Showing papers on "Waves and shallow water published in 2002"

A new Boussinesq method for fully nonlinear waves from shallow to deep water

Abstract: A new method valid for highly dispersive and highly nonlinear water waves is presented. It combines a time-stepping of the exact surface boundary conditions with an approximate series expansion solution to the Laplace equation in the interior domain. The starting point is an exact solution to the Laplace equation given in terms of infinite series expansions from an arbitrary z-level. We replace the infinite series operators by finite series (Boussinesq-type) approximations involving up to fifth-derivative operators. The finite series are manipulated to incorporate Pade approximants providing the highest possible accuracy for a given number of terms. As a result, linear and nonlinear wave characteristics become very accurate up to wavenumbers as high as kh = 40, while the vertical variation of the velocity field becomes applicable for kh up to 12. These results represent a major improvement over existing Boussinesq-type formulations in the literature. A numerical model is developed in a single horizontal dimension and it is used to study phenomena such as solitary waves and their impact on vertical walls, modulational instability in deep water involving recurrence or frequency downshift, and shoaling of regular waves up to breaking in shallow water.

A numerical study of submarine-landslide-generated waves and run-up

Abstract: A mathematical model is derived to describe the generation and propagation of water waves by a submarine landslide. The model consists of a depth–integrated continuity equation and momentum equations, in which the ground movement is the forcing function. These equations include full nonlinear, but weak frequency–dispersion, effects. The model is capable of describing wave propagation from relatively deep water to shallow water. Simplified models for waves generated by small seafloor displacement or creeping ground movement are also presented. A numerical algorithm is developed for the general fully nonlinear model. Comparisons are made with a boundary integral equation method model, and a deep–water limit for the depth–integrated model is determined in terms of a characteristic side length of the submarine mass. The importance of nonlinearity and frequency dispersion in the wave–generation region and on the shoreline movement is discussed.

Barotropic waves generated by storms moving rapidly over shallow water

Abstract: [1] In the falls of both 1999 and 2000, waves with characteristics similar to tsunami hit the southeast coast of Newfoundland, Canada. The waves were large enough to cause local flooding, damage to docks, and other destruction. There is, however, no evidence of seismic events, underwater landslides, or slumping events on either occasion. Other explanations, such as storm surge, also appear unlikely, and local weather conditions at the coast were not exceptional at the time. On both occasions, tropical storms moved rapidly across the Grand Banks of Newfoundland from southwest to northeast, with a translation speed of � 30 m s � 1 . A significant, nonisostatic response to atmospheric pressure forcing can be expected over the shallow water of the banks since the translation speed of the storms is comparable to the local shallow water gravity wave speed. We speculate that the atmospheric pressure forcing associated with the storms generated a barotropic wake, and we use a numerical model to argue that as the storm moved back over the deep ocean, the wake was refracted and/or reflected by the variable bathymetry at the edge of the banks and that it was the refraction of the wake toward the coast that led to the unusual sea level events in southeastern Newfoundland. The numerical model results are in general agreement with the eye witness reports. The model-computed wave activity hits the southeast coast of Newfoundland at about the right time and in the right areas for both events, although for the 1999 event the model response is weaker than is observed at Port Rexton in Trinity Bay. The reason for the poorer model performance in the 1999 case is not known, although we do find that the model results are sensitive to uncertainty in the exact track taken by the storm across the banks. The model results demonstrate that the period and wavelength of the gravity waves comprising the wake are, in general, proportional to the length scale of the pressure forcing, an exception being the model response in Conception Bay, Newfoundland, where a resonant seiche response is found to dominate. INDEX TERMS: 4504 Oceanography: Physical: Air/sea interactions (0312); 4564 Oceanography: Physical: Tsunamis and storm surges; 4219 Oceanography: General: Continental shelf processes; 3339 Meteorology and Atmospheric Dynamics: Ocean/atmosphere interactions (0312, 4504); 4255 Oceanography: General: Numerical modeling; KEYWORDS: tsunami, barotropic, tropical storm, modeling, air-sea

