Showing papers on "Waves and shallow water published in 2009"

Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation

Abstract: A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \cite{matsuno3} and Choi \cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equations with the fully nonlinear shallow water Green-Naghdi equations represents a relevant model for describing ocean wave propagation from deep to shallow waters.

Reciprocal influence of crops and shallow ground water in sandy landscapes of the

Abstract: 1. IntroductionIn regions with shallow water tables, crops and ground watercan interact through several mechanisms. Depending on theprevailing water table depth, ground water may be eitherunavailable to crops, a valuable water source, or a stress factorbecause of waterlogging or salinity (Kahlown et al., 2005; Ayarset al., 2006). Reciprocally, crops can influence ground water,alteringwatertabledepthand chemicalcomposition(Jobba´gyandJackson, 2004). Here we quantify these reciprocal influences alongnatural gradients of groundwater depth in flat sedimentarylandscapes of the Pampas occupied by annual crops.When water tables lie near the bottom of the rooting zone ofcrops, ground water may act as a valuable water source through

On some consequences of the canonical transformation in the Hamiltonian theory of water waves

Abstract: We discuss some consequences of the canonical transformation in the Hamiltonian theory of water waves (Zakharov, J. Appl. Mech. Tech. Phys., vol. 9, 1968, pp. 190–194). Using Krasitskii's canonical transformation we derive general expressions for the second-order wavenumber and frequency spectrum and the skewness and the kurtosis of the sea surface. For deep-water waves, the second-order wavenumber spectrum and the skewness play an important role in understanding the so-called sea-state bias as seen by a radar altimeter. According to the present approach but in contrast with results obtained by Barrick & Weber (J. Phys. Oceanogr., vol. 7, 1977, pp. 11–21), in deep water second-order effects on the wavenumber spectrum are relatively small. However, in shallow water in which waves are more nonlinear, the second-order effects are relatively large and help to explain the formation of the observed second harmonics and infra-gravity waves in the coastal zone. The second-order effects on the directional-frequency spectrum are as a rule more important; in particular it is shown how the Stokes-frequency correction affects the shape of the frequency spectrum, and it is also discussed why in the context of the second-order theory the mean-square slope cannot be estimated from time series. The kurtosis of the wave field is a relevant parameter in the detection of extreme sea states. Here, it is argued that in contrast perhaps to one's intuition, the kurtosis decreases while the waves approach the coast. This is related to the generation of the wave-induced current and the associated change in mean sea level.

Observations of Polarity Reversal in Shoaling Nonlinear Internal Waves

Abstract: Observations off the New Jersey coast document the shoaling of three groups of nonlinear internal waves of depression over 35 km across the shelf. Each wave group experienced changing background conditions along its shoreward transit. Despite different wave environments, a clear pattern emerges. Nearly symmetric waves propagating into shallow water develop an asymmetric shape; in the wave reference frame, the leading edge accelerates causing the front face to broaden while the trailing face remains steep. This trend continues until the front edge and face of the leading depression wave become unidentifiable and a near-bottom elevation wave emerges, formed from the trailing face of the initial depression wave and the leading face of the following wave. The transition from depression to elevation waves is diagnosed by the integrated wave vorticity, which changes sign as the wave’s polarity changes sign. This transition is predicted by the sign change of the coefficient of the nonlinear term in the KdV equation, when evaluated using observed profiles of stratification and velocity.

Ecohydrology of groundwater-dependent ecosystems: 1. Stochastic water table dynamics

Abstract: [1] Areas with a relatively shallow water table are environments where the groundwater plays a key role on the ecosystem function, and important interactions exist between hydrology and ecosystem processes. We propose here an analytical model to study the interactions between rainfall, water table, and vegetation in groundwater-dependent ecosystems. The water table dynamics are studied as a random process stochastically driven by a marked Poisson noise representing rainfall events. Infiltration, root water uptake, water flow to/from an external water body, and capillary rise are accounted for in a probabilistic description of water table fluctuations. We obtain analytical expressions for the steady state probability distribution of water table depth, which allows us to investigate the long-term behavior of water table dynamics, and their sensitivity to changes in climate, vegetation cover, and water management.

