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This study aims to investigate characteristics of continental shelf wave (CSW) on the northwestern continental shelf of the South China Sea (SCS) induced by winter storms in 2021. Mooring and cruise observations, tidal gauge data at stations Hong Kong, Zhapo and Qinglan and sea surface wind data from January 1 to February 28, 2021 are used to examine the relationship between along-shelf wind and sea level fluctuation. Two events of CSWs driven by the along-shelf sea surface wind are detected from wavelet spectra of tidal gauge data. The signals are triply peaked at periods of 56 h, 94 h and 180 h, propagating along the coast with phase speed ranging from 6.9 m/s to 18.9 m/s. The dispersion relation shows their property of the Kelvin mode of CSW. We develop a simple method to estimate amplitude of sea surface fluctuation by along-shelf wind. The results are comparable with the observation data, suggesting it is effective. The mode 2 CSWs fits very well with the mooring current velocity data. The results from rare current help to understand wave-current interaction in the northwestern SCS. [ABSTRACT FROM AUTHOR]

For isolated oceanic structures above sea level in synoptic-scale wind fields, shielding causes a wind wake with reduced wind intensity on the lee side of the structure. This generates a wind-stress curl that may act as a source term for continental shelf waves (CSWs) propagating around the structure, if the bottom is sloping. We investigate CSW propagation in the case where the structure (a wind farm or an island) is circular and the depth over the shelf slope increases exponentially with radial distance. For free waves, the wave number, and hence the frequency, is quantized. We demonstrate that for circular banks with narrow continental margins, the resulting eigenfrequencies are close to those obtained for a straight shelf. Modelling the stress in the wind wake as a solitary pulse that moves along a straight shelf, we find, in the absence of friction, a forced solution that increases linearly in time when the pulse moves with the same speed as the free wave speed. For strong winds over longer periods of time, the along-shore wave velocity in the case of resonance may be of the order m / s for topographic parameters characteristic of the Taiwan Bank. Velocities of this magnitude could potentially cause harmful erosion as well as affect the ecosystem on the bank slopes. • Off-shore windfarms cause a wind-stress curl on the lee side of the farm. • The wind-stress curl may act as a source term for continental shelf waves (CSW). • Wave numbers for CSWs propagating along a circular shelf are quantized. • A moving wind stress may create resonance with CSWs of the same speed. [ABSTRACT FROM AUTHOR]

Previous studies reported coastal trapped waves (CTWs) in the Caspian Sea (CS). This study deals with the generation mechanisms, the temporal and spatial variability of CTWs in this area, and their transformations during propagation from the origin to the destination using recent measurements and high-resolution numerical simulations. CTWs are observed at all stations with periods of 2–6 days after northerly storms. The Absheron Peninsula, old Sefidrud delta, and Nur coasts were identified as the CTWs prone regions. The generation of CTWs in these locations was confirmed using numerical experiments. The propagation away from the generating location of CTWs was analyzed using a representative real wind storm. In the west part of the CS, the generation mechanism of CTWs is mainly similar to the barotropic Kelvin waves; in contrast, it is similar to the continental shelf waves in the southern shelves. The results can be used to study the contribution of generated CTWs to the transport of sediment and biological materials in all large lakes. [ABSTRACT FROM AUTHOR]

The fact that ocean currents must flow parallel to the coast leads to the dynamics of coastal sea level being quite different from the dynamics in the open ocean. The coastal influence of open-ocean dynamics (dynamics associated with forcing which occurs in deep water, beyond the continental slope) therefore involves a hand-over between the predominantly geostrophic dynamics of the interior ocean and the ageostrophic dynamics which must occur at the coast. An understanding of how this hand-over occurs can be obtained by considering the combined role of coastal trapped waves and bottom friction. We here review understanding of coastal trapped waves, which propagate cyclonically around ocean basins along the continental shelf and slope, at speeds which are fast compared to those of baroclinic planetary waves and currents in the open ocean (excluding the large-scale barotropic mode). We show that this results in coastal sea-level signals on western boundaries which, compared to the nearby open-ocean signals, are spatially smoothed, reduced in amplitude, and displaced along the coast in the direction of propagation of coastal trapped waves. The open-ocean influence on eastern boundaries is limited to signals propagating polewards from the equatorial waveguide (although a large-scale diffusive influence may also play a role). This body of work is based on linearised equations, but we also discuss the nonlinear case. We suggest that a proper consideration of nonlinear terms may be very important on western boundaries, as the competition between advection by western boundary currents and a counter-propagating influence of coastal trapped waves has the potential to lead to sharp gradients in coastal sea level where the two effects come into balance. [ABSTRACT FROM AUTHOR]

