Waves and currents near the continental shelf edge

The abrupt depth increase which characterises the edge of many continental shelves determines a reduced horizontal length scale and a localised transition from shelf seas to the deep ocean. Particular forms of motion which may arise from the steep slopes include topographically guided currents along the slope, shelf-break upwelling, topographic Rossby waves and internal lee waves in the tidal current. The ocean/shelf mismatch may lead to a clear separation of water types, substantial reflection (from the shelf-edge neighbourhood) of all oceanic and shelf motions with periods greater than a few hours, and interaction between barotropic and baroclinic motions. Unstable longshelf currents, interleaving water masses, strong internal tides and internal waves, and narrow canyons enhance mixing across the shelf edge.     

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.     

Continental shelf waves off the Fukushima coast

Past observations and theories have indicated the importance of the constitution of the lowest-mode of shelf waves to the velocity field. However, significant contributions of the higher mode waves to current velocity fluctuations in the vicinity of the coast are suggested in observational results obtained along the Fukushima coast in Pt. I of this study (Kubota et al., 1981). To understand the importance of the higher modes, the generation of shelf waves is investigated theoretically by two methods. First, the generation of long shelf waves by monochromatic forcing is examined, and it is concluded that near the coast the second mode's contribution to the longshore velocity is the largest for the Fukushima coast. Second, the response of shelf waves to broad-band forcing is investigated by taking the dispersive characteristics of shelf waves into consideration. It is concluded that shelf waves with zero group velocity are selectively excited if the forcing has a broad-band spectrum. According to observational results obtained along the Fukushima coast, the wind spectrum has a broad peak at about 100 hours (Kubota et al., 1981). Since the third mode of shelf waves has zero group velocity around the period of 100 hours, the third mode can be selectively generated off the Fukushima coast. From this it is suggested that the Fukushima coast is in the forced region and that observed current fluctuations are motions associated with the second- and third-mode shelf waves.     

Onset of coastal upwelling in a two-layer ocean by wind stress with longshore variation

On the assumption that motions of the barotropic mode are horizontally nondivergent, action of the wind stress with longshore variation on a two-layer ocean adjacent to the meridional east coast is studied. Only the equatorward wind stress is considered. Along the east coast, upwelling is induced by the direct effect of the coast and is confined in a narrow strip with the width of the order of the internal radius of deformation. The upwelling propagates poleward with the internal gravity wave speed. Coastal upwelling induced by the wind stress with longshore variation may be interpreted as the generation and propagation of internal Kelvin waves. Associated with the coastal upwelling, the equatorward flow in the upper layer and the poleward flow in the lower layer are formed as an internal mode of motions. When the bottom topography with the continental shelf and slope is taken into account, occurrence of the poleward undercurrent is delayed by a few days because of the generation of continental shelf waves. And, after the forcing is stopped, the shelf waves propagate poleward away from the upwelling region and the poleward undercurrent fully develops. At the margin of the continental shelf, another upwelling region is induced and propagates poleward.     

Effects of scattering and resonance on energy dissipation of an internal tide in a narrow shelf

The effects of scattering and resonance on the energy dissipation of an internal tide were investigated using a two-dimensional model which is a reassembled version of the theoretical generation model devised by Rattray et al. (1969) for internal tide. The basic character of the scattering process at the step bottom was first investigated with a wide shelf model. When the internal wave incited from a deep region (Region II) into the shallow shelf region (Region I), a passing wave into the shallow region, a reflected wave into the deep region, and a beam-like wave, i.e. a scattered wave (SW), emanated at the step bottom. The SW, which consists of the superposition of numerous internal modes, propagated upward/downward into both regions. The general properties of the SW were well expressed around the shelf edge, even in the present model with viscosity effect. The amplitude of the SW decreased dramatically when the depth of the velocity maximum of the incident internal wave in Region II corresponded with the depth of the shelf edge. In the narrow shelf model, where the decay distance of the internal wave in Region I is longer than the shelf width, the incident internal wave reflected at the coast to form a standing wave. When the internal wave in Region I is enhanced by the resonance, the energy of the SW in Region II is also intensified. Furthermore, the energy of the modes in Region II predominated when the velocity maximum is identical to that of the dominant mode in Region I. These results suggest that the spatial scale of shelf region is a very important factor governing the energy dissipation of the internal tide through reflection and scattering in a narrow shelf.     

