Short-Wave and Wave Group Scattering by Submerged Porous Plate

An analytical solution for waves propagating through a horizontal porous plate of finite thickness is obtained. The objective of the plate is to reduce the incident short-wave energy and the long-wave energy as well. Consequently, in this study the plate is analyzed in a global perspective [i.e., considering its response to obliquely incident short waves (both regular and irregular) and wave groups (with the consequent generation of free and locked long waves)]. To solve the propagation of regular and irregular waves, an eigenfunction expansion is used and the results are verified with experimental data showing good agreement. The propagation of a wave group past a horizontal porous plate is studied using a multiple-scale perturbation method, and an analytical solution is presented. The results show that the generated long waves are present on both sides of the plate and that maximum short-wave reflection is associated with maximum long-wave transmission.     

Interaction of Nonlinear Progressive Waves with Two Serially Arranged Submerged Obstacles

The purpose of the present study is to develop a numerical model for the investigation of water waves propagating over a pair of impermeable submerged obstacles. The mathematic model is formulated by coupling solutions of the Navier–Stokes equations and transport equations for the surface elevation using the volume of fluid method. Based on a staggered computational mesh, an explicit numerical algorithm is employed with a predictor–corrector procedure of pressure and velocity field. The proposed model provides good agreement with other experimental results and validates its good performance. Regarding the spatial harmonic evolutions of various cases, it is noted that the present fluctuating mode of harmonic amplitudes exists upstream and at the gap between obstacles. The results show that the nonlinearity of propagating waves becomes stronger than the initial wave in such areas, and reveals much steeper wave profiles compared to the initial ones. The fluctuating harmonic amplitudes vary with the gap width and form two hydrodynamic cycles. The vortices play an important role in the wave reflection as they form a water column wall to reflect the incoming waves. The reflection ratio depends on the extent of vortex development near the upstream obstacle. The maximum wave reflection occurs in cases with dimensionless gap width S/L equal to 3/8 and 7/8 in this study.     

Analysis of Acoustic Surface Waveguide for AE Monitoring of Concrete Beams

The analysis of stress waves in an acoustic surface waveguide is presented. Elastic wave motions in a circular rod propagating through a rigid circular joint bonded on an elastic half-space were studied. The responses of four different harmonic wave motions—longitudinal, torsional, and two flexural—were investigated. Mode conversion, reflection, transmission, and phase change of these wave motions were observed. This analysis helps in understanding the signal transmission ability of a surface waveguide system, which is useful in the application of acoustic emission (AE) monitoring on high attenuation materials such as concrete. Numerical examples are presented to show the transmission and reflection coefficients at different frequencies and to examine the effect of mode conversion. The numerical analysis results were implemented into the design of an efficient waveguide system. Results from tests of concrete beams show that the AE monitoring range was significantly increased by using the proposed acoustic surface waveguide. The AE monitoring of a 210-cm concrete beam was accomplished by using only two sensors.     

Lagrangian Modeling of Weakly Nonlinear Nonhydrostatic Shallow Water Waves in Open Channels

A Lagrangian, nonhydrostatic, Boussinesq model for weakly nonlinear and weakly dispersive flow is presented. The model is an extension of the hydrostatic model—dynamic river model. The model uses a second-order, staggered grid, predictor-corrector scheme with a fractional step method for the computation of the nonhydrostatic pressure. Numerical results for solitary waves and undular bores are compared with Korteweg-de Vries analytical solutions and published numerical, laboratory, and theoretical results. The model reproduced well known features of solitary waves, such as wave speed, wave height, balance between nonlinear steepening and wave dispersion, nonlinear interactions, and phase shifting when waves interact. It is shown that the Lagrangian moving grid is dynamically adaptive in that it ensures a compression of the grid size under the wave to provide higher resolution in this region. Also the model successfully reproduced a train of undular waves (short waves) from a long wave such that the predicted amplitude of the leading wave in the train agreed well with published numerical and experimental results. For prismatic channels, the method has no numerical diffusion and it is demonstrated that a simple second-order scheme suffices to provide an efficient and economical solution for predicting nonhydrostatic shallow water flows.     

