Showing papers on "Waves and shallow water published in 2006"

Fate of rising methane bubbles in stratified waters: How much methane reaches the atmosphere?

Abstract: There is growing concern about the transfer of methane originating from water bodies to the atmosphere. Methane from sediments can reach the atmosphere directly via bubbles or indirectly via vertical turbulent transport. This work quantifies methane gas bubble dissolution using a combination of bubble modeling and acoustic observations of rising bubbles to determine what fraction of the methane transported by bubbles will reach the atmosphere. The bubble model predicts the evolving bubble size, gas composition, and rise distance and is suitable for almost all aquatic environments. The model was validated using methane and argon bubble dissolution measurements obtained from the literature for deep, oxic, saline water with excellent results. Methane bubbles from within the hydrate stability zone (typically below ∼500 m water depth in the ocean) are believed to form an outer hydrate rim. To explain the subsequent slow dissolution, a model calibration was performed using bubble dissolution data from the literature measured within the hydrate stability zone. The calibrated model explains the impressively tall flares (>1300 m) observed in the hydrate stability zone of the Black Sea. This study suggests that only a small amount of methane reaches the surface at active seep sites in the Black Sea, and this only from very shallow water areas (<100 m). Clearly, the Black Sea and the ocean are rather effective barriers against the transfer of bubble methane to the atmosphere, although substantial amounts of methane may reach the surface in shallow lakes and reservoirs.

Wave–Current Interactions in Finite Depth

Abstract: The energy, momentum, and mass-flux exchanges between surface waves and underlying Eulerian mean flows are considered, and terms in addition to the classical wave “radiation stress” are identified. The formulation is made in terms of the vertically integrated flow. The various terms are identified with other analyses and interpreted in terms of physical mechanisms, permitting reasonable estimates of the associated depth dependencies. One term is identified with the integrated “CL vortex force” implemented, for example, in simulations of Langmuir circulation. However, as illustrated with a simple example of steady refraction across a shear zone, other terms of the same order can significantly alter the results. The classic example of long waves forced by short-wave groups is also revisited. In this case, an apparent singularity arising in shallow water is countered by finite-amplitude dispersion corrections, these being formally of the same order as the forced long-wave response, and becoming significant or dominant as shallow water is approached.

When Katrina hit California

Abstract: [1] Beamforming of seismic noise recorded on 150 Southern California stations was used to identify body and surface waves generated by Katrina. Surface wave microseisms are commonly associated with oceanic storms; there are no previous comprehensive body wave observations. The temporal evolution of the surface and body waves was different, indicating a different source mechanism for the two wave types. The body-waves originated in shallow water east of New Orleans and propagated deep inside the Earth. The surface waves have source location that varies with frequency with the lowest frequency surface waves originating west of the hurricane track and the higher frequency ones to the east. The seismic observations are consistent with ocean wave hindcasts and provide clear association of microseism noise with storm activity.

Water level control over submerged macrophyte development in five shallow lakes of Mediterranean Turkey

Abstract: The functioning of shallow lakes is supposedly very sensitive to water level fluctuations (WLF). Relationships between WLF and submerged macrophyte development were investigated in five Turkish shallow lakes located in a semi-arid to arid Mediterranean climate where the hydrological event of WLF is a common phenomenon. In all lakes, WLF emerged as a major factor determining submerged plant development. High submerged plant coverage was observed in four of the study lakes, Lake Beysehir, Lake Uluabat, Lake Marmara and Lake Mogan when the water level was low throughout the year or during growing season, submerged plants expanded; however, in Lake Isikli extensive submerged plant development was observed at high water levels during winter. In Lake Isikli, an increase of 25 % in the surface area was recorded, which, in turn, might have resulted in an increased potential for expansion of submerged plants. Furthermore, in all the lakes excluding Lake Beysehir, high submerged plant coverage coincided with a significant decrease in the amplitude of intra-annual water level fluctuations. The depth profile, expressed as the morphometry index (Z mean /Z max ), appeared to be critical for the development of extensive vegetation. Expansion of vegetation coincided with either an increased morphometry index or a flatter bottom profile. However, the impact of hydrology on lake morphometry differed between the lakes. In Lake Isikli, the high water level generated a slightly flatter, albeit not significantly so, bottom; however, in the remaining lakes the same effect was observed at low water level. Differences in the morphometry index in response to WLF appeared to depend on the original bottom profile, which is either conical or ellipsoid. Therefore, the impact of hydrology on the bottom profile of a lake may profoundly affect the extent of the littoral zone. Biomass of carp (Cyprinus carpio) had a strong inverse correlation with vegetation development in Lake Marmara and Lake Uluabat, therefore, carp might also have been important in macrophyte development. It may be concluded that littoral plant communities in shallow lakes located in semi-arid to arid regions appear to be particularly susceptible to water level fluctuations.

