Shelf Waves Research Articles

Fast accurate computation of shelf waves for arbitrary depth profiles

A simple fast and straightforward, accurate numerical method is proposed for calculating barotropic non-divergent continental shelf waves, above general shelf profiles. The problem is reduced to a linear eigenvalue problem for the along-stream wavenumber k, that can be solved directly with exponential accuracy, using any standard linear eigenvalue package.

Numerical study of three-dimensional shelf circulation on the Scotian Shelf using a shelf circulation model

A numerical shelf circulation model was developed for the Scotian Shelf, using a nested-grid setup consisting of a three-dimensional baroclinic inner model embedded inside a two-dimensional barotropic outer model. The shelf circulation model is based on the Princeton Ocean Model and driven by three-hourly atmospheric forcing provided by a numerical weather forecast model and by tidal forcing specified at the inner model's open boundaries based on pre-calculated tidal harmonic constants. The outer model simulates the depth-mean circulation forced by wind and atmospheric pressure fields over the northwest Atlantic Ocean with a horizontal resolution of 1/12°. The inner model simulates the three-dimensional circulation over the Gulf of St. Lawrence, the Scotian Shelf, and the adjacent slope with a horizontal resolution of 1/16°. The performance of the shelf circulation model is assessed by comparing model results with oceanographic observations made along the Atlantic coast of Nova Scotia and in the vicinity of Sable Island (on the Scotian Shelf) during two periods: October 2000–March 2001 and April–June 2002. Analysis of model results on Sable Island Bank indicates that tidal currents account for as much as ∼80% of the total variance of near-bottom currents, and currents driven by local winds account for ∼30% of the variance of the non-tidal near-bottom currents. Shelf waves generated remotely by winds and propagating into the region also play an important role in the near-bottom circulation on the bank.

A new high‐resolution unstructured grid finite volume Arctic Ocean model (AO‐FVCOM): An application for tidal studies

A spherical coordinate version of the unstructured grid 3‐D FVCOM (finite volume coastal ocean model) has been applied to the Arctic Ocean to simulate tides with a horizontal resolution ranging from 1 km in the near‐coastal areas to 15 km in the deep ocean. By accurately resolving the irregular coastlines and bathymetry in the Arctic Ocean coastal regions, this model reproduces the diurnal (K1 and O1) and semidiurnal (M2 and S2) tidal wave dynamics and captures the complex tidal structure along the coast, particularly in the narrow straits of the Canadian Archipelago. The simulated tidal parameters (harmonic constituents of sea surface elevation and currents) agree well with the available observational data. High‐resolution meshes over the continental shelf and slope capture the detailed spatial structure of topographic trapped shelf waves, which are quite energetic along the Greenland, Siberia, and Spitsbergen continental slope and shelf break areas. Water stratification influences the vertical distribution of tidal currents but not the water transport and thus tidal elevation. The comparison with previous finite difference models suggests that horizontal resolution and geometric fitting are two prerequisites to simulate realistically the tidal energy flux in the Arctic Ocean, particularly in the Canadian Archipelago.

Biweekly periodic variation of the Kuroshio axis northeast of Taiwan as revealed by ocean high-frequency radar

An analysis of surface current data obtained from 2002 to 2005 using long-range high-frequency radar provides the first evidence for the presence of biweekly (11–14 day) periodic variations of the Kuroshio axis northeast of Taiwan. This analysis clarifies the spatiotemporal characteristics of these variations and reveals that cyclonic/anticyclonic eddies propagating along the shelf slope from the vicinity of the deep channel east of Taiwan induce these variations northeast of Taiwan. The behavior of the cyclonic/anticyclonic eddies on the shelf slope is well explained by 2nd-mode interior shelf waves advected by the Kuroshio's mean flow. Remote effects from the vicinity of the deep channel east of Taiwan, or from outside the East China Sea, are believed to play an important role in the generation of these biweekly periodic variations of the Kuroshio axis northeast of Taiwan. Moreover, on the shelf slope, these variations cause an onshore current across the shelf slope, suggesting topographically controlled upwelling. Therefore, the biweekly periodic variations of the Kuroshio axis northeast of Taiwan might contribute not only to the onshore transport of Kuroshio surface water but also to transport nutrient-rich Kuroshio subsurface water onto the shelf in the East China Sea.