Data analysis of continental shelf currents and coastal sea level, together with the application of a semi-analytical model, are used to estimate the importance of remote wind forcing on the subinertial variability of the current in the central and northern areas of the South Brazil Bight. Results from both the data analysis and from the semi-analytical model are robust in showing subinertial variability that propagates along-shelf leaving the coast to the left in accordance with theoretical studies of Continental Shelf Waves (CSW). Both the subinertial variability observed in along-shelf currents and sea level oscillations present different propagation speeds for the narrow northern part of the SBB (~ 6-7 m/s) and the wide central SBB region (~ 11 m/s), those estimates being in agreement with the modeled CSW propagation speed. On the inner and middle shelf, observed along-shelf subinertial currents show higher correlation coefficients with the winds located southward and earlier in time than with the local wind at the current meter mooring position and at the time of measurement. The inclusion of the remote (located southwestward) wind forcing improves the prediction of the subinertial currents when compared to the currents forced only by the local wind, since the along-shelf-modeled currents present correlation coefficients with observed along-shelf currents up to 20% higher on the inner and middle shelf when the remote wind is included. For most of the outer shelf, on the other hand, this is not observed since usually, the correlation between the currents and the synoptic winds is not statistically significant. [ABSTRACT FROM AUTHOR]

We consider barotropic coastally-trapped Kelvin waves of tidal origin along a straight coast that propagate from deeper water across a transverse bottom escarpment into a more shallow region. The M 2 component, which has a frequency above the inertial frequency f , is modified by crossing the escarpment, but continues basically as a Kelvin wave into the shallow region. For tidal components that have frequencies smaller than f , like K 1 , some of the energy in the Kelvin wave is converted into a continental shelf wave (CSW) that follows the escarpment with shallow water to the right (in the northern hemisphere). The theory is applied to the shelf north-west of Norway where the deep Norwegian Sea is separated from the much shallower Barents Sea by an escarpment reaching from the north-Norwegian coast towards Spitsbergen. By introducing an idealized bottom topography and coastal geometry, analytical calculations and numerical modeling are used to investigate the energy flux in CSWs towards Spitsbergen caused by sub-inertial Kelvin wave motion along the west coast of Norway. Both analytical and numerical calculations indicate that the CSW energy flux towards Spitsbergen is about eighty percent of the incident sub-inertial Kelvin wave energy flux, and that only twenty percent of the energy flux is transmitted into the Barents Sea in the form of sub-inertial Kelvin waves. • Sub-inertial Kelvin waves of tidal origin along a straight coast are studied. • Application is made to the escarpment in Barents Sea Gap outside north Norway. • Propagation across this escarpment generates continental shelf waves (CSWs). • Energy flux along the escarpment towards Spitsbergen by CSWs is substantial. • About 20 percent of the Kelvin wave energy continues into the Barents Sea. [ABSTRACT FROM AUTHOR]

The existence of free continental shelf waves in the Western Mediterranean Sea is studied using a statistical approach. Hourly mean sea level at six locations extended along the northern and southern coast of the Alborán Sea were analyzed by standard correlation and spectral analysis techniques for two periods of 91 and 92 days, respectively. The mean sea level was adjusted for the effect of atmospheric pressure according to the hydrostatic approximation. The wind-coherent response of sea level was removed by calculating the transfer function between the input alongshore wind stress and the output adjusted sea level. The cross-correlation analyses indicate time lags that are consistent with the hypothesis of the propagation of the free shelf waves predicted by the continental shelf wave theory. The presence of a westward-travelling signal on the NCS and a west-to-east travelling signal on the SCS of the Alborán Sea is confirmed. The cross spectra between residual sea level at the six locations show significant coherence at long periods. For these periods, the phase difference spectra show that the directions of propagation of the free waves are consistent with the interpretation of the cross correlation analysis. There is evidence of a seasonal variation in the phase speed of the waves, which may be related to variations in the speeds of currents in the Alborán Sea. The observations suggest the presence of continental shelf waves on both coasts of the Alborán Sea. [ABSTRACT FROM AUTHOR]