Wave Generation in Open Channels by Vortex Shedding from Channel Obstructions

Transverse surface waves were produced in a rectangular open channel in the region where the otherwise steady, uniform, flow passed through a cluster of vertical circular cylinders. The cylinders could represent either naturally occurring obstacles such as vegetation or man-made structures such as a group of piles driven into the bed of a river. The waves were produced from the periodic forces created by the vortex shedding from the cylinders. These forces generated and then amplified transverse waves in the channel. In some experiments the waves had amplitudes of 35% of the mean flow depth. These resonance-generated waves produce a seiching that can occur in hydraulic models as well as prototype systems. Both laboratory experiments and a theory-based analysis were used to determine the relationship between the amplitude of the vortex-generated wave, average velocity of the approach flow, viscosity of the fluid, width of the rectangular channel, depth of flow, cylinder diameter, and cylinder placement configuration.     

Analysis of Debris Wave Development with One-Dimensional Shallow-Water Equations

The objective of this contribution is to analyze the formation of debris waves in natural channels. Numerical simulations are carried out with a 1D code, based on shallow-water equations and on the weighted averaged flux method. The numerical code represents the incised channel geometry with a power-law relation between local width and flow depth and accounts for all source terms in the momentum equation. The debris mixture is treated as a homogeneous fluid over a fixed bottom, whose rheological behavior alternatively follows Herschel-Bulkley, Bingham, or generalized viscoplastic models. The code is first validated by applying it to dam-break tests on mudflows down a laboratory chute and verifying its efficiency in the simulation of rapid transients. Then, following the analytical method developed by Trowbridge, the stability of a uniform flow for a generalized viscoplastic fluid is examined, showing that debris flows become unstable for Froude numbers well below 1. Applications of the code to real debris flow events in the Cortina d’Ampezzo area (Dolomites) are presented and compared with available measured hydrographs. A statistical analysis of debris waves shows that a good representation of wave statistics can be obtained with a proper calibration of rheological parameters. Finally, it is shown that a minimum duration of debris event and channel length are required for waves showing up, and an explanation, confirmed both by field data and numerical simulations, is provided.     

Classifying River Waves by the Saint Venant Equations Decoupled in the Laplacian Frequency Domain

The Saint Venant equations are often combined into a single equation for ease of solution. As a result however, this single equation gives rise to several redundant nonlinear terms that may impose significant limitations on model analyses. In order to avoid this, our paper employs a new procedure that separates, in the Laplace frequency domain, the governing equation of water depth from that of flow velocity and thus enables us to consider two independent equations rather than two coupled ones. The so-obtained analytical solutions are valid for prismatic channels of any shape. Solution validity is assured by repeated comparison with the corresponding numerical solutions based on Crump’s algorithm, which accelerates solution convergence. Utilizing this new procedure, this paper will construct a basic wave spectrum for classifying subcritical flow waves in a prismatic channel. The spectrum is basically a contour plot of the normalized specific energy loss for a small water wave moving in the channel for a finite distance of approximately 100?m. The distance is chosen so that four distinct regions with different contour patterns that represent kinematic, diffusion, gravity, and dynamic waves in a river are shown in the spectrum. By incorporating the spectrum with Ferrick’s criteria and Manning’s formula, a single contour line is also generated, which serves as the boundary of the four regions. Example computations show that the spectrum predicts a similar trend of wave attenuation for waves propagating in a trapezoidal channel. When the rising speed of a wave is of concern, the full Saint Venant equations are solved numerically to reconstruct a similar spectrum good for supercritical flow as well.     