Factors Influencing Suspended Sediment Flux in the Upper Gulf of California

Abstract: Few studies exist of sediment dynamics in inverse estuaries, which are characterized by hypersaline water bodies and associated gravity currents and arise in arid regions where little precipitation and runoff combine with a high evaporation. Observations of velocity, density and suspended sediment concentration profiles have been made using an acoustic Doppler current profiler, CTD, optical backscatter sensors and water sampling at a shallow water site in the Upper Gulf of California over a spring to neap tidal cycle. These revealed contrasting dynamic conditions in which gravity current events produced significant net near-bed suspended sediment fluxes of 2·5 g m−2 s−1 out of the Gulf during neap tides. Instantaneous suspended sediment fluxes exceeded 30 g m−2 s−1during spring tides due to tidal resuspension, but net fluxes were near zero. The baroclinic gravity current is shown to be the dominant mechanism for net flux of suspended sediment toward deeper waters, at least during quiescent summer conditions. This flux is proposed to be confined within a wide, western along-Gulf channel. This is consistent with evidence that the Colorado River delta system is exporting sediments to deeper water after becoming unstable due to switching off of river discharge since 1930.

Temporal and azimuthal dependence of sound propagation in shallow water with internal waves

Abstract: The short time scale (minutes) and azimuthal dependence of sound wave propagation in shallow water regions due to internal waves is examined Results from the shallow water acoustics in random media (SWARM-95) experiment are presented that reflect these dependencies Time-dependent internal waves are modeled using the dnoidal solution to the nonlinear internal wave equations, so that the effects of both temporal and spatial variability can be assessed A full wave parabolic equation model is used to simulate broadband acoustic propagation It is shown that the short term temporal variability and the azimuthal dependence of the sound field are strongly correlated to the internal wave field

Nonlinear interaction of ice cover with shallow water waves in channels

Abstract: A nonlinear analysis of the interaction between a water wave and a floating ice cover in river channels is presented. The one-dimensional weakly nonlinear equation for shallow water wave propagation in a uniform channel with a floating ice cover is derived. The ice cover is assumed to be a thin uniform elastic plate. The weakly nonlinear equation is a fifth-order KdV equation. Analytical solutions of the nonlinear periodic wave equation are obtained. These solutions show that the shape, wavelength and celerity of the nonlinear waves depend on the wave amplitude. The wave celerity is slightly smaller than the open water wave celerity. The wavelength decreases as the wave amplitude increases. Based on these solutions the fracture of the ice cover is analysed. The spacing between transverse cracks varies form 50 m to a few hundred metres with the corresponding wave amplitude varying from 0.2 to 0.8 m, depending on the thickness and strength of the cover. These results agree well with limited field observations.

Three-dimensional nonlinear solitary waves in shallow water generated by an advancing disturbance

Abstract: The nonlinear long waves generated by a disturbance moving at subcritical, critical and supercritical speed in unbounded shallow water are investigated. The problem is formulated by a new modified generalized Boussinesq equation and solved numerically by an implicit finite-difference algorithm. Three-dimensional upstream solitary waves with significant amplitude are generated with a periodicity by a pressure distribution or slender strut advancing on the free surface. The crestlines of these solitons are almost perfect parabolas with decreasing curvature with respect to time. Behind the disturbance, a complicated, divergent Kelvin-like wave pattern is formed. It is found that, unlike the wave breaking phenomena in a narrow channel at Fh [ges ] 1.2, the three- dimensional upstream solitons form several parabolic water humps and are blocked ahead of the disturbance at supercritical speed in an unbounded domain for large time.

Spectral solution of time-dependent shallow water hydroelasticity

Abstract: The spectral theory of a thin plate floating on shallow water is derived and used to solve the time-dependent motion. This theory is based on an energy inner product in which the evolution operator becomes unitary. Two solution methods are presented. In the first, the solution is expanded in the eigenfunctions of a self-adjoint operator, which are the incoming wave solutions for a single frequency. In the second, the scattering theory of Lax-Phillips is used. The Lax-Phillips scattering solution is suitable for calculating only the free motion of the plate. However, it determines the modes of vibration of the plate-water system. These modes, which both oscillate and decay, are found by a complex search algorithm based contour integration. As well as an application to modelling floating runways, the spectral theory for a floating thin plate on shallow water is a solvable model for more complicated hydroelastic systems.

