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.     

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.     

Application of the data filtration algorithm in reconstructing the structure of trapped waves over the Crimean shelf

The data collected in the course of a local dynamic experiment near the Crimean shore during the summer of 1991 are interpreted, using the filtration algorithm based on variation principles. As a result, the ratio between the mode amplitudes of the long-shore velocity structure has been obtained, which is consistent with the physical views about shelf water dynamics. Translated by Vladimir A. Puchkin.     

Equilibrium conditions for curved shape bays with application to an ancient coast

The seaward concave shape of beaches located between two headlands and exposed to a predominant direction of wave attack has been assimilated previously by a logarithmic spiral.In this study, a similar mathematical concept is applied to the Galé coast (Portugal) and an ancient coast located around 50 m deep on the continental shelf.The shape of the present-day coastline corresponds to a long-term equilibrium form reached almost one century ago. Application of such a model to the ancient coast, parallel to this coastline, suggests that the swell direction likely has not changed during the last 10,000 to 11,000 years.     

On the stability of a class of shoreline planform models

The evolution of beaches in response to the incident wave conditions has long attracted the attention of researchers and engineers. A popular mathematical model describing the change in the position of a single height contour on the coastline assumes that the beach profile is stable and the plan shape evolves due to wave-driven long-shore transport. Extensions of this model include more contours and allow for beach profile alteration through cross-shore transport of sediment. Despite this advantage, models with multiple contours remain relatively underused. In this paper we examine the stability of this class of model for the cases of one to three contours. Unstable modes may exist when there is more than one contour. These include short waves whose growth rate is strongly dependent upon wavenumber. For the case of three contours an additional long wave instability is possible. A necessary, but not sufficient, condition for instability is found. It requires a reversal of transport direction amongst the contours. The existence of these instabilities provides a possible explanation for the difficulties found in implementing computational multi-line models, particularly where structures alter the natural longshore transport rates so they satisfy, locally, the condition for instability.     

Numerical study of pollutant movement in waves and wave-induced long-shore currents in surf zone

Water waves, wave-induced long-shore currents and movement of pollutants in waves and currents have been numerically studied based on the hyperbolic mild-slope equation, the shallow water equation , as well as the pollutant movement equation, and the numerical results have also been validated by experimental data. It is shown that the long-shore current velocity and wave set-up increase with the increasing incident wave amplitude and slope steepness of the shore plane ; the wave set-up increases with the in- creasing incident wave period;and the pollutant morement proceeds more quiekly with the increasing incident wave amplitude and slope steepness of the shore palane. In surf zones, the long-shore currents induced by the inclined incident waves have effectively affected the pollutant movement.     

Observation of ocean current response to 1998 Hurricane Georges in the Gulf of Mexico

1 Introduction Hurricane is an extremely high wind event, which injects momentum into the oceanic mixed layer along its passage for a very short duration. If our interest is not at the surface, but in a depth away from the imme-diate surface wave influenc…     

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.     

人工采掘坑影响下珊瑚礁海岸波浪传播变形试验

基于礁坪上高分辨率的波浪测量,通过波浪水槽试验分析了短波、低频长波、平均水位、波形参数和非线性参数的沿礁变化规律,重点探讨礁坪中部存在人工采掘坑对上述波浪传播变形特征的影响,并与无坑的情况进行对比.研究表明:当人工采掘坑存在时,短波波高在坑前和坑内分别增大和减小,在礁后岸滩附近却无显著变化;低频长波波高在坑附近变化不大...     

Second-Oorder Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a constant plane sloping bottom is presented in this paper. For special case of slope angle b=p/2, this solution can be reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves were also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves were also discussed. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoretical autocorrelation and spectral density functions of the first and second orders are derived. The boundary conditions for the determining determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated.     

Experimental and Numerical Study of Wave-Induced Long-Shore Currents on A Mild Slope Beach

1.Introduction Long shorecurrenthasbecomethesubjectofextensiveworldwideresearchformanyyears.The purposeofthestudyistounderstandandpredicttheprocessesofsedimenttransport,shorelineevolu tionandpollutanttransportinthenear shorezoneundertheactionofwaves.Goda(2001)regarded thesuspendedsedimentastheprincipalloadinsedimenttransportandtheeffectoflong shorecurrents wasemphasized.Theeffectofwavesonpollutanttransportwasstudiedbynumericalmodelandfield experiment(TaoandHan,2002;Rodriguezetal.,1995),andth…     

Second-Order Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation,a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper.For special case of slope angle β=π/2,this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline.Interactions between two edge waves including progressive,standing and partially reflected standing waves are also discussed.The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given.The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated,and the corresponding theoretical autocorrelation and spectral density functions of the first and the second orders are derived.The boundary conditions for the determination of the parameters of short edge wave are suggested,that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory.Finally some computation results are demonstrated.     

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.     