近岸沿岸流及污染物运动的数值模拟

基于双曲型缓坡方程和近岸浅水方程对近岸波浪斜向入射破碎所生成的沿岸流及污染物在沿岸波流作用下的运动进行了数值模拟,并对数值模拟结果进行了验证分析。数值模拟结果表明,在相近工况参数下,随着入射波高的增大,沿岸流流速和平均水面升高值均明显增大;随着岸坡坡度的增加,沿岸流流速和平均水面升高值明显增大;随着入射波浪周期的增大,平均水面升高值明显增大。在沿岸缓坡区域,由斜向入射波浪破碎所产生的沿岸流对污染物的运动起着不可忽略的影响。     

Glimpses of Arctic Ocean shelf–basin interaction from submarine-borne radium sampling

Evidence of shelf-water transfer from temperature, salinity, and ²²⁸Ra/²²⁶Ra sampling from the nuclear submarine USS L. Mendel Rivers SCICEX cruise in October, 2000 demonstrates the heterogeneity of the Arctic Ocean with respect to halocline ventilation. This likely reflects both time-dependent events on the shelves and the variety of dispersal mechanisms within the ocean, including boundary currents and eddies, at least one of which was sampled in this work. Halocline waters at the 132 m sampling depth in the interior Eurasian Basin are generally not well connected to the shelves, consonant with their ventilation within the deep basins, rather than on the shelves. In the western Arctic, steep gradients in ²²⁸Ra/²²⁶Ra ratio and age since shelf contact are consistent with very slow exchange between the Chukchi shelf and the interior Beaufort Gyre. These are the first radium measurements from a nuclear submarine.     

Topographically trapped waves over the continental shelf and slope

General characteristics of topographically trapped subinertia waves are discussed from the viewpoint of an eigenvalue problem and ray theory. Special attention is paid to the slope parameterS(x) (=(dh/dx)/h, wherex denotes the coordinate perpendicular to the shoreline, increasing seaward, andh(x) is the depth) which is a measure of the strength of the restoring force of the waves. Three cases for theS distribution are considered, in whichS is assumed to be positive at the coast and to tend to zero far from the coast. The first is whereS(x) decreases monotonically towards the open ocean. It is found in this case that waves are trapped near the coast. The second is whereS(x) does not decrease monotonically, but has a maximum. It is concluded that this case may contain two types of waves, i.e., those trapped near the coast and those trapped near the maximum, and the dispersion curves corresponding to different types may nearly intersect, namely, result in “kissing”. The third is whereS(x) has a negative region (corresponding to the presence of a trench). It is found in this case that an infinite sequence of waves is trapped in the negativeS region which propagate with the coast to their left (right) in the northern (southern) hemisphere besides the waves trapped near the coast. The topography in the second case corresponds to a typical continental shelf and a typical continental slope. It is shown by model calculation that trapped waves are present over the continental slope as well as over the continental shelf. Almost the same results are obtained for superinertia waves ifS is replaced by 1/h which is a measure of the restoring force of superinertia waves.     

Numerical study of wave and longshore current interaction

Wave and longshore current interaction was examined based on the numerical models.In these models,water waves in the presence of longshore currents were modeled by parabolic mild slope equation,and wave breaking induced longshore currents were modeled by shallow water equation.Water wave provided the radiation stress gradients to drive current.Wave and longshore current interactions were considered by cycling the wave and longshore current models to a steady state.The experiments for regular and irregular breaking wave induced longshore currents by Hamilton and Ebersole（2001） and Reniers and Battjes（1997） were simulated.The numerical results indicate that the present models are effective for simulating the interaction of wave and breaking wave induced longshore currents,and the numerically simulated longshore current at wave breaking point considering wave and longshore current interaction show some disagreement with those neglecting the wave-current interaction,and the breaking wave induced longshore current effect on wave transformation is not obvious.     