A study on the hydrogeology and hydrogeochemistry of groundwater from different depths in a coastal aquifer: Annamalai Nagar, Tamilnadu, India.

Abstract: Chemical characterization of groundwater is essential to bring out its nature and utility. Samples from shallow and deep ground water of the same location were collected and studied for their geochemical characteristics following standard procedures (APHA 1998). Sediment samples from different depths were collected and analysed for minerals using FTIR and SEM. Resisitivity logging was carried out in the bore well to understand the variations in depth to fresh water potential. The shallow ground water is dominated by Na–Cl–HCO3–SO4 and deeper groundwater by Na–HCO3–SO4–Cl types. It is observed that there is a significant ionic variation with depth. The ionic strength of the deeper samples is lesser than in the shallower samples. Wide pH variations in the shallow water samples are due to ion exchange process. Thermodynamic stability plot was used to identify the state of stability. It is inferred that there is no major significant difference in the thermodynamic state of stability in the shallow and the deeper aquifers as the aquifer matrix for the shallow and deeper aquifers are almost similar. Saturation index of Gibbsite, Kaolinite, Calcite, Dolomite and anhydrite, were studied for shallow and deep aquifers, to identify the difference in hydro chemical signatures. The Si/Al ratios of shallow samples are less when compared with the deeper samples. Leaching of secondary salts was the chief mechanism controlling the ground water chemistry of the region.

Hydrology-Driven Regime Shifts in a Shallow Tropical Lake

Abstract: Shifts between alternative stable states have become a focus of research in temperate shallow lakes. Here we show that sharp transitions between a clear, macrophyte-dominated state and a turbid state without submerged plants can also occur in tropical floodplain lakes, albeit driven by a largely different set of mechanisms. We show how a shallow lake in the Pantanal becomes covered by an exploding population of the submerged macrophyte Egeria najas Planchon as the water level rises during the annual high-water period. Water clarity increases spectacularly in this period due to flushing with river water that has lost most of its suspended matter during its slow flow over the flooded vegetated plains. A few months later when the water level drops again, the submerged plant beds die and decompose rapidly, triggering a phase of increasing turbidity. During this period an increase in dissolved organic matter, suspended matter, and phytoplankton biomass results in a sharp deterioration in water clarity. The concomitant water level decrease largely counteracts the effects on the underwater light climate, so that the amount of light at the bottom may not differ in comparison with the high-water period. Therefore, changes in light climate seem unlikely to be the sole driver of the vegetation shifts, and other mechanisms may prevent recovery of the submerged vegetation until the next high-water episode. Also, contrary to what is found in temperate lakes, there is no evidence for top-down control of phytoplankton biomass associated with the macrophyte-dominated state in our tropical lake.

Global Shallow Water Magnetohydrodynamic Waves in the Solar Tachocline

Abstract: We derive analytical solutions and dispersion relations of global magnetic Poincare (magneto-gravity) and magnetic Rossby waves in the approximation of shallow water magnetohydrodynamics. The solutions are obtained in a rotating spherical coordinate system for strongly and weakly stable stratification separately in the presence of a toroidal magnetic field. In both cases, magnetic Rossby waves split into fast and slow magnetic Rossby modes. In the case of strongly stable stratification (valid in the radiative part of the tachocline), all waves are slightly affected by the layer thickness and the toroidal magnetic field, while in the case of weakly stable stratification (valid in the upper overshoot layer of the tachocline) magnetic Poincare and magnetic Rossby waves are found to be concentrated near the solar equator, leading to equatorially trapped waves. The frequencies of all waves are smaller in the upper weakly stable stratification region than in the lower strongly stable stratification one.