Numerical investigation of solitary internal wave-induced global instability in shallow water benthic boundary layers

Abstract: The time-dependent boundary layer induced by a weakly nonlinear solitary internal wave in shallow water is examined through direct numerical simulation. Waves of depression and elevation are both considered. The mean density field corresponds to that typical of the coastal ocean and lakes where the lower fraction of the water column is subject to the stabilizing effect of a diffuse stratification. Sufficient resolution of the “inviscid” dynamics of the boundary layer is ensured through use of a Legendre spectral multidomain discretization scheme in the vertical direction. At higher Reynolds numbers, where the simulations become underresolved, because of restrictions in available computational resources, spectral accuracy and numerical stability at the scales of physical interest are preserved through use of a penalty scheme in the vertical and explicit spectral filtering. Thus, a highly accurate description of the qualitative dynamics of the wave-induced global instability is possible and finesca...

Numerical study of three-dimensional overturning waves in shallow water

Abstract: Simulations in a three-dimensional numerical wave tank are performed to investigate the shoaling and breaking of solitary waves over a sloping ridge. The numerical model solves fully nonlinear potential flow equations with a high-order boundary-element method combined with an explicit time-integration method, expressed in a mixed Eulerian-Lagrangian formulation. Analyses of shoaling and breaking-wave profiles and kinematics (both on the free surface and within the flow) are carried out. It is observed that the transverse modulation of the ridge topography induces three-dimensional effects on the time evolution, shape and kinematics of breaking waves. Comparisons of two- and three-dimensional results in the middle cross-section of the ridge, however, show remarkable similarities, especially for the shape and dynamics of the plunging jet.

When Katrina hit California

Abstract: [1] Beamforming of seismic noise recorded on 150 Southern California stations was used to identify body and surface waves generated by Katrina. Surface wave microseisms are commonly associated with oceanic storms; there are no previous comprehensive body wave observations. The temporal evolution of the surface and body waves was different, indicating a different source mechanism for the two wave types. The body-waves originated in shallow water east of New Orleans and propagated deep inside the Earth. The surface waves have source location that varies with frequency with the lowest frequency surface waves originating west of the hurricane track and the higher frequency ones to the east. The seismic observations are consistent with ocean wave hindcasts and provide clear association of microseism noise with storm activity.

A shallow-water approximation to the full water wave problem

Abstract: We demonstrate that the system of the Green-Naghdi equations as a two-directional, nonlinearly dispersive wave model is a close approximation to the two-dimensional full water wave problem. Based on the energy estimates and the proof of the well-posedness for the Green-Naghdi equations and the water wave problem, we compare solutions of the two systems, showing that without restrictions on the wave amplitude, any two solutions of the two systems remain close, at least in some finite time within the shallow-water regime, provided that their initial data are close in the Banach space Hs × Hs+1 for some s > . As a consequence, we show that if the depth of the water compared with the wavelength is sufficiently small, the two solutions exist for the same finite time using the uniformly bounded energies defined in the paper. © 2006 Wiley Periodicals, Inc.

Moving boundary shallow water flow above parabolic bottom topography

Abstract: Exact solutions of the two dimensional nonlinear shallow water wave equations for flow involving linear bottom friction and with no forcing are found for flow above parabolic bottom topography. These solutions also involve moving shorelines. The motion decays over time. In the solution of the three simultaneous nonlinear partial differential shallow water wave equations it is assumed that the velocity is a function of time only and along one axis. This assumption reduces the three simultaneous nonlinear partial differential equations to two simultaneous linear ordinary differential equations . The solutions found are useful for testing numerical solutions of the nonlinear shallow water wave equations which include bottom friction and whose flow involves moving shorelines.