Numerical analysis of the transformation of tsunami waves in the south crimea shelf area

The paper analyses the transformation of tsunami-type solitary waves, propagating from the abyssal part of the Black Sea towards its shelf zone. The study is performed by solving numerically unidimensional non-linear equations for non-dispersive long waves, using the finite-difference slope and shelf, with the full wave reflection prescribed at a 10 m depth contour. The non-linearity of the process is shown to throughly impact the reflection of waves by the shore and the shape of the reflected wave. Tsunami wave heights have been seen to increase by several times in the Black sea shelf area. Translated by Vladimir A. Puchkin.     

A morphological stability analysis for a long straight barred coast

A morphological stability analysis is carried out for a long straight coast with a longshore bar. The situation with oblique wave incidence and a wave-driven longshore current is considered. The flow and sediment transport are described by a numerical modelling system. The models comprise: (i) a wave model with depth refraction, shoaling and wave breaking, (ii) a depth integrated model for wave driven currents and (iii) a sediment transport model for the bed load transport and the suspended load transport in combined waves and current. The direction of the sediment transport is taken to be parallel to the depth integrated mean current velocity, neglecting the effects of a bed slope and secondary currents. An instability is found to develop around the bar crest. The instability is periodic in the alongshore direction, and tends to form rip channels and to steepen the offshore face of the bar between the rip channels. The alongshore wave length of the most unstable perturbation is determined for different combinations of the wave conditions and the geometry of the profile.     

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.Translated by Mikhail M. Trufanov.     

A possible generation mechanism of the strong current over the northwestern shelf of the South China Sea

Continuous observation in late April 2005 on the northwestern shelf of the South China Sea reveals vigorous strong currents, the maximum velocity of which exceeds 3.8 m/s. The strong currents occurred around spring tide period, when the internal tide waves were also expected to be vigorous. Analysis shows that the major peaks of the current power spectrum are in low frequency band. Using a numerical method applied to the actual ocean stratification, we find that the amplitude profiles of the strong current are similar to that of the currents induced by some low-mode internal waves (at diurnal or semi-diurnal frequency). It indicates that the temporal and spatial features of strong currents were possibly induced by low frequency internal waves.     

Transformation of internal waves over an uneven bottom: Analytical results

The transformation of internal waves over the oceanic shelf of variable depth is studied analytically within a linear theory of a two-layer flow. It is shown that, at a specific character of depth variation, the internal wave propagates without reflection from the slope even if it is sufficiently steep. The properties of such progressive waves are studied—their form and the current structure in the upper and lower layers. The transformation of the wave propagating from the open ocean, where the depth is assumed to be constant, is considered. It is shown that the wave is transformed at the shelf edge and does not change its form in the course of time during its further propagation over the shelf. The height and form of the internal wave are calculated at the interface of the transition of the two-layer flow into the one-layer flow. Applications of the developed analytical theory to the estimation of internal wave transformation over a real shelf are discussed.     

Effect of stratification on long period trapped waves on the shelf

The effect of stratification on very long-period waves trapped on a straight continental shelf of constant depth is examined for a two-layer model. There are 4 modes in this system. The characteristics of the mode with the largest phase velocity can be approximated by the barotropic mode. The mode corresponding to the barotropic shelf-wave mode is modified by the baroclinic motions significantly, and in the limit of very narrow shelf width, the mode characteristics are transformed from those of the barotropic shelf-wave to the baroclinic Kelvin wave if the long-shore wave length is larger than the internal deformation radius. In this case, the stratification has an apparent effect of increasing phase velocity of barotropic shelf-waves. The remaining two modes are dominated by baroclinic motions with significant contribution from barotropic motions: among which the one has a shelf-wave characteristics for small values of the shelf width and approaches the mode corresponding to the baroclinic Kelvin wave in shallower water for large shelf width and the other is a stationary mode. If the long-shore wave length is much shorter than the internal deformation radius, the motions in the upper and lower layers are decoupled: the surface and bottom modes analogous to those discussed byRhines (1970) appears.If the interface is deeper than the shelf depth, the stationary mode is absent and the characteristics of the third mode approaches those of the baroclinic double Kelvin wave mode as the shelf width increases.     

