Arbitrary Bathymetry Research Articles

Effects of Bathymetry, Friction, and Rotation on Estuary–Ocean Exchange

An analytical model that includes pressure gradient, friction, and the earth’s rotation in both components of the flow is used to study the transverse structure of estuarine exchange flows and the nature of transverse circulation in estuaries of arbitrary bathymetry. Analytical results are obtained for generic bathymetry and also over real depth distributions and are compared with observations. This study extends previous efforts on the topic of transverse structure of density-induced exchange flows in three main aspects: 1) the analytical model explores any arbitrary bathymetry; 2) the results reflect transverse asymmetries, relative to a midchannel centerline, associated with the effects of the earth’s rotation; and 3) the transverse circulation produced by the analytical model is examined in detail. Analytical results over generic bathymetry show, in addition to the already reported dependence of exchange flow structure on the Ekman number, two new features. First, the transverse structure of along-estuary flows shows the earth’s rotation effects, even in relatively narrow systems, thus producing transverse asymmetries in these flows. The asymmetries disappear under strongly frictional (high Ekman number) conditions, thus illustrating the previously documented pattern of inflow in channels and outflows over shoals for typical estuaries. Second, transverse flows resemble a ‘‘sideways gravitational circulation’’ when frictional effects are apparent (Ekman number greater than ;0.1) responding to a transverse balance between pressure gradient and friction. These transverse flows reverse direction under very weak friction and reflect Coriolis deflection of along-estuary flows, that is, geostrophic dynamics. All examples of observed flows are satisfactorily explained by the dynamics included in the analytical model.

Wave transformation by two-dimensional bathymetric anomalies with sloped transitions

The reflection and transmission of normally incident waves by two-dimensional trenches and shoals of finite width with sloped transitions between the depth changes are studied. Three methods are developed using linearized potential theory. The step method is valid in arbitrary water depth and is an extension of the solution of Kirby and Dalrymple [J. Fluid Mech. 133 (1983) 47] for asymmetric trenches that allows for sloped transitions to be approximated by a series of steps. The slope method is an extension of Dean [J. Waterw. Harb. Div., ASCE 90 (1964) 1] that allows trenches and shoals with a linear transition between changes in depth to be modeled in the shallow water limit. A numerical method is also developed using a backward space-stepping routine commencing from the downwave side of the trench or shoal to model the wave field for arbitrary bathymetry in the shallow water limit. The reflection and transmission coefficients are compared for both symmetric and asymmetric trenches and shoals with abrupt transitions and sloped transitions. The sloped transitions cause a reduction in the reflection coefficient; a reduction that increases as the waves progress from long waves to shorter period waves. For symmetric bathymetric anomalies complete transmission is found for certain dimensionless wavelengths, a result not found for asymmetric trenches. The wave transformation by transitions with Gaussian forms is also investigated with results indicating minimal reflection for waves beyond the shallow water limit. Comparison between the three methods indicates good agreement in the shallow water range for the cases studied. A comparison of the step method to the numerical model FUNWAVE 1.0 [1-D] indicates satisfactory agreement between the models for linear incident waves. Several new results were established during the study. The wave field modification is shown to be independent of the incident wave direction for asymmetric changes in depth, a result shown by Kreisel [Q. Appl. Math. 7 (1949) 21] for a single step. For asymmetrical bathymetric anomalies with the same depth upwave and downwave of the anomaly, a zero reflection coefficient occurs only at k 1 h 1=0. For asymmetrical bathymetric anomalies with unequal depths upwave and downwave of the anomaly, the only k 1 h 1 value at which the reflection coefficient equals zero is that approached asymptotically at deep-water conditions.

Wave field modification by bathymetric anomalies and resulting shoreline changes: a review with recent results

This paper provides a review of available studies on wave transformation by bathymetric changes and the resulting shoreline impacts. Three case studies of beach nourishment projects with significant nearshore borrow areas are examined: Grand Isle, Louisiana constructed in 1984, Anna Maria Key, Florida in 1993, and Martin County, Florida in 1996. A review is presented of field and laboratory scale studies that have examined the impact of offshore pits on the local wave field and sediment dynamics. Solutions for wave transformation by changes in bathymetry are outlined primarily in chronological order following the development from analytical solutions for long waves in one horizontal dimension (1-D) through numerical models for arbitrary bathymetry that include many wave-related nearshore processes. Modeling of shoreline responses due to wave field modification owing to changes in offshore bathymetry is examined with models that include both wave field and shoreline changes and by coupling models that evaluate these processes independently. The wave transformation processes included in nearshore models are important factors in the capability to predict a salient leeward of a pit; the shoreline responses observed in the limited laboratory experiments and at Grand Isle, LA.