Zooplankton inside an Arctic Ocean cold-core eddy: Probable origin and fate

Abstract: In September 2004, an extensive survey of a cold-core eddy in the Canada Basin, western Arctic was carried out with high-horizontal-resolution physical and chemical sampling and lower-horizontal-resolution biological sampling. The eddy was located over the continental slope north of the Chukchi Shelf and had a radius of ∼8 km. Its core was centered at a depth of ∼160 m. Water mass characteristics and the presence of copepods from the North Pacific Ocean ( Neocalanus flemingeri and Metridia pacifica ) demonstrated that the core contained water of Pacific origin. Vertical distributions of zooplankton were associated with the physical structure of the water column. For most taxa, concentrations in the eddy core were elevated compared with those in similar density water in the surrounding Basin. Based on tracer-age estimates and previous observations of eddy formation, the eddy is believed to have been formed during the previous spring/summer from the Chukchi shelfbreak jet. Surprisingly, the eddy also contained elevated abundances of Arctic-origin copepods ( Metridia longa and Calanus glacialis ). Analysis of a shelf–basin transect occupied in the region in August 2004 showed that these species were present in high abundances in relatively shallow water (50 m) inshore of the shelfbreak due to upwelling of deeper basin water, and copepods, onto the shelf in response to easterly winds. If the formation of the observed eddy occurred during, or shortly after, a period of such winds, upwelled Arctic-origin copepods on the shelf might have been entrained into the feature. Our observations suggest that formation and subsequent migration of such eddies may provide a mechanism for transporting zooplankton from the Chukchi Shelf into the interior Canada Basin. The periodic input of high abundances of zooplankton from productive shelf areas could affect food webs in the less productive basin.

Clinoforms, Paleobathymetry, and Mud Dispersal Across the Western Canada Cretaceous Foreland Basin: Evidence from the Cenomanian Dunvegan Formation and Contiguous Strata

Abstract: Large-scale muddy clinoform stratification is rare in Cretaceous marine strata of the Western Canada Foreland Basin; most offshore mudstone units show near-parallel to gently diverging stratification that reflects differential basin subsidence. The early to middle Cenomanian Dunvegan Formation, of broadly deltaic character, is unusual in that it comprises a spectacular set of clinothems. These clinothems have been mapped over a 950 km dip transect, and downlap from NW to SE onto a phosphatic condensed section termed the FSU marker. Our regional mapping shows that the FSU marker is of basin-wide extent and marks the abrupt cessation of deposition for up to about 2 My in the south. In the northwest, the Dunvegan Formation forms a prominent wedge over 300 m thick, interpreted to fill a high-accommodation area. Muddy clinothems in this high-accommodation area are relatively tall (~ 80 m; 115 m decompacted) and extend about 80 km from the delta front to a zero edge at the downlap surface. Wave-rippled and hummocky cross-stratified fine sandstones of the upper delta front record the effects of storms, and extend about 30 m (~ 42 m decompacted) below contemporaneous beach facies, suggesting that effective wave base for sand transport was at about 40 m water depth; mud was transported in deeper water, presumably by storm-driven flows. Towards the SE, the Dunvegan Formation gradually changes from a wedge to a tabular shape, interpreted to indicate deposition in a low-accommodation area. In the transition from high- to low-accommodation areas, clinothems become progressively less tall (50 to about 20 m; 70 to about 29 m decompacted) but longer (150 to > 250 km). The most down-dip “clinothems” are essentially tabular and > 400 km in extent. In the high-accommodation area, offshore mud dispersal is inferred to have been limited by episodic geostrophic flows, and possibly by permanent along-shelf flows that swept mud (probably suspended, flocculated, and pelleted) into a shore-parallel prism, producing relatively short, steep clinothems. Muddy clinothems downlap onto sandy condensed facies of the FSU marker, the latter interpreted to have been deposited in shallow water prior to Dunvegan deposition, but which subsided below wave base in response to loading by the advancing deltaic clinothems. In the southern, low-accommodation area, tabular Dunvegan mudstones suggest that the sea floor was able to aggrade to effective wave base (i.e., about 40 m or less), at which point, wave resuspension of mud became frequent, resulting in efficient off- and along-shore dispersal of mud by geostrophic currents. The initiation of clinothem deposition is interpreted to coincide (a) with a phase of accelerated flexural subsidence in the northwest, related to renewed tectonic loading, and (b) possibly with the onset of large-scale anticlockwise marine circulation at the inception of the Greenhorn Seaway in the early Cenomanian. Together, these tectonic and oceanographic events formed an effective sediment trap along the western margin of the seaway. Only after the western sediment trap had filled, in late Dunvegan time, was mud again dispersed widely across the basin by storm processes in water less than about 40 m deep.