Measurements of diurnal tides over the continental slope between the Norwegian Sea and the Barents Sea shelf are presented. Numerical 3D simulations, in agreement with field data, show strong cross-slope velocities and large vertical displacements of the interface between Atlantic Water and intermediate water over the slope. The striking correspondence between the prominent observed and modeled diurnal oscillations gives confidence that this is well represented by the model. This variability, interpreted as tidally induced diurnal period topographic waves, is confined to the diverging topography of the continental slope west of Tromsøflaket. The model results reveal highly variable magnitudes of the oscillations and the cross shelf currents in time, related to variable strength of the background flow, the Norwegian Atlantic Current. We suggest that the diurnal topographic wave can be an effective mechanism for cross slope exchange between the Norwegian Sea and the Barents Sea shelf, and important for benthic and pelagic biological processes on the shelf and slope. [ABSTRACT FROM AUTHOR]

We study attenuation of free waves in the homogeneous ocean. Using the Cauchy–Riemann relations and then energy equation, we derive a novel equation that relates temporal and spatial decay to the energy dissipation in the fluid. In particular, for spatially damped waves we find that the attenuation coefficient is inversely proportional to the group velocity. We discuss the consequences of this for continental shelf waves where the group velocity may tend to zero in wave number space, and hence the spatial attenuation coefficient may become infinitely large. We show that generally for a travelling wave solution, the spatial damping will remain unchanged in a frame of reference moving with the group velocity, revealing the different physics behind temporal wave damping and spatial wave damping. • Temporal and spatial wave damping is related to the energy dissipation. • The spatial damping rate is inversely proportional to the group velocity. • Energy may accumulate locally for continental shelf waves with zero group velocity. [ABSTRACT FROM AUTHOR]

Abstract: The time- and depth-averaged mean drift induced by barotropic continental shelf waves (CSW’s) is studied theoretically for idealized shelf topography by calculating the mean volume fluxes to second order in wave amplitude. The waves suffer weak spatial damping due to bottom friction, which leads to radiation stress forcing of the mean fluxes. In terms of the total wave energy density E̅̅ over the shelf region, the radiation stress tensor component S̅ 11 for CSW’s is found to be different from that of shallow water surface waves in a non-rotating ocean. For CSW’s, the ratio S̅11/E̅ depends strongly on the wave number. The mean Lagrangian flow forced by the radiation stress can be subdivided into a Stokes drift and a mean Eulerian drift current. The magnitude of latter depends on ratio between the radiation stress and the bottom stress acting on the mean flow. When the effect of bottom friction acts equally strong on the waves and the mean current, calculations for short CSW’s show that the Stokes drift and the friction-dependent wave-induced mean Eulerian current varies approximately in anti-phase over the shelf, and that the latter is numerically the largest. For long CSW’s they are approximately in phase. In both cases the mean Lagrangian current, which is responsible for the net particle drift, has its largest numerical value at the coast on the shallow part of the shelf. Enhancing the effect of bottom friction on the Eulerian mean flow, results in a general current speed reduction, as well as a change in spatial structure for long waves. Applying realistic physical parameters for the continental shelf west of Norway, calculations yield along-shelf mean drift velocities for short CSW’s that may be important for the transport of biological material, neutral tracers, and underwater plumes of dissolved oil from deepwater drilling accidents. [Copyright &y& Elsevier]