Reflection and Transmission of Waves over Submerged Breakwaters

This work has a twofold objective. First, a new method to separate incident and reflected wave components, using measurements from one wave probe, is presented. This technique is based on local variations in amplitude and phase of the measured wave and uses wavelet analysis. Second, the method is applied to perform a parametric study to compare the reflection and transmission characteristics of flexible and rigid breakwaters. Results are discussed for different depths of submergence of the models, different internal pressures in the case of the flexible breakwater, and a wide range of wave steepnesses. The results show that, in general, the rigid model has a higher reflection coefficient than the flexible model. On the other hand, the flexible model has a much higher energy-loss coefficient. Optimal breakwater widths for reflection, transmission, and energy-loss coefficients for waves with different wavelengths are also presented.     

Linear Analysis of Shallow Water Wave Propagation in Open Channels

Flood wave movement in an open channel can be treated as disturbances imposed at the upstream and downstream boundaries of a channel to an initially steady uniform flow. Linearized, cross sectionally integrated continuity and momentum equations are introduced to describe one-dimensional, unsteady, gradually varied flow in open channels. The Laplace transform method is adopted to obtain first-order analytical spatio-temporal expressions of upstream and downstream channel response functions. These expressions facilitate a critical comparison among different wave approximations in terms of their mathematical properties and physical characteristics. One or two families of characteristic waves, parameterized by an attenuation factor and a wave celerity, are found for various wave approximations. The effects of the downstream boundary condition on different wave approximations are discussed and compared. Wave translation, attenuation, reflection, distortion, and configuration from the analyses are further investigated and interpreted; thus, the differences and similarities in the propagating mechanism among the various wave approximations are revealed.     

Analytical Study of Porous Wave Absorber

Linear potential theory is applied to the analysis of wave reflection from a composite porous wave absorber that lies on a solid foundation with a seaward slope. By adopting the mathematical model of wave-induced flow in a porous medium, the interaction between water waves and a porous wave absorber is investigated. An extended linear refraction-diffraction model for surface waves is applied to the sloping region in front of the porous absorber. Using the eigenfunction expansions and the finite-difference method, an analytical study is undertaken to predict the wave reflection from such a composite porous absorber. The reflection behavior is discussed for several wave conditions, and the functional efficiency of this absorber is evaluated. It is noted that the present numerical results agree very well with the experimental results available in the literature.     

Celerity and Amplification of Supercritical Surface Waves

The amplification of supercritical waves in steep channels is examined analytically using a one-dimensional dynamic solution of the Saint-Venant equations. Existing methods were modified to describe the amplification of surface waves over a normalized channel length rather than over a single wavelength. The results are strikingly different, and a generalized graph shows that short waves amplify the most over a fixed channel length. The maximum amplification parameter over a normalized channel length is 0.53 when F = 3.44. Applications to the flood drainage channel F1 in Las Vegas indicate that the amplitude of waves shorter than 100 m would increase by 65% over a channel length of 543 m. These theoretical results await field verification. Supercritical waves could be dampened by increasing channel roughness to reduce the Froude number below 1.5.     

Oblique Impact of Water Waves on Thin Porous Walls

There is a paradoxical phenomenon in earlier studies when the incoming water wave is parallel to a porous breakwater, the water wave permeates completely without regard to the largeness of the the porosity of the porous breakwater. For solving the problem of the water waves obliquely impacting upon the thin porous wall, a new boundary condition on the thin porous wall—which can remedy the above mentioned paradoxical phenomenon—is proposed based on the concept that the incident angle remains unchanged when the water wave permeates into the wall. According to this new boundary condition, an analytic solution of an oblique water wave impacting on a thin porous wall of any permeability is obtained. It is found that the above paradoxical phenomenon, as the water wave is parallel to a thin porous wall, disappears. And, as the incident angle approaches 90°, the reflection coefficient and the transmission coefficient reasonably converge to 1 and 0, respectively, while on the contrary, those in the earlier investigations converge to 0 and 1.     