Vertical structure of water masses and silicon-phosphorus ratios in the west Bering Sea and in the Sea of Okhotsk

Using the data obtained from CTD stations and hydrochemical measurements (oxygen, silicates, and phosphates) performed by the Pacific Scientific Research Fishery Center (TINRO Center) in 2001–2004, vertical structures of water masses were considered for the western Bering Sea and for the deep-water depression of the Sea of Okhotsk. It was shown that definite values of the Si/P molar ratio were characteristic for the water mass boundaries within which linear relationships between these two elements were observed. The lower boundaries of cold intermediate layers in both seas are characterized by a value of Si/P = 23. The ratio for the main halocline (the layer of nutrient concentration jump) is equal to 32, while that for the intermediate layer is equal to 43 (47 in the Sea of Okhotsk). In the Bering Sea, linear relationships between the concentrations of these elements are determined by mixing of waters of different origin. The deep convection, regeneration of phosphates in the lower part of the surface layer, and the significant oxygen deficiency in the intermediate layer determine the doubled inclination of their ratio compared to the Redfield’s parameter. At the same time, in the Sea of Okhotsk, the determining role in linear relationships between the elements considered is played by the aeration of intermediate layer with near-bottom shelf waves, and by tidal mixing.

Structure and variability of the Filchner overflow plume

Properties of the dense ice shelf water plume emerging from the Filchner Depression in the southwestern Weddell Sea are described, using available current meter records and CTD stations. A mean hydrography, based on more than 300 CTD stations gathered over 25 yr points to a cold, relatively thin and vertically well-defined plume east of the two ridges cross-cutting the continental slope about 60 km from the Filchner sill, whereas the dense bottom layer is warmer, more stratified and much thicker west of these ridges. The data partly confirm the three major pathways suggested earlier and agree with recent theories on topographic steering by submarine ridges. A surprisingly high mesoscale variability in the overflow region is documented and discussed. The variability is to a large extent due to three distinct oscillations (with periods of about 35 h, 3 and 6 d) seen in both temperature and velocity records on the slope. The oscillations are episodic, barotropic and have a horizontal scale of ∼20–40 km across the slope. They are partly geographically separated, with the longer period being stronger on the lower part of the slope and the shorter on the upper part of the slope. Energy levels are lower west of the ridges, and in the Filchner Depression. The observations are discussed in relation to existing theories on eddies, commonly generated in plumes, and continental shelf waves.

Dynamics of the Wind-Driven Sea Level Variation around Antarctica

Abstract Coastal sea level variation around Antarctica is characterized by a coherent (circumpolarly in-phase) fluctuation, correlated with the Antarctic Oscillation (AAO). This study addresses the dynamics of the wind-driven sea level variation around Antarctica. A realistic barotropic numerical model reproduced well the observed sea level around Antarctica. From numerical model experiments, the authors demonstrate that the forcing responsible for the coastal sea level is the wind stress at the coastal boundary. Both the dominant coherent signal and westward propagating signals are identified in the model, and these signals are trapped over the shelf and slope around Antarctica. As a mechanism of these trapped signals, the authors consider analytical solutions of the oceanic response to alongshore wind stress over the shelf and slope in the circumpolar domain. In these solutions, besides the shelf wave mode, a wavenumber-zero mode appears and characterizes the coastal dynamics around Antarctica. At periods from 10 to 200 days, the coherent sea level can be explained quantitatively by the solution of this wavenumber-zero mode with a 5–10-day damping time scale. The spectral peaks of the westward propagating signals can be explained by the resonance of the shelf wave mode. The wavenumber-zero mode can respond to the wavenumber-zero forcing at any frequency and the degree of response increases with decreasing frequency. In addition, the wavenumber-zero component of wind stress, corresponding to the AAO variation, is a dominant forcing. Therefore, the coherent sea level variation around Antarctica is preferably generated and becomes a dominant feature in the circumpolar domain, particularly at lower frequencies.