Abstract: For mathematical and numerical reasons the physical boundary condition of regularity of solutions (i.e. finite amplitude) at the singular point of vanishing water depth (the shoreline) imposed on wavelike solutions on the continental shelf is replaced by “no normal flow” condition in analytical and numerical studies of continental shelf waves. This “no normal flow” condition that circumvents the mathematical subtlety associated with the singularity of the equations at the shoreline applies only to channel problems where a wall bounds the flow on the shoreline side. To assess the ramifications of this simplification on the phase speeds and radial (cross-shore) structure of the solutions, data from laboratory experiments are compared with predictions of models that employ the two boundary conditions. The phase speed and radial structure are measured in experiments carried out in a turntable with linearly sloping bottom in which the mean water depth vanishes on the shallow side and waves with known frequencies are generated at a point along the perimeter. The dispersion relation and wave’s radial structure are estimated by following particles floating in the water; the measured dispersion relation agrees well with that predicted by a theory that employs the shelf boundary condition and disagrees with the prediction of a theory that employs the channel conditions. This disagreement between the dispersion relation predicted by the channel theory and that predicted by the shelf theory is relevant to typical frequencies that are observed on continental shelves. Although the shelf break condition does not affect the dispersion relation, better agreement is found between the predicted and measured velocity structure when a flat bottom is assumed there instead of a wall. [Copyright &y& Elsevier]

Abstract: A set of numerical experiments has been performed in order to analyze the long-wave response of the coastal ocean to a translating mesoscale atmospheric cyclone approaching the coastline at a normal angle. An idealized two-slope shelf topography is chosen. The model is forced by a radially symmetric atmospheric pressure perturbation with a corresponding gradient wind field. The cyclone''s translation speed, radius, and the continental shelf width are considered as parameters whose impact on the long wave period, modal structure, and amplitude is studied. Subinertial continental shelf waves (CSW) dominate the response under typical forcing conditions and on the narrower shelves. They propagate in the downstream (in the sense of Kelvin wave propagation) direction. Superinertial edge wave modes have higher free surface amplitudes and faster phase speeds than the CSW modes. While potentially more dangerous, edge waves are not as common as subinertial shelf waves because their generation requires a wide, gently sloping shelf and a storm system translating at a relatively high (∼10ms−1 or faster) speed. A relatively smaller size of an atmospheric cyclone also favors edge wave generation. Edge waves with the highest amplitude (up to 60% of the forced storm surge) propagate upstream. They are produced by a storm system with an Eulerian time scale equal to the period of a zero-mode edge wave with the wavelength of the storm spatial scale. Large amplitude edge waves were generated during Hurricane Wilma''s landfall (2005) on the West Florida shelf with particularly severe flooding occurring upstream of the landfall site. [Copyright &y& Elsevier]

Abstract: This paper presents a combined analytical and numerical extension to recent theoretical work on trapped continental shelf waves over smoothly curved coastlines. The geometry considered consists of an annular region joining two semi-infinite straight sections and, even though the isobaths remain evenly spaced, trapped modes appear in the annular region due entirely to the longitudinal curvature of the shelf there. Expanding in alongshore modes and requiring that the error is orthogonal to the transverse modes gives a linear algebraic system of equations for the frequency of trapping. Solutions for barotropic, non-divergent shelf waves show that trapped modes always exist if the coastline curves to form a headland. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: 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 10km 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, 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>150m in the vertical over a horizontal distance of 10km.The cross-slope gradient of the low-frequency long-slope velocity, , 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. [Copyright &y& Elsevier]

The barotropic and baroclinic tides in the Ross Sea were simulated using a primitive equation, sigma-coordinate model, the Regional Ocean Model System (ROMS), for four tidal constituents, M2, S2, K1, and O1. Small elevation amplitudes were predicted over most of the basin, with a combined standard deviation of 30-50 cm. Larger amplitudes, with standard deviations ranging from 50-70 cm, occurred deep within the ice shelf cavity, over the continental slope, and over Iselin Bank. Most of the elevation response was associated with the diurnal constituents (K1 and O1), as was most of the depth-independent (barotropic) velocity response. Baroclinic tides were generated at locations of steep topography for the semidiumal constituents, but not the diurnal. Diurnal continental shelf waves were generated by the diurnal tides and found to amplify the semidiurnal elevations and baroclinic tidal velocities over the continental slope. Comparisons with observations in both elevation and velocities showed very good agreement for the semidiurnal constituents (M2 and S2) and moderate agreement for the diurnal constituents (K1 and O1). The disagreement for the diurnal constituents was associated with diurnal frequency continental shelf waves, which were overexcited along the shelf break. The baroclinic tides induced both small-scale horizontal and vertical shear in the velocity fields in the Ross Sea. [ABSTRACT FROM AUTHOR]