Array element localization for towed marine seismic arrays

This paper presents an approach to array element localization (AEL) for towed marine seismic arrays based on regularized inversion of direct and bottom-reflected acoustic ray travel times picked from recorded seismic sections. Depth-sensor measurements at a number of points along the array are included as a priori estimates (with uncertainties) in the inversion. The smoothest array shape consistent with the acoustic data and prior estimates is determined by minimizing the array curvature or roughness. A smooth array shape is physically reasonable; in addition, minimizing curvature provides a priori information about the correlation between hydrophone positions that allows the estimation of both the offset and depth of hydrophones that record only one (or even no) acoustic arrival due to the shadowing effects of water-column refraction or reflection from arbitrary bathymetry. The AEL inversion is applied to a 102-sensor, 1.2-km towed array to correct receiver positions in the seismic velocity analysis of a seabed gas hydrate survey.

Bathymetry, stratification, and internal seiche structure

Internal seiches play a significant role in a broad range of physical, chemical, and biological processes in lakes. A detailed assessment of the impact of seiching requires an understanding of seiche structure, which is determined by bathymetry and stratification. In this study, internal seiche solutions are evaluated for arbitrary bathymetry and continuous stratification using a two‐dimensional numerical model. Formulated in terms of a stream function, the model produces a finite set of linear internal wave eigenmodes and allows the computation of the complete velocity field (over a grid) associated with each seiche mode. Several idealized configurations of continuous stratification and variable bathymetry are used to explore the effect of nonuniform systems on internal wave structure. In particular, we focus on bed velocity distribution and the resulting potential impact on scalar fluxes, sediment transport, and internal wave damping. Model results are also compared to thermistor chain data collected in the Upper Mystic Lake (UML, Winchester, Massachusetts). Using an idealized description of the UML bathymetry and density profiles which emulate the seasonal variation of stratification in the lake, the evolution of bed velocities during the autumnal breakdown in stratification is assessed, providing insight into the fate of the contaminants entering the lake.

Spectrum-Based Prediction Model for Random Wave Transformation over Arbitrary Bottom Topography

This paper proposes a one-dimensional and a horizontally two-dimensional random wave transformation models based on a spectral wave equation with a probabilistic bore-type energy dissipation term, and examines the validity of the wave models by comparing the predictions with the observations. The present spectrum-based prediction models with a probabilistic dissipation term axe rather heuristic but robust to use. Since the present random wave transformation models consist of spectral and probabilistic models, the wave model can be called as a hybrid random wave transformation model. The model solves the spatial evolution of complex Fourier amplitudes from which energy spectra are calculated. In addition, water surface elevations are obtained from the calculated complex amplitudes by using the inverse Fast Fourier Transform. Furthermore, representative wave heights and periods are obtained from the water surface elevations.We apply the one-dimensional wave model to predict transformations of double peak spectral waves, small and prototype scales' experimental waves and field waves over uniform slope and arbitrary bathymetry. In addition, the horizontally two-dimensional wave model is applied to predict transformations over an elliptic shoal, a conic shoal and field bathymetry, and also employed to investigate the mach-reflection. The comparison between the various observations by laboratory and field experiments and the predictions by the wave models shows good agreements.

A third‐generation wave model for coastal regions: 1. Model description and validation

A third‐generation numerical wave model to compute random, short‐crested waves in coastal regions with shallow water and ambient currents (Simulating Waves Nearshore (SWAN)) has been developed, implemented, and validated. The model is based on a Eulerian formulation of the discrete spectral balance of action density that accounts for refractive propagation over arbitrary bathymetry and current fields. It is driven by boundary conditions and local winds. As in other third‐generation wave models, the processes of wind generation, whitecapping, quadruplet wave‐wave interactions, and bottom dissipation are represented explicitly. In SWAN, triad wave‐wave interactions and depth‐induced wave breaking are added. In contrast to other third‐generation wave models, the numerical propagation scheme is implicit, which implies that the computations are more economic in shallow water. The model results agree well with analytical solutions, laboratory observations, and (generalized) field observations.