Structure and variability of the Filchner overflow plume

Properties of the dense ice shelf water plume emerging from the Filchner Depression in the southwestern Weddell Sea are described, using available current meter records and CTD stations. A mean hydrography, based on more than 300 CTD stations gathered over 25 yr points to a cold, relatively thin and vertically well-defined plume east of the two ridges cross-cutting the continental slope about 60 km from the Filchner sill, whereas the dense bottom layer is warmer, more stratified and much thicker west of these ridges. The data partly confirm the three major pathways suggested earlier and agree with recent theories on topographic steering by submarine ridges. A surprisingly high mesoscale variability in the overflow region is documented and discussed. The variability is to a large extent due to three distinct oscillations (with periods of about 35 h, 3 and 6 d) seen in both temperature and velocity records on the slope. The oscillations are episodic, barotropic and have a horizontal scale of ∼20–40 km across the slope. They are partly geographically separated, with the longer period being stronger on the lower part of the slope and the shorter on the upper part of the slope. Energy levels are lower west of the ridges, and in the Filchner Depression. The observations are discussed in relation to existing theories on eddies, commonly generated in plumes, and continental shelf waves.

Process study of coastal circulation over the inner Scotian Shelf using a nested-grid ocean circulation model, with a special emphasis on the storm-induced circulation during tropical storm Alberto in 2006

This study examines main physical processes affecting the three-dimensional (3D) circulation and hydrographic distributions over the inner Scotian Shelf (ISS) in June and July 2006 using a nested-grid coastal ocean circulation modeling system known as the NCOPS-LB. The nested-grid system has five relocatable downscaling submodels, with the outermost submodel of a coarse horizontal resolution of (1/12)° for simulating storm surges and barotropic shelf waves over the Eastern Canadian shelf and the innermost submodel of a fine resolution of ∼180 m for simulating the 3D coastal circulation and hydrography over Lunenburg Bay of Nova Scotia in the default setup. The NCOPS-LB is driven by meteorological and astronomical forcing and used to study the storm-induced circulation over the ISS during tropical storm Alberto. Model results demonstrate that the coastal circulation and hydrographic distributions over the ISS are affected significantly by tides, local wind forcing, and remotely generated coastal waves during the study period.

Sea level response to wind field fluctuation around the tip of the Izu Peninsula

The mechanism of a characteristic sea level response (barotropic coastal ocean response) to wind field fluctuation around the tip of the Izu Peninsula observed during the middle of December 2000 to the middle of January 2001 was investigated based on three types of numerical experiments using the Princeton Ocean Model with various parameters. The response was characterized by the relaxation of sea level falling (rising) during eastward upwelling (westward downwelling) favorable wind regime. Analyses of quasi-realistic numerical model results in terms of the vertically integrated momentum balances and vorticity balance for the barotropic mode revealed that: 1) development/abatement of two anomalous circulations generated around the tip of the Izu Peninsula controls the sea level response through the acceleration/deceleration of a quasi-geostrophic barotropic coastal current between the circulations; 2) nonlinear vorticity advection by the Kuroshio Current and by the coastal current, coupled with vorticity diffusion, decelerates the quasi-geostrophic coastal current in the latter half of the wind regimes, which induces the relaxation of sea level rise/fall. The results of the quasi-realistic numerical experiment suggest that an analysis of the vorticity balance for the barotropic mode contributes to a better understanding of sea level responses to wind in coastal regions with strong currents and complex topography. In addition, a numerical experiment with idealized spatially uniform density stratification and a quasi-realistic wind field shows that if the Kuroshio Current had been shifted far offshore from the Izu Peninsula during the observation period, westward propagating continental shelf waves would have controlled the coastal sea level response.

