and lower (0.06) near the coast.

Wind-driven coastal upwelling along the western boundary of the Bay of Bengal during the southwest monsoon

A hydrographic survey during the southwest monsoon (July–August 1989) showed that along most of the western boundary of the Bay of Bengal, in an approximately 40 km wide band, isopycnals from depths up to about 70 m surfaced due to upwelling forced by local winds, in a fashion similar to that observed along eastern boundaries. Below the upwelling band there were often signatures of downwelling, suggestive of an undercurrent. There were no indications of a large-scale remotely forced western boundary current. Geostrophic velocity in the upwelling band was in the direction of the winds. The dynamic topography outside the upwelling band had cellular structures possibly indicating the presence of shelf waves with longshore wavelength of 400–500 km. The near-surface stratification was dominated by salinity, a consequence of high freshwater input to the Bay. The upwelling led to a coastward increase in salinity, except near the northern end where the freshwater influx from the Ganges and the Brahmaputra rivers overwhelmed other processes and gave rise to a freshwater plume offshore of the upwelling band. This plume moved equatorward against local winds.

The Scattering at Low Frequencies of Coastally Trapped Waves

The scattering of coastally trapped waves is described in a particular low frequency limit where the fundamental results are independent of the relative importance of stratification and rotation in the dynamics. Progress is made possible by restricting attention to frequencies small compared to a “profile” frequency, N0H/L that estimates the combined effect of the density and shelf profiles through the product of a typical buoyancy frequency N0 and the average shelf slope (for ocean depth H and shelf width L. Combined with results on the scattering of barotropic shelf waves, the present results describe scattering irrespective of the strength of any stratification provided solely that the frequency of the motion is small compared to either the inertial frequency or the profile frequency. In all cases the transmitted wavefield follows directly by tracing an incident pressure field along coastal isobaths. Strong notification is shown to suppress scattering at all subinertial frequencies, leading to particularly simple flow fields. At moderate stratification all energy is scattered forwards. An example is given where isobath tracing determines explicitly the amount of internal wave energy that passes over a ridge abutting a coastal wall. Various flows are possible if stratification is weak. In each flow the transmitted field is given by the barotropic connection formula. If the scatterer is conservative, this is the whole field. If the scatterer is nonconservative and the incident frequency is small compared to the profile frequency, so stratification dominates locally, then energy is carried forward in a narrow, intense boundary current. Over larger distances the current disperses into an internal Kelvin wave field. If the scatterer is nonconservative but the incident frequency is large compared to the profile frequency, then energy is dissipated or reflected as short barotropic waves. It is noted briefly that the results describe how coastal energy can split at the mouths of bays and straits and may be relevant to observations of long period motions near the Gulf of California and energy propagation through Bass Strait.

Low-Frequency Barotropic Scattering on a Shelf Bordering an Ocean

Abstract BY restricting attention to low frequencies this note solves the problem of continental shelf waves scattered at an abrupt change in width of an exponential shelf abutting a flat open ocean. Short reflected waves are treated by removing their rapid phase variation to leave an envelope governed by the long-wave equation with the direction of propagation reversed. In all cases a weak flow is forced in the open ocean by the width change. This flow is strongest for narrowing and terminating shelves, which are discussed in detail. Energy is conserved with the flux across any cross-shelf plane given by the difference between the energy carried by the long waves and the energy carried in the opposite direction by the envelope of short waves.

Sea-level variations with a several-day period along the southwestern Japan sea coast

Daily mean sea-level data obtained along the southwestern Japan Sea coast (the San'In coast of Japan and the east coast of Korea) are analysed using a spectral analysis technique. It is found that a prominent peak period of sea-level variations exists at 3–5 days from January to April. These sea-level variations disappear from May to August. The remaining season, from September to December, has a broad peak at a period of 3–10 days. These sea-level variations are highly coherent with the wind variations. The wind-induced sea-level variations in the frequency band from a 2.5- to 6-day period propagate with the coast to the right-hand side and were non-dispersive. The progressive waves along the San'In coast and the east coast of Korea propagate independently. The wave along the San'In coast can be explained by a first mode shelf wave and begins to propagate from the Tsushima Straits. We cannot specify the type of wave along the east coast of Korea, since it propagates at a speed intermediate between that of a shelf wave and an external Kelvin wave.

Simulations of shelf sea response due to travelling storms

A layered ocean model has been implemented for the numerical simulation of baroclinic shelf sea response, due to travelling storms. Atmospheric forcing by wind stress and surface pressure gradients is simulated by a circular cyclone model, corresponding to typical extratropical and tropical storms. Both Eulerian and Lagrangian coordinate descriptions have been used. The latter method enables also a more direct tracking of density interfaces, intersecting with the bottom topography. Three test examples have been investigated; storm response on a continental shelf and an escarpment at high latitudes; and the response of a tropical storm at a narrow shelf in low latitudes. The first two examples may simulate typical conditions over northwest European shelves: the latter may simulate hurricane response along the western coast of Mexico and the Gulf of California. The results of the simulations demonstrate typical features of storm response in these shelf regions, as narrow-banded barotropic shelf wave oscillations, near inertial period, and long periodic baroclinic wave modes. The performances of different numerical schemes have been investigated, in order to assess the accuracy of the numerical results.

The trapping and scattering of topographic waves by estuaries and headlands

This paper extends recent theoretical work on sub-inertial trapped modes in bays to consider trapping of energy in the neighbourhood of estuary mouths on coastal shelves. The qualitative form of the theoretical predictions accords well with recent observations on the Scotian Shelf that show energy trapped near the Laurentian Channel at a frequency higher than that of the propagating waves on the shelf.The trapping and scattering of shelf waves is modelled for a shelf-estuary or shelf-headland system by considering barotropic waves in a straight, infinite channel with an attached rectangular estuary or interrupted by a rectangular headland. Taking the depth to increase exponentially with distance from the coast and expanding in cross-shelf modes reduces the problem to a system of real linear algebraic equations.Trapped modes with frequencies above the cutoff frequency of propagating waves are found near the mouth of the estuary. Waves propagating towards the estuary are strongly scattered and, for particular frequencies, incident energy can be either perfectly transmitted or totally reflected. An incident wave can be in resonance with the estuary causing energy to penetrate the estuary. Bounds on the frequencies of trapped and resonant solutions are given and allow an easy modal interpretation.If the frequency of an incident wave is sufficiently high, waves cannot propagate past a headland. Energy at these frequencies can however tunnel through the region and appear as an attenuated wave on the far side. For particular frequencies all energy passes the headland and none is reflected. For headlands long compared with the incident wave, transmission coefficients for single-mode scattering follow from spatially one-dimensional wave mechanics.