Long waves in erodible channels and morphodynamic influence

Abstract: [1] Like most media, open channel flows propagate information through waves When the channel boundary is fixed, the vectors of information consist typically of surface gravity waves In the less straightforward case of channels with cohesionless bed and possibly erodible banks, other types of waves arise from the erodible nature of the boundaries and the ability of the stream to transport sediments In this paper we restrict our attention to the important case of long waves, which can be described by employing the shallow water approximation for the flow field and a quasi-equilibrium assumption for sediment transport on weakly sloping beds We focus on a major issue: In which direction is information propagated? This is a problem raised and partially solved by de Vries in the context of one-dimensional morphological modeling as early as 1965 We review some of the available knowledge on this subject, viewed in a more general context where vectors of information can be a variety of waves: purely longitudinal one-dimensional sediment waves, two-dimensional waves driven by large-scale bed forms (bars), and plan form waves carrying information related to the planform shape of the channel Both linear and nonlinear, migrating and stationary waves are considered It turns out that the role played by the Froude number in determining the direction of one-dimensional perturbations of bed topography is somewhat taken by the aspect ratio of the channel when large-scale two-dimensional bed forms as well as planform waves are considered

Wave Dispersion Study in the Indian Ocean-Tsunami of December 26, 2004

Abstract: A numerical study which takes into account wave dispersion effects has been carried out in the Indian Ocean to reproduce the initial stage of wave propagation of the tsunami event that occurred on December 26, 2004. Three different numerical models have been used: the nonlinear shallow water (nondispersive), the nonlinear Boussinesq, and the full Navier-Stokes aided by the volume of fluid method to track the free surface. Numerical model results are compared against each other. General features of the wave propagation agreed very well in all numerical studies. However some important differences are observed in the wave patterns, i.e., the development in time of the wave front is shown to be strongly connected to the dispersion effects. Discussions and conclusions are made about the spatial and temporal distribution of the free surface reaffirming that the dispersion mechanism is important for tsunami hazard mitigation.

Spatial patterns and response to wave exposure of shallow water algal assemblages across the Canarian Archipelago: a multi-scaled approach

Abstract: We conducted a mensurative survey to investigate spatial variability and the effect of wave exposure at a range of spatial scales including islands (100s of km apart), locations within islands (10s of km apart), and sites within locations (100s of m apart), on the composition, abundance and distribution of shallow water algal assemblages across subtidal hard bottoms of the Canarian Archipelago (eastern Atlantic). A multi-scaled hierarchical sampling design provided the framework for quantifying the variation among samples due to spatial scale and level of wave exposure. Ran- domly placed 50 × 50 cm squares were deployed in shallow rocky-reefs to assess community struc- ture and dominance. Non-parametric multivariate techniques, as well as univariate tests, provided evidence to collectively suggest that shallow water algal assemblages differed between protected (leeward) and exposed (windward) shores, with a consistency of effects across islands, while differ- ent spatial scales were also involved in the variability and patchiness of these assemblages. In this sense, differences were clearly taxon and/or group-specific. In general, the presence and abundance of frondose fucoid species was greater on exposed shores than on protected shores, whereas turf- algae dominated along the protected shores of each island. Dissimilarities between islands with regard to the overall algal assemblage generally increased with the distance between islands. In par- ticular, the presence and abundance of fucoid species was greater in the eastern islands, while turf and bush-like algae increased in the western islands. The large-scale gradient of the oceanographic conditions in an east-to-west direction across the Canarian Archipelago provided a partial explana- tion for this observation although some inconsistencies were observed in the overall regional pattern.

Solitary wave transformation, breaking and run-up at a beach

Abstract: A validated one-dimensional Boussinesq–non-linear shallow water equations numerical model was used to investigate the interaction of solitary waves with beaches. The numerical model requires two adjustable parameters: the bed friction coefficient and a wave breaking parameter. Excellent agreement was achieved between the numerical predictions of solitary wave transformation and run-up at a plane beach with two sets of high-quality laboratory measurements: one a large number of experiments in a wave flume by Synolakis, the other in the UK Coastal Research Facility. A parameter study investigated the effect of uniform offshore water depth, bed friction and bed slope on solitary wave run-up. A uniform water depth may be associated with a continental shelf region. The non-dimensional run-up was found to be an asymptotic function of non-dimensional wave amplitude at high and low values of initial wave steepness. Both asymptotes scale as (R/ho)∼α(Ao/ho)β where R is run-up (defined as the vertical elevation reac...