Five years of Florida Current structure and transport from the Royal Caribbean Cruise Ship Explorer of the Seas

Using ship‐of‐opportunity platform Explorer of the Seas, five years of full‐depth velocity data have been collected across the Florida Straits at 26°N. Between May 2001 and May 2006 the mean transport of the Florida Current was 31.0 ± 4.0 Sv. This compares to a mean transport of 32.4 ± 3.2 Sv inferred from cable voltages at 27°N over the same period, implying an average 1.4 Sv transport into the Straits through the Northwest Providence Channel. The climatological core of the Florida Current is 170 cms−1 and is positioned at 79.8°W, about 10 km east of the shelf break. The largest variability in velocity occurs over the shelf and shelf break and is likely related to shelf waves. A secondary maximum occurs across much of the Straits over the top 100 m of the water column and may be associated with wind events. The annual cycle of Florida Current transports has a range of 4.7 Sv, with a maximum in May–June–July and a minimum in January. The difference between the summer and winter current structure appears as a first baroclinic mode with zero crossing at 150 m. The maximum difference is about 15 cms−1 at the surface and is centered just offshore of the mean current core. On interannual timescales, low‐pass filtered Explorer and cable transports show similar downward trends between 2002 and 2005, but diverge over the last year or so of the record.

The response of circulation and salinity in a micro-tidal estuary to sub-tidal oscillations in coastal sea surface elevation

Conceptual models of circulation theorise that the dominant forces controlling estuarine circulation are freshwater discharge from the riverine section (landward), tidal forcing from the ocean boundary, and gravitational circulation resulting from along-estuary gradients in density. In micro-tidal estuaries, sub-tidal water level changes (classified as those with periods between 3 and 10 days) with amplitudes comparable to the spring tidal range can significantly influence the circulation and distribution of water properties. Field measurements obtained from the Swan River Estuary, a diurnal, micro-tidal estuary in south-western Australia, indicated that sub-tidal water level changes at the ocean boundary were predominantly from remotely forced continental shelf waves (CSWs). The sub-tidal water levels had maximum amplitudes of 0.8 m, were comparable to the maximum tidal range of 0.6 m, propagated into the estuary to its tidal limit, and modified water levels in the whole estuary over several days. These oscillations dominated the circulation and distribution of water properties in the estuary through changing the salt wedge location and increasing the bottom water salinity by 7 units over 3 days. The observed salt wedge excursion forced by CSW was up to 5 km, whereas the maximum tidal excursion was 1.2 km. The response of the residual currents and the salinity distribution lagged behind the water level changes by ∼24 h. It was proposed that the sub-tidal forcing at the ocean boundary, which changed the circulation, salinity, and dissolved oxygen in the upper estuary, was due to a combination of two processes: (1) a gravity current generated by a process similar to a lock exchange mechanism and (2) amplified along-estuary density gradients in the upper estuary, which enhanced the gravitational circulation in the estuary. The salt intrusions under the sub-tidal forcing caused the rapid movement of anoxic water upstream, with significant implications for water quality and estuarine health.

Alongshore Wind Forcing of Coastal Sea Level as a Function of Frequency

Abstract The amplitude of the frequency response function between coastal alongshore wind stress and adjusted sea level anomalies along the west coast of the United States increases linearly as a function of the logarithm (log10) of the period for time scales up to at least 60, and possibly 100, days. The amplitude of the frequency response function increases even more rapidly at longer periods out to at least 5 yr. At the shortest periods, the amplitude of the frequency response function is small because sea level is forced only by the local component of the wind field. The regional wind field, which controls the wind-forced response in sea level for periods between 20 and 100 days, not only has much broader spatial scales than the local wind, but also propagates along the coast in the same direction as continental shelf waves. Hence, it has a stronger coupling to and an increased frequency response for sea level. At periods of a year or more, observed coastal sea level fluctuations are not only forced by the regional winds, but also by joint correlations among the larger-scale climatic patterns associated with El Niño. Therefore, the amplitude of the frequency response function is large, despite the fact that the energy in the coastal wind field is relatively small. These data show that the coastal sea level response to wind stress forcing along the west coast of the United States changes in a consistent and predictable pattern over a very broad range of frequencies with time scales from a few days to several years.