Trapping and Generation of Waves by Vertical Porous Structures

The trapping and generation of surface waves by submerged vertical permeable barriers or plates kept at one end of a semi-infinitely long channel of finite depth are investigated for various barrier and plate configurations. The various fixed barrier configurations are (1) a surface-piercing barrier; (2) a bottom-touching barrier; (3) a barrier with a gap; and (4) a fully submerged barrier. The different moving plate (or wavemaker) configurations are of types 1, 2, and 4, respectively. The boundary value problems are converted to dual∕triple series relations by a suitable application of the eigenfunction expansion method and then the full solutions are obtained by the least-squares method. The variations of reflection coefficients are obtained and discussed for different values of the porous-effect parameter, the normalized distance between the barrier and the channel end-wall, and the length of submergence of barriers for all types of barrier configurations. The dynamic pressure distributions for various porous-effect parameters are analyzed for the three types of wavemakers. The wave amplitudes at large distances are obtained and analyzed for different values of the porous-effect parameter and the distance between the wavemaker and the channel end-wall.     

Multimodal Approach to Seismic Pavement Testing

A multimodal approach to nondestructive seismic pavement testing is described. The presented approach is based on multichannel analysis of all types of seismic waves propagating along the surface of the pavement. The multichannel data acquisition method is replaced by multichannel simulation with one receiver. This method uses only one accelerometer-receiver and a light hammer-source, to generate a synthetic receiver array. This data acquisition technique is made possible through careful triggering of the source and results in such simplification of the technique that it is made generally available. Multiple dispersion curves are automatically and objectively extracted using the multichannel analysis of surface waves processing scheme, which is described. Resulting dispersion curves in the high frequency range match with theoretical Lamb waves in a free plate. At lower frequencies there are several branches of dispersion curves corresponding to the lower layers of different stiffness in the pavement system. The observed behavior of multimodal dispersion curves is in agreement with theory, which has been validated through both numerical modeling and the transfer matrix method, by solving for complex wave numbers.     

Using Finite-Element Method to Simulate Wave Transformations in Surf Zone

In this study, a finite element method proposed by Hsu et al. in 2003 is extended to develop a numerical model for the simulation of wave transformation in the surf zone. The governing equation is the elliptic mild-slope equation including the energy dissipation of wave breaking. At the open boundaries with varying depth, the reflected waves caused by shoaling are adopted to the radiation boundary conditions. The rationality of the present numerical model is examined through the cases of offshore parallel breakwater problems. The results of calculation are in good agreement with experimental results.     

Damping Effect on Waves Propagating Past a Submerged Horizontal Plate and a Vertical Porous Wall

A set of analytical solutions for waves propagating past a combined submerged horizontal plate and vertical porous wall breakwater system is presented. The wave damping effect caused by the horizontal plate induced flow constriction is considered in the analysis. The velocity potentials in each fluid domain are derived based on the linear wave theory and the unknown coefficients are determined from the matching conditions using three sets of orthogonal eigenfunctions. Reflection and transmission coefficients are presented to evaluate the performance of the breakwater system. The analytical solutions in terms of the reflection and transmission coefficients as well as the hydrodynamic force on the vertical porous wall are found in good agreement with published laboratory measurements. In comparison with the solutions without taking into account the wave damping effect, the present analytical solutions significantly improve the accuracy of the wave predictions, especially for the reflected waves.     

Analysis and Synthesis of Transmission Loss Hydrographs

Accounting for transmission losses properly is critical in hydrologic analyses in arid and semiarid climates. The objective of this research was to develop a model that could account for the spatial and temporal variations of transmission losses while routing the flow hydrograph through the channel reach. This model was based on Hortonian infiltration methods and hydrologic channel routing. While most transmission loss models predict flow volumes, the model developed herein uses hydrographs of individual storm events. A numerical optimization procedure was used to identify optimum parameter values for each of Horton’s parameters and the routing coefficient, which were then used in modeling transmission losses. Flow gauge data were obtained from the Walnut Gulch Experimental Watershed, which is located near Tucson, Ariz. Testing of this model indicates that it is able to account for transmission losses and predict downstreamflow with reasonable accuracy. To provide a measure of verification, the model was compared to predictions from Lane’s model, which is a commonly used method of accounting for transmission losses based on upstreamflow and downstreamflow volumes. Overall the two methods were found to agree fairly well though differing assumptions in the methods influence the results.     