Electromagnetic wave wireless communication in shallow water coastal environment: theoretical analysis and experimental results

Abstract: Shallow water coastal environments are very important from the biological, social and economic point of view. Wireless technologies - and in particular wireless sensor networks (WSN) - are critical for enabling their efficient and pervasive monitoring. Electromagnetic (EM) communication is considered as the physical layer because, in shallow water coastal environments, it presents distinct advantages with respect to acoustic and optical communication. The benefit of lateral wave EM propagation in shallow water environment is explained. A theoretical analysis of EM propagation in a typical shallow water environment is then conducted, where the maximum distance coverable for a given transmitter power is calculated. The results are then compared with simulations and measurements: their differences with respect to theoretical predictions are assessed. A prototype of underwater communication system constituted by an underwater sensor and a hub buoy that relays data to the mainland is finally presented. Conclusions are drawn in terms of its performance, also in comparison with existing underwater EM communication systems and solutions.

Optics and remote sensing of Bahamian carbonate sediment whitings and potential relationship to wind-driven Langmuir circulation

Abstract: Regions of milky white seas or "whitings" peri- odically occur to the west of Andros Island along the Great Bahama Bank where the bottom sediment consists of fine- grained aragonite mud. We present measurements of inher- ent optical properties within a sediment whiting patch and discuss the potential for monitoring the frequency, extent, and quantity of suspended matter from ocean colour satellite imagery. Sea spectral reflectance measured in situ and re- motely from space revealed highly reflective waters elevated across the visible spectrum (i.e., "whitened") with a peak at 490 nm. Particulate backscattering was an order of magni- tude higher than that measured at other stations throughout the region. The whiting also had one of the highest backscat- tering ratios measured in natural waters (0.05-0.06) consis- tent with water dominated by aragonite particles with a high index of refraction. Regular periodicity of 40 and 212 s ev- ident in the light attenuation coefficient over the sampling period indicated patches of fluctuating turbidity on spatial scales that could be produced from regular rows of Lang- muir cells penetrating the 5-m water column. We suggest that previously described mechanisms for sediment resuspension in whitings, such as tidal bursting and fish activity, are not fully consistent with these data and propose that wind-driven Langmuir cells reaching the full-depth of the water column may represent a plausible mechanism for sediment resuspen- sion and subsequent whiting formation. Optics and remote sensing provide important tools for quantifying the linkages between physical and biogeochemical processes in these dy- namic shallow water ecosystems.

Functional shell geometry of symbiont-bearing benthic Foraminifera.

Abstract: An important function of symbiont-bearing benthic foraminifera is to provide their endosymbiotic microalgae with light At the same time, these foraminifera have to resist hydrodynamic forces Foraminifera match these demands by constructing shells (tests) functioning as glasshouses In shallowest regions of oligotrophic tropical seas, at the one end of the scale, foraminifera with spherical and thick lenticular tests develop special fixing mechanisms to resist extreme water motion In the deepest euphotic zone, at the other end of the scale with extremely weak light and quiet water, foraminifera with flat discoid and blade-shaped tests possessing a high surface/volume-ratio position their symbionts just beneath the transparent test walls, intensifying the weak light through elevated test surface structures Between these two extremes, foraminifera react to decreasing light intensity and water motion by the transition in shell form from spherical to extremely flat tests A second way in test form from high energetic shallow water to less, but still energetic water is the transition from spherical to fusiform tests, again raising the surface/volume-ratio but not in the same degree as performed by test flattening

SPH modeling of shallow-water coastal flows

Abstract: In the present paper, a Smoothed Particle Hydrodynamics (SPH) modeling of the shallow water equations is presented. The objective of this modeling is to perform flooding simulations involving complex bathymetries of sea bottom and dry land. The formulation is first detailed. Its implementation is then described, including specific procedures making possible to follow the expansion of the fluid domain during flooding simulations. An anisotropic kernel with variable smoothing length is especially used, as well as a periodic redistribution of the particles.A number of validation tests are performed. The model results are first checked on the case of a dam break on a flat dry bottom in one and two dimensions. Then more complex two-dimensional cases are simulated and compared to other models and experiments, e.g. a dam break flooding a slope of complex shape, and a solitary wave running up an island.

