Fully Nonhydrostatic Modeling of Surface Waves

A fully nonhydrostatic model is tested by simulating a range of surface-wave motions, including linear dispersive waves, nonlinear Stokes waves, wave propagation over bottom topographies, and wave–current interaction. The model uses an efficient implicit method to solve the unsteady, three-dimensional, Navier-Stokes equations and the fully nonlinear free-surface boundary conditions. A new top-layer pressure treatment is incorporated to fully include the nonhydrostatic pressure effect. The model results are verified against either analytical solutions or experimental data. It is found that the model using a small number of vertical layers is capable of accurately simulating both the free-surface elevation and vertical flow structure. By further examining the model’s performance of resolving wave dispersion and nonlinearity, the model’s efficiency and accuracy are demonstrated.     

Wave Velocities in Granular Materials under Microgravity

Velocities of primary (P) and shear (S) waves in granular materials are highly dependent on confining stress. These wave velocities are related to mechanical properties of the materials such as stiffness, density, and stress history. Measurements of the wave velocities using piezoelectric sensors provide scientists and engineers a technique for nonintrusive characterization of those mechanical properties. For aerospace engineering, measuring the wave velocities under microgravity, which simulates low loading and stress conditions, has a number of potential applications. It can help the understanding of the soil mechanics and the development of appropriate materials handling technologies in extraterrestrial environments, which will be crucial to meeting NASA’s future space exploration goals. This paper presents the technique and results of experiments conducted at NASA Glenn Research Center using the 2.2?s drop tower. Velocities of P and S waves in three sizes of glass beads and one size of alumina beads were measured under initially dense or loose compaction states. It was found that under microgravity, the wave signals were significantly weaker and the velocities were much slower. The material that makes up the beads has a strong influence on the wave velocities as well. The initial compaction state also has some influence on the wave velocities.     

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.     

Hydrodynamic Investigation of Coastal Bridge Collapse during Hurricane Katrina

A number of U.S. coastal bridges have been destroyed by hurricanes, including three highway bridges in Mississippi and Louisiana during Hurricane Katrina (2005). This paper addresses three fundamental questions on the coastal bridge failures: (1) what were the hydrodynamic conditions near the failed bridge during the hurricane; (2) what was the cause of the bridge collapse; and (3) what was the magnitude of the hydrodynamic loading on the bridge under the extreme hurricane conditions. Guided by field observations of winds, waves, and water levels, two numerical models for storm surges and water waves are coupled to hindcast the hydrodynamic conditions. Fairly good agreement between the modeled and measured high watermarks and offshore wave heights is found, allowing an estimate of the surge and wave conditions near the bridges in nested domains with higher resolutions. The output of the coupled wave-surge models is utilized to determine the static buoyant force and wave forces on the bridge superstructure based on empirical equations derived from small-scale hydraulic tests for elevated decks used in the coastal and offshore industry. It is inferred that the bridge failure was caused by the wind waves accompanied by the storm surge, which raised the water level to an elevation where surface waves generated by strong winds over a relatively short fetch were able to strike the bridge superstructure. The storm waves produced both an uplift force and a horizontal force on the bridge decks. The magnitude of wave uplift force from individual waves exceeded the weight of the simple span bridge decks and the horizontal force overcame the resistance provided by the connections of the bridge decks to the pilings. The methodology for determining the hydrodynamic forcing on bridge decks can be used to produce a preliminary assessment of the vulnerability of existing coastal bridges in hurricane-prone areas.     