Active Flood Hazard Mitigation.?II: Omnidirectional Wave Control

Active mitigation of unimodal flood waves is achieved by selective boundary flow withdrawal. This is shown to create omnidirectional depression waves that can reduce the impact of hazardous flood waves in wide rivers, harbors, and reservoirs. Boundary outflow is induced by a deliberate levee breach or through an emergency side channel spillway generating disturbances that reflect on the banks of the channel further complicating the wave pattern. An adjoint sensitivity method based on the 2D shallow-water equations is presented to aid in the mitigation of an extreme flooding event by identifying optimal locations and times for the selective withdrawal of flood waters. The efficiency of the method allows adaptive flood control to proceed in real time. It is shown that wave reflections from solid boundaries create a complex pattern of sensitivity waves and multiple options for control. The adjoint sensitivity results become less accurate as the magnitude and duration of the perturbation become large. However, the adjoint sensitivities provide reliable information for identifying optimal locations and times for a selective withdrawal of large magnitude and a fair indication of the spatial dependence of the objective function sensitivity to large changes in flow.     

Downstream Hydraulic Geometry of Alluvial Channels

This study extends the earlier contribution of Julien and Wargadalam in 1995. A larger database for the downstream hydraulic geometry of alluvial channels is examined through a nonlinear regression analysis. The database consists of a total of 1,485 measurements, 1,125 of which describe field data used for model calibration. The remaining 360 field and laboratory measurements are used for validation. The data used for validation include sand-bed, gravel-bed, and cobble-bed streams with meandering to braided planform geometry. The five parameters describing downstream hydraulic geometry are: channel width W, average flow depth h, mean flow velocity V, Shields parameter τ*, and channel slope S. The three independent variables are discharge Q, median bed particle diameter ds, and either channel slope S or Shields parameter τ* for dominant discharge conditions. The regression equations were tested for channel width ranging from 0.2 to 1,100?m, flow depth from 0.01 to 16?m, flow velocity from 0.02 to 7?m/s, channel slope from 0.0001 to 0.08, and Shields parameter from 0.001 to 35. The exponents of the proposed equations are comparable to those of Julien and Wargadalam (1995), but based on R2 values of the validation analysis, the proposed regression equations perform slightly better.     

Agonist-induced calcium waves in oscillatory cells: a biological example of Burgers' equation

Oscillations in cytosolic Ca2+ concentrations in living cells are often a manifestation of propagating waves of Ca2+. Numerical simulations with a realistic model of inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ wave trains lead to wave speeds that increase linearly at long times when (a) IP3 levels are in the range for Ca2+ oscillations, (b) a gradient of phase is established by either an initial ramp or pulse of IP3, and (c) IP3 concentrations asymptotically become uniform. We explore this phenomenon with analytical and numerical methods using a simple two-variable reduction of the De Young-Keizer model of the IP3 receptor that includes the influence of Ca2+ buffers. For concentrations of IP3 in the oscillatory regime, numerical solution of the resulting reaction diffusion equations produces nonlinear wave trains that shows the same asymptotic growth of wave speed. Due to buffering, diffusion of Ca2+ is quite slow and, as previously noted, these waves occur without appreciable bulk movement of Ca2+. Thus, following Neu and Murray, we explore the behavior of these waves using an asymptotic expansion based on the small size of the buffered diffusion constant for Ca2+. We find that the gradient in phase of the wave obeys Burgers' equation asymptotically in time. This result is used to explain the linear increase of the wave speed observed in the simulations.