Application of wavelet transform in the study of coastal trapped waves off the west coast of South America

Wavelet transform and cross wavelet transform were applied for analyzing long time series of sea level and alongshore wind stress to identify intraseasonal variability off western South America and the relations with remote and local forcings. Hydrographic data were used to estimate properties of coastal trapped waves with a theoretical model. For El Niño years, we found the existence of intraseasonal oscillations with periods 20–90 days, between 2S and 27S. At the peak of 91–92 and 97–98 EL Niños, we found perturbations in the northern region, probably associated with remotely forced internal Kelvin waves, with periods 6–11 days and phase velocities 160–260 km/day. Between 12S and 15S, during two El Niño events, our calculations show perturbations which appear to be barotropic shelf waves propagating southward with velocities between 110 and 150 km/day and periods between 30 and 50 days.

Numerical study of the storm-induced circulation on the Scotian Shelf during Hurricane Juan using a nested-grid ocean model

A nested-grid ocean circulation modelling system is used to assess the upper ocean response of the Scotian Shelf and adjacent slope to Hurricane Juan in September 2003. The nested-grid system consists of a fine-grid inner model covering the Scotian Shelf/slope and a coarse-grid outer model covering the northwest Atlantic Ocean. The model-calculated upper ocean response to Hurricane Juan is characterized by large divergent surface currents forced by the local wind forcing under the storm, and intense near-inertial currents in the wake of the storm. The sea surface temperature (SST) cooling produced by the model is biased to the right of the storm track and agrees well with a satellite-derived analysis. Over the deep water, off the Scotian Shelf, some of the near-inertial energy input by the storm is advected eastward by the Gulf Stream away from the storm track. The hurricane also generates shelf waves that propagate equatorward with the coastline on their right. In comparison with the outer model results, the inner model captures more meso-scale structures, greater SST cooling and stronger near-inertial currents in the study region.

Sub-inertial modulation of semi-diurnal currents over the continental slope in the Faeroe-Shetland Channel

Observations were made over the continental slope in the Faeroe-Shetland Channel with the purpose of studying motions in the semidiurnal tidal frequency band and their interaction with background conditions. Specifically, the study focused on internal (baroclinic) tidal motions associated with internal gravity waves. In the internal tide (IT) source region, kinetic energy spectra reveal a fall-off rate with frequency of σ −2 which is associated with the passage of strongly non-linear fronts at the sea-bed. At a distance of 10 km off shore from the source region spectra from both the permanent pycnocline and weakly stratified interior exhibit a fall-off rate of σ −3, indicative of a regime in which internal waves are dominated by higher harmonics of the M 2 semidiurnal tidal frequency as a result of non-linear advection. The bandwidth, Δ σ = 0.23 – 0.3 cycles per day (cpd) of the semidiurnal band determined from the distribution of baroclinic energy outside the deterministic tidal frequencies, implies a modulation period of 3.3–4.3 days and which is observed as pulses of semidiurnal energy that are not related to the spring–neap cycle. The period of modulation is related to changes in the background stratification and the low-frequency vorticity. Variations in stratification are sufficient to modify the IT path by>150 m in the vertical over a horizontal distance of 10 km.The cross-slope gradient of the low-frequency ( σ < 0.75 cpd ) long-slope velocity, ∂ V / ∂ x , which represents one component of the vorticity varies with a periodicity of 3–4 days and has a magnitude sufficient to increase the effective Coriolis frequency to a value larger than M 2 so that the IT is unable to propagate as a free internal gravity wave. The source of the subinertial variability in the background conditions is attributed to meteorologically forced continental shelf waves which respond in two ways to prevailing winds and which perturb the pre-existing geostrophic balance that exists over the slope; oscillatory, clockwise rotating currents with a frequency of 0.7× f, where f is the Coriolis frequency, result from short impulsive winds whilst a quasi-steady long-slope flow persists as long as stronger winds of longer duration prevail. The impact of the observed subinertial variability in low-frequency vorticity and stratification raises doubts as to whether an ‘attractor’, along which internal wave energy is found following repeated reflections within a confined basin, may be observed in such a dynamic environment.

Existence of Eigenvalues of a Linear Operator Pencil in a Curved Waveguide---Localized Shelf Waves on a Curved Coast

The question of the existence of nonpropagating, trapped continental shelf waves (CSWs) along curved coasts reduces mathematically to a spectral problem for a self-adjoint operator pencil in a curved strip. Using methods developed for the waveguide trapped mode problem, we show that such CSWs exist for a wide class of coast curvature and depth profiles.