Effects of the Source on Wave Propagation in Pile Integrity Testing

One-dimensional stress wave theory is widely used to analyze quantitatively the reflections in low-strain integrity testing of piles. However, a point or disk loading produces body and Rayleigh waves near the pile top. The multireflections of these waves from the lateral surface of a pile are present in the wave field near the pile top. Effects of three-dimensional waves on the near field responses are obvious. These effects can be interpreted erroneously by an inexperienced user as “noises” or “pile anomalies.” To investigate wave propagation in the longitudinal direction, the behavior of the waves in the far field (some distance below the pile top) is studied by theoretical analysis of the longitudinal modes in free cylinders and numerical simulations. The wave pattern at the pile top is analyzed based on the response of an elastic half-space to a harmonic disk loading. The results show that when the ratio of the characteristic length of an impact pulse to the cylinder radius is large enough, the components of Rayleigh waves in the wave field at the pile top are diminished; the waves in the far field behave approximately as plane waves; the responses at positions between 1/2R and 3/4R from the pile axis are less affected by the multireflections. The results from numerical simulations support the practical recommendation to use a ratio of characteristic wavelength to pile radius larger than four. Under this condition, the reflections from the far field (say deeper than two pile diameters) can be analyzed from the responses at receiver positions about 0.6R from the pile axis based on one-dimensional stress wave theory.     

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.     

Finite-Element Analysis of Lamb Wave Propagation in a Thin Aluminum Plate

Structural health monitoring (SHM) is an emerging technology that can be used to identify, locate, and quantify structural damages before failure. Among SHM techniques, Lamb waves are widely used since they can cover large areas from a single location. The development of various structural simulation programs has lead to increasing interest in whether SHM data obtained from the simulation can be verified by experimentation. The objective of this research is to determine the Lamb wave responses of SHM models using the finite-element software package ABAQUS CAE as a computational tool for an isotropic plate. These results are compared to experimental results and theoretical predictions under isothermal and thermal gradient conditions to assess the sensitivity of piezoelectric generated Lamb wave propagation. Simulations of isothermal tests are conducted over a temperature range of 0–190°F using 100 and 300?kHz as excitation frequencies. The changes in temperature-dependent material properties are used to measure the differences in the response signal’s waveform and propagation speed. An analysis of the simulated signal response data demonstrated that elevated temperatures delay the Lamb wave propagation, although the delays are found to be minimal at the temperatures tested.     

Quantitative Structural Health Monitoring by Ultrasonic Guided Waves

This paper presents a global-local (GL) method to simulate the interaction of ultrasonic guided waves with structural defects in isotropic and multilayered composite platelike structures. The GL method uses a full finite-element (FE) discretization of the defected region to properly represent wave diffraction phenomena and a suitable set of wave functions to simulate regions away from the joint. Displacement and stress continuity conditions are imposed at the boundary between the global and the local regions. The radiated wave field can be then calculated by using standard techniques (least-squares method). The novelty of the proposed approach over previous GL techniques is the use of semianalytical FE (SAFE) modeling for the “global” simulation. The SAFE method, which only requires the discretization of the waveguide’s cross section, allows handling complex structures (multilayered composites, arbitrary cross sections, etc.) in a computationally efficient manner. Applications of the GL method to damage quantification will be shown for the cases of notches in aluminum plates and delaminationlike defects in aircraft composite panels.     

Stochastic Analysis of a Single-Degree-of-Freedom Nonlinear Experimental Moored System Using an Independent-Flow-Field Model

Stochastic characteristics of the surge response of a nonlinear single-degree-of-freedom moored structure subjected to random wave excitations are examined in this paper. Sources of nonlinearity of the system include a complex geometric configuration and wave-induced quadratic drag. A Morison-type model with an independent-flow-field formulation and a three-term-polynomial approximation of the nonlinear restoring force is employed for its proven excellent prediction capability for the experimental results investigated. Wave excitations considered in this study include nearly periodic waves, which take into account the presence of tank noise, noisy periodic waves that have predominant periodic components with designed additive random perturbations, and narrow-band random waves. A unified wave excitation model is used to describe all the wave conditions. A modulating factor governing the degree of randomness in the wave excitations is introduced. The corresponding Fokker–Planck formulation is applied and numerically solved for the response probability density functions (PDFs). Experimental results and simulations are compared in detail via the PDFs in phase space. The PDFs portray coexisting multiple response attractors and indicate their relative strengths, and experimental response behaviors, including transitions and interactions, are accordingly interpreted from the ensemble perspective. Using time-averaged probability density functions as an invariant measure, probability distributions of large excursions in experimental and simulated responses to various random wave excitations are demonstrated and compared. Asymptotic long-term behaviors of the experimental responses are then inferred.     