Effects of freshwater input on shallow-water infaunal communities in Doubtful Sound, New Zealand

Abstract: Infaunal community structure is sensitive to both the range of salinity values and timing of exposure wrought by the time course and magnitude of freshwater input to estuaries. We sampled macro-infauna (> 1 mm) from soft sediment habitat at 8 shallow sites (2 m below MHW; mean high water) within 4 regions in the Doubtful-Thompson Sound complex, a fjord in southwestern New Zealand. This fjord receives a large influx of freshwater from natural and anthropogenic sources that form a distinct low salinity surface layer and drive mean estuarine circulation. Shallow water soft sediment habitat in the fjord is highly fragmented and subject to strong environmental gradients shaped by freshwater input patterns. Infaunal community structure in the inner region of Doubtful Sound was consistently different from other regions of the fjord. This was evidenced by a low abundance of bivalves, decapods, and polychaetes in the family Orbiniidae, and elevated abundance of amphipods and polychaetes in the family Neredidae. An analysis of taxonomic richness among regions revealed that the inner regions of Doubtful Sound are also the least rich in the complex. Both taxonomic richness and patterns in abundance of the major taxa covary with physical information on the return times for low salinity events, thickness, and patterns in mixing in the freshwater layer. These results are consistent with a large impact of the persistent discharge of freshwater from the Manapouri power station on shallow water infaunal communities in the fjord. The loss of bivalves in particular has large implications for patterns in food-web structure and function in this system.

Generalized evolution equations for nonlinear surface gravity waves over two-dimensional topography

Abstract: Evolution equations are derived for weakly nonlinear, multi-frequency and directional surface gravity waves propagating from deep to shallow water over weakly two-dimensional bottom topography. A uniform transition from cubic resonances in deep-intermediate water (Stokes regime) to quadratic near resonances in shallow water (Boussinesq regime) is obtained by extending the ordered solution to include additional higher-order terms for the bound wave components. The model assumes a leading-order, alongshore-uniform bottom with a two-dimensional depth perturbation that is incorporated through a Taylor series expansion of the bottom boundary condition. Numerical implementations of the model and comparisons to experimental data are presented that demonstrate the model's ability to describe: (i) cubic wave-wave interactions in deep-intermediate water depth; (ii) harmonic generation over a one-dimensional submerged obstacle; (iii) harmonic generation over two-dimensional topography.

Numerical modelling of generation, propagation and run‐up of tsunamis caused by oceanic impacts: model strategy and technical solutions

Abstract: SUMMARY Hypervelocity impacts of asteroids in marine environments produce tsunami waves independent of the water depth and the diameter of the projectile. However, the characteristics of the induced waves are affected by these parameters. We present a model, consisting of the wellknown SALE impact model and a non-linear wave propagation model, to study the generation and subsequent spread out of the initial wave pattern caused by the strike of an asteroid or comet in the ocean. The numerical simulation of oceanic impacts requires some changes and extensions to the original SALE code. Especially, the handling of different materials (water and solid rocks) is crucial as they are involved in the cratering process. For the simulation of the propagation of tsunami waves that are generated by the impact process we use a newly developed wave propagation model, which is based on the non-linear shallow water theory with boundary conditions derived from the impact model. The run-up of the tsunami wave on the coastline is implemented as a special case of reflection and is realized by the wellestablished MOST code. Besides the model description we exemplify the capability of our modelling scheme by the simulation of the strike of an asteroid 800 m in diameter on a 5000-m-deep ocean at 10.2 km s −1 , the subsequent propagation of the induced tsunami waves over an artificial bathymetry and the run-up of the wave on the coast.

Recent Mathematical Results and Open Problems about Shallow Water Equations

Abstract: The purpose of this work is to present recent mathematical results about the shallow water model. We will also mention related open problems of high mathematical interest.