Diurnal continental shelf waves (CSWs) are studied theoretically for an idealized shelf topography. Wave attenuation is caused by the exchange of fluid on the sloping shelf with an inner region through a permeable coastline. As an example, we consider the region outside Lofoten-Vesterålen in north Norway. Here CSWs with diurnal tidal frequencies are possible in a small wave number range centered around zero group velocity. A previous investigation with a Robin condition (a weighted combination of Dirichlet and Neumann conditions) at the permeable boundary has shown that the spatial damping coefficient becomes infinitely large when the group velocity of the CSWs approaches zero. Here we demonstrate that this is not a result of the mathematical formulation, but reflects a physical reality. We show this by modelling the highly convoluted inner archipelagic region as a series of densely packed vertical Hele Shaw cells. By comparing the two ways of describing a permeable coastal boundary (Robin/Hele Shaw), we may express the Robin parameter in terms of the physical parameters (permeability, eddy viscosity) that characterize the flow on the inner porous shelf. The radiation stresses that drive the Lagrangian mean currents are the same in the two cases. This means that the spatial mean current distribution over the sloping shelf becomes unaltered when we compare the Robin case and the porous inner shelf case. • Continental shelf waves are forced by diurnal tides. • Inner continental shelf is modelled as a porous medium. • Spatial damping coefficient is inversely proportional to the group velocity. • Group velocity tends to zero over the sloping shelf. [ABSTRACT FROM AUTHOR]

This study investigates the propagation of coastal trapped waves (CTWs) along the Brazilian continental shelf between 34°S and 11°S using in situ data combined with the outputs from a high-resolution ocean simulation with HYCOM. The CTWs generation area covers a wide region ranging from the Patagonian shelf to the southern Brazilian shelf. The spectral analysis of coastal sea level series between 54°S and 10.5°S shows three bands of high energy associated with periods from 5 to 12 days, 15–22 days, and 25–40 days. The energy of the CTWs decreases along their propagation for all frequency bands, showing a drastic reduction north of 22°S, due to abrupt variations in the width and depth of the continental shelf between Tubarão Bight and Abrolhos Bank. Their phase speed propagation varies along the coast, being faster (>25 m/s) in the southernmost region (between 42°S and 41°S), reaching ~11 m/s north of 41°S, and reducing to ~3 m/s further north (equatorward of 24°S). The free Continental Shelf Wave theory supports the notion that the intense deceleration north of 24°S can be explained by the narrowing of the continental shelf. The stratification parameter indicates that the Brazilian continental shelf has a barotropic response to wind-generated disturbances. [ABSTRACT FROM AUTHOR]

Coastally Trapped Waves (CTWs) are studied along the east and north shelves of the Arabian Sea (AS) through field measurements and numerical modeling. A nondispersive barotropic wave, induced by Cyclone Ashobaa, with periods of 10–14 days propagated in wider parts of the shelf. The phase velocities and CTW amplitudes significantly decreased in narrower parts, where a stronger stratification also exists. The long waves are represented by first barotropic and lower bottom trapped modes in deeper and shallower parts of these narrow shelves, respectively. Although the low frequency oscillations, with peak periods of 10–14 days, can be detected in shallow water level data, the wavelet transforms of alongshore currents reveal these long waves exist only in deep waters. This can be attributed to the effect of bottom friction, which causes the effective coastal boundary to move offshore. The Ras al Hadd jet was deflected by the interaction of Cyclone Ashobaa with preexisting eddies and an intensified current was observed where the Ras al Hadd jet crossed the northern shelf. • Coastally Trapped Waves (CTWs), induced by Cyclone Ashobaa, are studied through field measurements and numerical modeling. • CTWs show barotropic modal structures in shallow waters of eastern shelf. • Approaching to Strait of Hormuz, the modal structures of CTWs are transited to baroclinic bottom-trapped mode. • Decreasing of phase velocities and amplitudes of CTWs can be attributed to narrowing the shelf and higher stratification. • The interaction between Cyclone Ashobaa and preexisting ocean eddies deflects Ras al Hadd Jet streamline. [ABSTRACT FROM AUTHOR]