Upper slope sands: Late Quaternary shallow-water sandy contourities of Campos Basin, SW Atlantic Margin

Abstract: Upper slope sand deposits comprise a widespread but thin elongate accumulation of coarse to very fine-grained sand resulting from the action of slope boundary currents upon shelf-derived sediments. Sediment distribution on the Campos Basin upper slope responds to the action of the southward-flowing western boundary Brazil Current (BC). Linear, multi-source sediment supply to the slope is provided by shelf overspill due to the action of different forcing mechanisms: tides, storm fronts, and BC current onshelf penetration as gyres and meanders. On the slope, the sediment is pirated and redistributed by the BC Coarse-grained sediments (pebbles to very coarse sand) are found below the zone of maximum acceleration of the BC. Down–stream, fining is observed as a consequence of the morphologically controlled BC deceleration. The resultant accumulation is an elongate (c. 70 km long) and thin (> 50 m) wedge-shaped deposit. This depositional model is based on hydrographic, physiographic and sedimentologic characteristics of the modern Campos Basin margin, SE Brazil and characterizes a shallow water contouritic deposit

Deepwater habitat and fish resources associated with the big creek marine ecological reserve

Abstract: Big Creek Marine Ecological Reserve (BCER), located off the central California coast, has been closed to fishing since January 1994. We used side scan sonar and an occupied submersible to collect baseline information on species-habitat relationships, density, and species and size composition of fish inside and outside BCER. Forty-three dives were made in the fall of 1997 and 1998, at depths of 20‐250 m. From 142 video transects, we identified over 70,000 fish from 82 taxa, including 36 species of rockfish. About 93% of the 25,159 fish inside BCER were rockfishes representing at least 20 species. Young-of-the-year rockfishes dominated rock outcrops in 20‐90 m depth inside and outside BCER. Four distinct fish assemblages were associated with (1) fine, smooth sediment in deep water; (2) bedrock with uneven surface in deep water; (3) sand waves and shell hash in shallow water; and (4) boulders and organic habitats on rock in shallow water. There were no significant differences in fish density among locations (inside and outside BCER) and depths or between years. Density was significantly higher in high-relief rock habitat than in low-relief soft and mixed sediments, regardless of location. There were no consistent patterns of larger fish inside compared to outside the protected area. We recommend development of a monitoring program to continue these surveys after increased time of protection and with increased assessment effort in the appropriate habitats of economically valuable species. In addition, extending the boundaries of BCER seaward would protect habitats and fish in water depths greater than 100 m.

New approach for quantifying water depth applied to the enigma of drowning of carbonate platforms

Abstract: This research illustrates application of a fluid-inclusion technique for quantifying water depth of ancient carbonate platforms. Jurassic limestones of Monte Kumeta, Italy, were cemented with submarine calcite during a transition to carbonate platform termination. The calcite cements contain fluid inclusions consisting of Jurassic seawater and immiscible gas bubbles trapped during the growth and penecontemporaneous recrystallization of the cements. Crushing analysis indicates that gas bubbles are under pressures indicative of entrapment in water depths of 23–112 m. Assuming simple deepening and acknowledging chronostratigraphic errors, rates of relative rise in sea level were initially less than 7 m/m.y. followed by a rate of at least 33 m/m.y. These slow rates are evidence that the platform's demise was caused by an environmental perturbation other than rapid sea-level rise. The facies transitions and regional studies indicate that the perturbation resulted from nutrient excess or eutrophication in shallow water followed by deepening into ephemeral dysoxic waters at depths perhaps as shallow as 23 m.