Three-dimensional instabilities of periodic gravity waves in shallow water

Abstract: A linear stability analysis of finite-amplitude periodic progressive gravity waves on water of finite depth has extended existing results to steeper waves and shallower water. Some new types of instability are found for shallow water. When the water depth decreases, higher-order resonances lead to the dominant instabilities. In contrast with the deep water case, we have found that in shallow water the dominant instabilities are usually associated with resonant interactions between five, six, seven and eight waves. For small steepness, dominant instabilities are quasi two-dimensional. For moderate and large steepness, the dominant instabilities are three-dimensional and phased-locked with the unperturbed nonlinear wave. At the margin of instability diagrams, these results suggest the existence of new bifurcated three-dimensional steady waves.

The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid

Abstract: The motion of a large-amplitude internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid is investigated experimentally. Measurements of the velocity fields close to the bottom boundary are presented to illustrate the generation of an unsteady boundary jet along the bed. The formation of the jet, the structural characteristics of which show striking similarities with those predicted by recent numerical model studies by Diamessis and Redekopp [J. Phys. Oceanogr. (in press)], is attributed to boundary layer separation in the adverse pressure gradient region of the wave-induced flow.

Tsunami Wave Runup on Coasts of Narrow Bays

Abstract: The runup of tsunami waves on the coasts of the barrow bays, channels and straits is studied in the framework of the nonlinear shallow water theory. Using the narrowness of the water channel, the onedimensional equations are applied; they include the variable cross-section of channel. It is shown that the analytical solutions can be obtained with use of the hodograph (Legendre) transformation similar to the wave runup on the plane beach. As a result, the linear wave equation is derived and all physical variables (water displacement, fluid velocity, coordinate and time) can be determined. The dynamics of the moving shoreline (boundary of the flooding zone) is investigated in details. It is shown that all analytical formulas for the moving shoreline can be obtained explicitly. Two examples of the incident wave shapes are analysed: sine wave and parabolic pulse. The last example demonstrates that even for approaching of the crest only, the flooding can appear very quickly; then water will recede relatively slowly, and then again quickly return to the initial state. Correspondence: Professor Efim Pelinovsky Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, 46 Uljanov Street, Nizhny Novgorod, 603950 Russia Email: Pelinovsky@hydro.appl.sci-nnov.ru Phone: 007-8312-164839 Fax: 007-8312-365976

Flow resistance of Posidonia oceanica in shallow water

Abstract: Management of coastal waters and lagoons by mathematical circulation models requires determination of the hydraulic resistance of submerged vegetation. A plant typical of sandy coastal bottoms in the Mediterranean Sea is Posidonia oceanica, which is constituted by very thin and flexible ribbon-like leaves, about 1 cm wide and up to 1.5m long, and usually covers the bottom with a density of 500–1000 plants/m2. From the hydraulic viewpoint, P. oceanica constitutes a particular roughness, because, as the velocity increases, the leaves bend more and more until they lie down on the bottom. Although P. oceanica is widespread, in the technical literature it is difficult to find indications about flow resistance due to this plant. In this paper, the results of specific experimental research are reported. The runs were carried out in a laboratory flume, where the plants were reproduced assembling plastic strips. In these experiments, the leaf length was larger than the flow depth, reproducing a shallow water situa...

Modeling the buoyant flow of heated water discharged from surface and submerged side outfalls in shallow and deep water with a cross flow

Abstract: In this study, a three-dimensional model was used to numerically study the buoyant flow, along with its mixing characteristics, of heated water discharged from the surface and submerged side outfalls in shallow and deep water with a cross flow. Hydraulic experimental data were used to evaluate the applicability of the model. The simulation results agree well with the experimental results, particularly, the jet trajectories, the dimensions of the recirculating zone, and the distribution of the dimensionless excess temperature. The level of accuracy of the simulation results of the present study is nearly identical to that of the results conducted by McGuirk and Rodi (1978). If the heated water is discharged into shallow water where the momentum flux ratio and the discharge densimetric Froude number are high, the submerged discharge method is better than the surface discharge method in terms of the scale of the recirculating zone and the minimum dilution. In deep water, where the momentum flux ratio and discharge densimetric Froude number are low, however, the submerged discharge method had few advantages. In shallow water, the discharge jet is deflected by the ambient cross flow, while forcing the ambient flow to bend towards the far bank for the full depth. For a submerged discharge in shallow water, the recirculating zone is the largest in the lowest layer but becomes smaller in the upper layer. As the water depth increases, the ambient flow goes over the jet and diminishes the blocking effect, thereby decreasing the bending of the jet.