The spectral characteristics and kinematics of short-period internal waves on the Hawaiian shelf

Based on the results of analyzing the characteristics of currents and temperature measured in the water space of the Mamala Bay (the Island of Oahu, Hawaii), we investigate the main properties of the field of short-period internal waves, which is very complex. We focus on analyzing the spectral characteristics and orbit parameters for waves with a period of 20 minutes. The results of investigations reveal two types of short-period internal waves for this area: intense and fast waves propagating predominantly toward the ocean and weaker and slower waves propagating mainly toward the coast. Suppositions are made on how these waves form: the strong and fast waves are likely to be caused by the decay of locally generated internal tides near the shelf edge, while the weak and slow and very short waves seem to result from the specific interaction between the pycnocline and strong tidal currents over a steep slope.     

Breaking of a tidal internal wave on a steep shelf as inferred from temperature measurements

The structure, evolution, and breaking of a tidal internal wave on a steep shelf are discussed on the basis of the data of temperature measurements. The bottom slope at the measurement site is close to the critical slope for a tidal wave. The tidal wave and other waves are inclined coastward. The tidal-wave amplitude increases monotonically with increasing horizon depth. The tidal wave is nonlinear in amplitude and turns over on the outer shelf. On the inner shelf, the internal wave is close in shape to rectangular and generates harmonics of its own. The harmonics make the tidal wave steeper and form solitary rises similar to bilateral bores. All these features ensure a more rapid sink for the internal-tide energy.     

Ephemeral sand waves in the hurricane surf zone

Airborne bathymetric LIDAR observations along the Florida panhandle after Hurricane Dennis (2005) show the first unequivocal observations of surf-zone sand wave trains.

These are found in depths of 5m along the trough of the hurricane bar, where hindcasts show strong longshore currents only during severe storms. The waves extend over tens of kilometers of coast after Dennis but are absent from the same area in four other datasets. Observed wavelength to water depth ratios are comparable to river dunes and tidal sand waves but height to depth ratios are smaller, with the largest wave heights around 0.1 times the water depth. The sand wave generation mechanism is hypothesized to be from wind-and-wave-induced longshore currents, which were hindcast to be large during Dennis, with destruction from water wave orbital velocities.     

沿岸流不稳定运动传播特性的小波相干谱分析

沿岸流不稳定运动属于超低频运动,研究它的传播特性,有助于深入理解其对岸滩演变、污染物、鱼卵等输移、迁移的影响。本文基于小波相干谱对所选实验波况进行了研究,分析了规则波、随机波入射情况下沿岸流不稳定运动传播特性,并讨论了入射波高、周期、坡度等对其的影响。结果表明,不规则波更易诱导出沿岸流不稳定运动,且在不规则波情况下,不稳定运动在沿岸方向相距4 m的两个断面上产生的相位差都约为±30°,与波浪入射角相近;随着入射波高的增加,非线性随之增强,更易诱导出不稳定运动,生成的沿岸流不稳定运动周期范围将增大;入射波周期对沿岸流不稳定运动的传播特性影响较小;坡度越陡越易诱导出超低频的不稳定运动。     

Numerical study on water waves and wave-induced longshore currents in Obaky coastal water

In this paper, the water waves and wave-induced longshore currents in Obaky coastal water which is located at the Mediterranean coast of Turkey were numerically studied. The numerical model is based on the parabolic mild-slope equation for coastal water waves and the nonlinear shallow water equation for the wave-induced currents. The wave transformation under the effects of shoaling, refraction, diffraction and breaking is considered, and the wave provides radiation stresses for driving currents in the model. The numerical results for the water wave-induced longshore currents were validated by the measured data to demonstrate the efficiency of the numerical model. Then the water waves and longshore currents induced by the waves from main directions were numerically simulated and analyzed based on the numerical results. The numerical results show that the movement of the longshore currents was different while the wave propagated to a coastal zone from different directions.