Intermediate modelling of tidal inlet systems: spatial asymmetries in flow and mean sediment transport

Abstract: In order to identify mechanisms which determine the morphology of tidal inlet systems, experiments with a shallow water model and sediment transport model of intermediate complexity are carried out and interpreted. A highly schematised geometry is used, consisting of a rectangular outer area connected to a rectangular basin by a narrow strait. The bottom topography is either flat or constantly sloping in the landward direction and the bed is composed of fine sand. Forcing at the open boundary consists of prescribed water levels, which can represent a (shore-parallel) progressive tidal wave or a fully standing wave. The symmetry breaking effects of Coriolis force and a progressive Kelvin wave on the tidal motion, the mean flow field and the mean sediment transport field are investigated. Tidal ellipticity properties on the outer delta are also discussed. Experiments for a rectangular basin without outer area are carried out in order to compare the intermediate model results with those of a 1D idealised model. The overall agreement is satisfactory. Next the influence of earth rotation and of the progressive wave in the outer sea on mean sediment transport in the basin is investigated. It turns out that both effects, which cannot be included in the idealised model, lead to different patterns of erosion and deposition. In both sets of experiments the effects of a progressive Kelvin wave were found to be dominant over earth rotation effects in the flow and mean sediment transport fields.

High-Order Interaction of Solitary Waves on Shallow Water

Abstract: The interaction of solitary waves on shallow water is examined to fourth order. At first order the interaction is governed by the Korteweg-de Vries (KdV) equation, and it is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at third order. To resolve this, a mass conserving system of KdV equations, involving both right- and left-moving waves, is derived to third order. A fourth-order interaction term, in which the right- and left-moving waves are coupled, is also derived as this term is crucial in determining the fourth-order change in solitary wave amplitude. The form of the unidirectional KdV equation is also discussed with nonlocal terms derived at fourth order. The solitary wave interaction is examined using the inverse scattering method for perturbed KdV equations. Central to the analysis at fourth order is the left-moving wave, for which the solution, in integral form, is derived. A symmetry property for the left-moving wave is found, which is used to show that no change in solitary wave amplitude occurs to fourth order. Hence it is concluded that, for surface waves on shallow water, the change in solitary wave amplitude is of fifth order.

Muddy contourites in the Baltic Sea: an example of a shallow-water contourite system

Abstract: Bottom currents in the Baltic Sea have had a pronounced effect on the nature and distribution of sediments throughout the Holocene. Due to the intermittent nature of water exchange between the North and the Baltic Seas, the flow of bottom currents is impermanent. Well-developed nepheloid layers are commonly associated with these bottom currents, and provide evidence that active re-suspension and sediment transport is taking place. Periodically intensified inflow from the North Sea through the Baltic Sea gateway has led to erosion of narrow elongate channels, and associated deposition of small elongate patch drifts and contourite levees. The latter two are best developed on the left flanks of the channels. As a result of strong lateral sediment transport, the overall thickness of muddy contourite layers increases towards the steeper slopes of the sea which are situated on the right-hand side of the inflows. Muddy contourites of the Baltic Sea are predominantly terrigenous in composition, made up of soft, black sulphidic muds that are enriched in organic carbon and manganese. Both enrichments are caused by high biological productivity and periodic stagnation of near-bottom waters. Atypically for most oceanic contourites, these shallow-water organic-rich contourites are finely laminated and generally unbioturbated.

Modeling the 1100 bp paleotsunami in Puget Sound, Washington

Abstract: [1] Recent paleoseismic and geologic studies indicate that a tsunami occurred 1100 years ago in Puget Sound. This study aims to reproduce and validate the model tsunami, using a finite difference model based on nonlinear shallow water theory and abathymetry/topography computational grid that takes into account the 1-meter rise in sea level that has occurred in the region during the past 1100 years. Estimates of tsunami height, the extent of inundation, and the current velocity pattern are provided at the northern head of Cultus Bay, Whidbey Island, where paleotsunami sand deposits have been found. The model demonstrates that a tsunami generated when the background water level was at mean high water or above could have surged across the then-existing coastal marsh, penetrated the full length of the shallow bay, and deposited the observed sand layers.

Study of a novel range-dependent propagation effect with application to the axial injection of signals from the Kaneohe source.