Site and Size Optimization of Contaminant Sources in Surface Water Systems

A numerical method is developed to minimize the environmental impact of one or multiple contaminant point sources in a vertically mixed river or estuary. The algorithm is based on a finite-element solution of the adjoint to the fate and transport equation that permits efficient selection of optimal locations and mass loadings of outfalls in the presence of tidal action, secondary currents, river branches, and other two-dimensional factors. The evaluation is based on the cumulative effects of contaminants in one or more arbitrary target points in the system. The model is validated by comparison to repeated trial solutions and is shown to yield information comparable to that resulting from a large number of hypothetical simulations. Practical applications are presented for the Fox River and the upper Potomac Estuary verifying the method's applicability to rivers of arbitrary geometry and bathymetry.

Wave energy transformation on natural profiles

A wave energy transformation model, which includes wave breaking within the surf zone described by surface rollers, is developed for randomly varying waves over arbitrary bathymetry. The model includes roller energy gradients in the energy flux balance, and further specifies the dissipation function based on roller theory following Svendsen. Root-mean-square wave heights, H rms , are found across the surf zone by numerical iteration, and compare well with field data acquired on both barred and near-planar beaches. The model has two free parameters, σ, the mean angle to vertical of the wave/roller interface roughly representing the type of breaker, and γ, a measure of breaking wave saturation equal to the ratio of H rms to local depth. Optimal values of both parameters are chosen by model fitting, and show the model to be insensitive to σ. Although the model is sensitive to the choice of γ, values are consistent with field data. The surface roller model behaves similarly to the bore dissipation model of Thornton and Guza for a particular parameter choice, and is used to decrease model dependence to one input parameter, γ.

Horizontal refraction of 3-D curvilinear wedge modes

For shallow-water acoustic propagation, the wavelength is commensurate with the water depth but short compared to the horizontal extent of the problem. Under these conditions a sloping bottom causes the development of normal modes having wavefronts that are curved in the vertical direction. For simple slopes, such wedge modes have been shown to propagate with cylindrical wavefronts along characteristics in the horizontal plane. This work extends adiabatic wedge mode theory to regions of arbitrary bathymetry by constructing a three-dimensional curvilinear coordinate system that follows the contours of the ocean bottom. The requirement for separation of the depth coordinate from the coupled horizontal coordinates produces a nonlinear differential equation for a potential field. The gradient of this field then gives the depth scale factors and curved shape of the wedge modes. A standard normal mode problem is then solved to obtain the curvilinear wedge modes and a ray-trace method is used to study the horizontal motion of those modes. An overview of the model formulation and some examples will be presented.

A numerical model for beach profile development

A time-dependent numerical model that calculates beach profile development due to offshore sediment transport is developed. The model allows variable wave conditions, water level fluctuations due to tide, arbitrary bathymetry, and sediment size. The accuracy of the model is tested by comparison of calculations with laboratory and with field data. The agreement between calculated and measured beach profiles is good. Key words: numerical model, beach profile, laboratory tests, field data.

Flood Storage in Reservoirs

Flood storage in reservoirs controlled by free‐overflowing, rectangular spillways is investigated by accounting for arbitrary reservoir bathymetry and single‐peaked inflow hydrographs. The general solution of the storage equation depends only on a storage factor. It is found that adequate substitution of the effective hydrograph by a model hydrograph has only a secondary effect on the maximum reservoir outflow when using a proper shape factor. The proposed method allows an immediate application to realistic cases. In particular, the maximum reservoir outflow and the corresponding maximum reservoir level are represented graphically. Of further interest are cases in which the spillway crest length is varied for cost optimization purposes. Computations are explained in detail by examples, one of which includes a comparison of the present solution with the result of the numerically integrated basic equation.

ONSHORE-OFFSHORE SEDIMENT TRANSPORT NUMERICAL MODEL

A numerical model is presented for calculating beach profile development due to offshore sediment transport and tested with laboratory and field data. The model allows variable wave conditions, water level fluctuations due to tide and storm surge, arbitrary bathymetry, and arbitrary sediment size. The agreement between calculated and measured beach profile erosion is good.