Depth- and current-induced effects on wave propagation into the Altamaha River Estuary, Georgia

A study of sea surface wave propagation and its energy deformation was carried out using field observations and numerical experiments over a region spanning the midshelf of the South Atlantic Bight (SAB) to the Altamaha River Estuary, GA. Wave heights on the shelf region correlate with the wind observations and directional observations show that most of the wave energy is incident from the easterly direction. Comparing midshelf and inner shelf wave heights during a time when there was no wind and hence no wave development led to an estimation of wave energy dissipation due to bottom friction with corresponding wave dissipation factor of 0.07 for the gently sloping continental shelf of the SAB. After interacting with the shoaling region of the Altamaha River, the wave energy within the estuary becomes periodic in time showing wave energy during flood to high water phase of the tide and very little wave energy during ebb to low water. This periodic modulation inside the estuary is a direct result of enhanced depth and current-induced wave breaking that occurs at the ebb shoaling region surrounding the Altamaha River mouth at longitude 81.23°W. Modelling results with STWAVE showed that depth-induced wave breaking is more important during the low water phase of the tide than current-induced wave breaking during the ebb phase of the tide. During the flood to high water phase of the tide, wave energy propagates into the estuary. Measurements of the significant wave height within the estuary showed a maximum wave height difference of 0.4 m between the slack high water (SHW) and slack low water (SLW). In this shallow environment these wave–current interactions lead to an apparent bottom roughness that is increased from typical hydraulic roughness values, leading to an enhanced bottom friction coefficient.

Velocity Field of the Oyashio Region Observed with Satellite-Tracked Surface Drifters during 1999–2000

Based on the surface drifters that moved out from the Sea of Okhotsk to the Pacific, the surface velocity fields of mean, eddy, and tidal components in the Oyashio region are examined for the period September 1999 to August 2000. Along the southern Kuril Island Chain, the Oyashio Current, having a width of ∼100 km, exists with velocities of 0.2–0.4 m s−1. From 40°N to 43°N, the Subarctic Current flows east- or northeastward with velocities of 0.1–0.3 m s−1, accompanied by a meandering Oyashio or Subarctic front. Between the Oyashio and Subarctic current regions, an eddy-dominant region exists with both cyclonic and anticyclonic eddies. The existence of an eastward flow just south of Bussol' Strait is suggested. The 2000 anticyclonic warmcore ring located south of Hokkaido was found to have a nearly symmetric velocity structure with a maximum velocity of ∼0.7 m s−1 at 70 km from the eddy center. Diurnal tidal currents with a clockwise tidal ellipse are amplified over the shelf and slope off Urup and Iturup Islands, suggesting the presence of diurnal shelf waves. From Lagrangian statistics, the single-particle diffusivity is estimated to be ∼10 × 107 cm2s−1.

Baroclinic and barotropic tides in the Weddell Sea

Barotropic and baroclinic tides were simulated for the Weddell Sea using ROMS. The model estimates for both tidal elevations and velocities showed good agreement with existing observations. The rms differences were 9 cm for elevations and 1.2–1.7 cm s−1 for the major axes of the tidal ellipses for the semidiurnal constituents and 6–8 cm and 4.5 cm s−1 for the diurnal constituents, respectively. Most of the discrepancies occurred deep under the ice shelf for the semidiurnal tides and along the continental slope for the diurnal tides. Along the continental slope, the model overestimated the generation of diurnal continental shelf waves. The diurnal tides were barotropic throughout the basin. However, internal tides were generated at semidiurnal frequencies over rough topography. Over the continental slope, semidiurnal baroclinic tidal generation was enhanced by the existence of continental shelf waves, through their harmonics. Baroclinic tides generated over rough topography in the northern Weddell Sea incited inertial oscillations as they propagated south. These inertial oscillations varied with depth since they were incited at different depths at different times as the internal tide progressed. Both the baroclinic tides and inertial oscillations induced vertical shear in the water column and increased the divergence of the horizontal surface velocities.