Abstract: A novel range-dependent propagation effect occurs when a source is placed on the seafloor in shallow water with a downward refracting sound speed profile, and sound waves propagate down a slope into deep water Under these conditions, small grazing-angle sound waves slide along the bottom downward and outward from the source until they reach the depth of the sound channel axis in deep water, where they are detached from the sloping bottom and continue to propagate outward near the sound channel axis This "mudslide" effect is one of a few robust and predictable acoustic propagation effects that occur in range-dependent ocean environments As a consequence of this effect, a bottom mounted source in shallow water can inject a significant amount of acoustic energy into the axis of the deep ocean sound channel that can then propagate to very long ranges Numerical simulations with a full-wave range-dependent acoustic model show that the Kaneohe experiment had the appropriate source, bathymetry, and sound speed profiles that allows this effect to operate efficiently This supports the interpretation that some of the near-axial acoustic signals, received near the coast of California from the bottom mounted source located in shallow water in Kaneohe Bay, Oahu, Hawaii, were injected into the sound channel of the deep Pacific Ocean by this mechanism Numerical simulations suggest that the mudslide effect is robust

A model for predicting the temporal evolution of dissolved oxygen concentration in shallow estuaries

Abstract: The design of sewage discharge systems in estuaries needs to consider the dissolved oxygen concentration among other water quality indicators. Due to the great number of factors affecting the dissolved oxygen, the prediction of the temporal evolution of this element requires the use of mathematical tools. In the case of shallow estuaries with extensive intertidal zones, the complexity of this task increases since the water domain varies continuously. This work describes a numerical model which solves the vertical integrated transport equation including the effect of extensive tidal flats. The model makes use of the tidal velocities computed by a previous run of a hydrodynamic model. This procedure allows the dissolved oxygen modelling to be performed using a larger time step than that used for the velocity field calculation. The numerical scheme developed for the model guarantees that even in the drying and wetting of intertidal areas the water column dissolved oxygen concentration is not modified by numerical errors. The representations of the processes included in the model (advection, dispersion and reaction) have been validated successfully in several theoretical cases. An application to the Urdaibai Estuary, a shallow estuary in the Basque Country, Northern Spain, is also presented.

A new 3D seismic acquisition system for very high and ultra high resolution shallow water studies

Abstract: give the system a full wingspan of 14 m and provide spatial control for the spread of eight dual-channel streamers. The streamers are 7.5 m long, with a channel spacing of 2 m and two hydrophones per channel (hydrophone spacing of 0.25 m). The streamers are towed a few metres behind the modules, the distance depending on the desired offset. The surface-towed frames are kept under air pressure (± 0.5 bar), which allows convenient deployment and recovery by inflation and deflation. The inflatable frames are made of flexible hose of 10 cm diameter. Each frame consists of two length-wise floats connected by three cross-wise floats, the latter curving upwards in order to reduce contact with the water (Fig. 1). Their form has been ‘pre-shaped’ to increase the rigidity of the frames. The use of a modular system allows the dimensions of the acquisition system to be varied, by simply increasing or decreasing the number of modules and streamers. The central RIB has a catamaran structure to ensure optimum stability at sea, and it is wide enough to allow ample storage of the modular frames. Furthermore, the positioning antenna can be placed on it. The antenna is normally installed on the rear of the boat, near the source and streamers, in order to reduce relative positioning errors to a minimum. The source (IKB SEISTEC, a wide-band electrodynamic boomer with a dominant frequency of 2–3 kHz) is towed closely behind the RIB. The system is typically deployed from smallto mediumsized vessels, preferably with an A-frame or small crane. All components are folded within the RIB, and once deployed at the correct distance behind the vessel the modules are inflated. A central rope fixed to the RIB is used for towing with additional lines attached to the module tips, ensuring a good array layout. After the survey, the modules are deflated and rolled (with the streamers) inside the RIB, which is placed on the deck of the vessel. In protected waters (harbour areas, rivers, canals and lakes) and in the absence of strong currents, the system can also be used autonomously. To this end the central RIB is converted into a survey vessel unit with twin engines and a 1Renard Centre of Marine Geology, Geological Institute, University of Gent, Krijgslaan 281-S8, B-9000 Gent, Belgium. Introduction

Analytical solution of non-homogeneous wave equation

Abstract: Models for shallow water wave processes are routinely applied in coastal, estuarine and river engineering practice, to problems such as flood waves, tidal circulation, tsunami penetration, and stor...