Dynamics of wind‐forced coherent anticyclones in the open ocean

Abstract: We numerically study the dynamics of coherent anticyclonic eddies in the ocean interior. For the hydrostatic, rotating, stably stratified turbulence we use a high-resolution primitive equation model forced by small-scale winds in an idealized configuration. Many properties of the horizontal motions are found to be similar to those of two-dimensional and quasi-geostrophic turbulence. Major differences are a strong cyclone-anticyclone asymmetry linked to the straining field exerted by vortex Rossby waves, which is also found in shallow water flows, and the complex structure of the vertical velocity field, which we analyze in detail. Locally, the motion can become strongly ageostrophic, and vertical velocities associated with vortices can reach magnitudes and levels of spatial complexity akin to those reported for frontal regions. Transport and mixing properties of the flow field are further investigated by analyzing Lagrangian trajectories. Particles released in the pycnocline undergo large vertical excursions because of the vertical velocities associated to the vortices, with potentially important consequences for marine ecosystem dynamics.

Behavior of a shallow water table under periodic flow conditions

Abstract: A new laboratory data set on the behavior of a shallow water table in a sand column aquifer subject to simple harmonic periodic forcing at its base is presented and discussed. The data are analyzed using the dynamic effective porosity, which is defined as the ratio of the rate of change in total moisture to the rate of change in water table elevation; thus, a reduction in this parameter means that the extent of moisture exchange has been reduced relative to a given water table fluctuation. The data show a clear decrease in the dynamic effective porosity with increasing proximity of the water table to the sand surface, which is consistent with previous research under a steadily rising or falling shallow water table. The observed reduction in moisture exchange due to shallowness of the water table has implications for periodic flow scenarios such as the propagation of water table waves in coastal and beach groundwater systems. That is, as moisture exchange is reduced, less work is being done by the flow, and thus, energy dissipation rates for shallow water tables will be reduced relative to the case of a deeper water table. At present no account of the influence of water table shallowness has been included in theories describing water table wave dispersion. The present experiments, in conjunction with the dynamic effective porosity concept, provide a framework in which this gap in knowledge can be further investigated. Additional experiments were designed such that the free surface transgressed the sand surface for part of the oscillation period to investigate the influence of meniscus formation and deformation at the sand surface on periodic flow dynamics. The observed behavior is consistent with previous observations of steady infiltration above shallow water tables, namely, a rapid drop (rise) in pore pressure with the onset of meniscus formation (deformation). A simple "wetting and drying'' model is derived, accounting for the variation in effective porosity caused by the free surface transgressing the sand surface, which is shown to accurately capture the observed behavior. A finite element solution of the Richards equation in which the transient upper boundary condition is easily mimicked by means of a surface element with special storage features also shows excellent agreement with the observed data.

Wave breaking in the Ostrovsky--Hunter equation

Abstract: The Ostrovsky--Hunter equation governs evolution of shallow water waves on a rotating fluid in the limit of small high-frequency dispersion Sufficient conditions for the wave breaking in the Ostrovsky--Hunter equation are found both on an infinite line and in a periodic domain Using the method of characteristics, we also specify the blow-up rate at which the waves break Numerical illustrations of the finite-time wave breaking are given in a periodic domain

West Florida Shelf Mean Circulation Observed with Long-Term Moorings

Abstract: [1] The mean circulation on the West Florida Continental Shelf is described using long-term current measurements. Bounded by the Florida peninsula to the east and the Gulf of Mexico to the west, the West Florida Continental Shelf mean flow is oriented approximately along-isobath and southward. The mean velocity vectors veer systematically with depth, shoreward over shallow water and seaward over deeper water. This polarization change implies that the mean flow is upwelling over shallow water and downwelling seaward from the inner shelf. Such a well-organized, three-dimensional coastal ocean circulation pattern, revealed by an unprecedented set of observations, and explained on the basis of wind forcing and density field adjustment, has important implications for both fisheries and red tide occurrences.

Shallow Water Waves and Solitary Waves

Abstract: Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow Water Wave Equations of Geophysical Fluid Dynamics; Computation of Solitary Wave Solutions; Numerical Methods; Water Wave Experiments and Observations; Future Directions, and Bibliography.

A central scheme for shallow water flows along channels with irregular geometry

Abstract: We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well- balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical algorithm.