A two-dimensional finite volume hydrodynamic model for coastal areas: Model development and validation

A two dimensional implicit finite volume scheme for solving the shallow-water equations is developed. The effects of the Coriolis force, surface wind stress, and waves are included. A non-uniform rectilinear forward staggered grid is used with Cartesian coordinates. The time integration is performed using the Euler implicit technique. The convective flux is treated using the deferred correction method. The viscous terms are discretized using a second order central difference approximation. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is used for coupling the velocity components and the water elevation gradient for the water level correction. The system of equations is solved sequentially using the Strongly Implicit Procedure (SIP). To simulate wave driven current, a phase averaged wave model is used first to simulate wave transformation and calculate radiation stresses. The performance of the developed model is validated for different sources of external forces and different combinations of boundary conditions. The validation cases include tidal circulation in a harbor and wave induced currents behind a breakwater parallel to the coastline. The model is finally applied to simulate the flow pattern in a closed artificial lagoon and along the coastline near Damietta Port located along the Northern coast of Egypt. Results of the developed model agree well with the published results for the considered cases.     

Disintegration of linear edge waves

It is demonstrated that offshore wavenumbers of edge waves change from imaginary wavenumbers in deep water to real wavenumbers in shallow water. This finding indicates that edge waves in the offshore direction exist as evanescent waves in deep water and as propagating waves in shallow water. Since evanescent waves can stably exist in a limited region while propagating waves cannot, energy should be released from nearshore regions. In the present study, the instability region is predicted based on both the full water wave solution and the shallow-water wave approximation.     

Subsurface control on seafloor erosional processes offshore of the Chandeleur Islands,Louisiana

The Chandeleur Islands lie on the eastern side of the modern Mississippi River delta plain, near the edge of the St. Bernard Delta complex. Since abandonment approximately 2,000 years b.p., this delta complex has undergone subsidence and ravinement as the shoreline has transgressed across it. High-resolution seismic-reflection, sidescan-sonar, and bathymetry data show that seafloor erosion is influenced by locally variable shallow stratigraphy. The data reveal two general populations of shallow erosional depressions, either linear or subcircular in shape. Linear depressions occur primarily where sandy distributary-channel deposits are exposed on the seafloor. The subcircular pits are concentrated in areas where delta-front deposits crop out, and occasional seismic blanking indicates that gas is present. The difference in erosional patterns suggests that delta-front and distributary-channel deposits respond uniquely to wave and current energy expended on the inner shelf, particularly during stormy periods. Linear depressions may be the result of the sandy distributary-channel deposits eroding more readily by waves and coastal currents than the surrounding delta-front deposits. Pits may develop as gas discharge or liquefaction occurs within fine-grained delta-front deposits, causing seafloor collapse. These detailed observations suggest that ravinement of this inner shelf surface may be ongoing, is controlled by the underlying stratigraphy, and has varied morphologic expression.     

Sediment distribution and transport along a rocky, embayed coast: Monterey Peninsula and Carmel Bay, California

Field measurements of beach morphology and sedimentology were made along the Monterey Peninsula and Carmel Bay, California, in the spring and summer of 1997. These data were combined with low-altitude aerial imagery, high-resolution bathymetry, and local geology to understand how coastal geomorphology, lithology, and tectonics influence the distribution and transport of littoral sediment in the nearshore and inner shelf along a rocky shoreline over the course of decades. Three primary modes of sediment distribution in the nearshore and on the inner shelf off the Monterey Peninsula and in Carmel Bay were observed. Along stretches of the study area that were exposed to the dominant wave direction, sediment has accumulated in shore-normal bathymetric lows interpreted to be paleo-stream channels. Where the coastline is oriented parallel to the dominant wave direction and streams channels trend perpendicular to the coast, sediment-filled paleo-stream channels occur in the nearshore as well, but here they are connected to one another by shore-parallel ribbons of sediment at depths between 2 and 6 m. Where the coastline is oriented parallel to the dominant wave direction and onshore stream channels are not present, only shore-parallel patches of sediment at depths greater than 15 m are present. We interpret the distribution and interaction or transport of littoral sediment between pocket beaches along this coastline to be primarily controlled by the northwest-trending structure of the region and the dominant oceanographic regime. Because of the structural barriers to littoral transport, peaks in wave energy appear to be the dominant factor controlling the timing and magnitude of sediment transport between pocket beaches, more so than along long linear coasts. Accordingly, the magnitude and timing of sediment transport is dictated by the episodic nature of storm activity.     

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.     

Vertical variations of wave-induced radiation stress tensor

INTRODUcrIONThe concept of radiation stress was deve1oPed by tonguet--Higgins and Stewart (1964 ),who intreduced the definition of radiation stress as the excess mornentum due to the presence ofwaves, on the basis of time-averaged laws of Newtonian fluid mechanics and the assmption ofa unifOrm velocity distribution over depth. Subequently, the theory has been applied success-fully in the investigation of phenomena such as wave set-up and set--down (Bowen et al.,l968), longshore currents …     

基于二阶斯托克斯波理论的辐射应力垂向分布

基于二阶斯托克斯波理论推导了辐射应力的垂向分布表达式,通过算例讨论了辐射应力在深水和有限水深条件下的垂向分布规律,并与基于微幅波理论的辐射应力进行了比较.结果表明,在波浪非线性不强时,基于二阶斯托克斯波理论的辐射应力与基于微幅波理论的辐射应力表达式计算结果接近;而当水深较浅波浪非线性较强时,基于二阶斯托克斯波理论的辐射应力在近表面处明显大于基于微幅波理论的辐射应力.采用二阶斯托克斯波理论推导的波浪辐射应力更为合理地反映了波浪非线性效应.