Wave and Flow Response to an Artificial Surf Reef: Laboratory Measurements

Waves and currents are essential elements in the design of an artificial surfing reef (ASR). ASRs are primarily designed to optimize the surfing conditions (i.e., increase the surfability of the incoming waves) possibly in combination with the shoreline protection from erosion. The currents generated by waves breaking on the ASR play an important role in the surfability through the wave-current interaction (WCI). Depending on the design, the WCI may negatively affect the surfability by causing the waves to break prematurely due to the current-induced wave steepening. In addition, wave breaking tends to become more irregular due to the temporal variability of the underlying currents. To mitigate the negative effects of wave breaking induced currents on the surfability, three ASR layouts are examined through detailed laboratory experiments. The layouts differ in the alongshore separation distance between two symmetrical reef sides. The ensuing flow circulations are examined in detail with both in situ current meters and video observations of surface drifters. This is done for regular incident waves, bichromatic incident waves, and irregular incident waves, all with equal energy. A data analysis shows that for a given layout the mean flow patterns for regular, bichromatic, and irregular waves are qualitatively similar, with oblique rip currents exiting at either side of the reef and strong flow circulations onshore of the gap in between the two reef sides. Increasing the separation distance leads to a significant reduction of the obliquely exiting rip currents at the outer sides of the reef, but an increase in the flow circulation onshore of the gap. This has a positive effect on the surfability by reducing the negative effects associated with the WCI on the wave breaking, thus, providing longer rides.     

Pressure Waves in Porous Medium Saturated with Liquid Containing Gas Bubbles

Theoretical analyses on nonlinear pressure waves evolution in porous medium saturated with a liquid containing gas bubbles is carried out. The evolution equations for fast and slow longitudinal modes are derived for slightly nonlinear, disperse, and dissipation processes. The pressure wave distribution in gas bubble liquid-saturated porous media was investigated experimentally. It was revealed that both modes might have oscillating structure induced by bubble oscillation in the wave. It is shown that the wave damping is determined by a combined impact of heat losses due to gas cooling in the bubbles and dissipation due to longitudinal displacement of liquid and porous skeleton, both influenced by the wave. Experimental data on the velocity and structure of fast and slow modes are compared with results of theoretical modeling.     

Wave Damping in Reed: Field Measurements and Mathematical Modeling

Wave damping in vegetation in shallow lakes reduces resuspension and thereby improves the light climate and decreases nutrient recycling. In this study, wave transformation in reed (Phragmites australis) was measured in a shallow lake. Theoretical models of wave height decay, based on linear wave theory, and transformation of the probability density function (PDF), using a wave-by-wave approach, were developed and compared to the collected data. Field data showed an average decrease in wave height of 4–5%?m?1 within the first 5–14 m of the vegetation. Incident root-mean-square wave height was 1–8 cm. A species-specific drag coefficient CD was found to be about 9 (most probable range: 3–25). CD showed little correlation with a Reynolds number or a Keulegan-Carpenter number. The PDF for the wave heights did not change significantly, but for longer distances into the vegetation and higher waves it tended to be more similar to the developed transformed distribution than to a Rayleigh distribution. Relationships developed in this study can be employed for management purposes to reduce resuspension and erosion.     

Nonhydrostatic Modeling of Nonlinear Deep-Water Wave Groups

A nonhydrostatic model with a higher-order top-layer pressure treatment is developed. Accuracy with respect to linear wave dispersion and wave nonlinearity is carefully examined. The model is thereafter applied to simulate nonlinear deep-water wave groups. For slowly modulated wave groups, the model well predicts the characteristics of bichromatic waves better than those obtained by the fourth-order nonlinear Schr?dinger equation and the multilayer Boussinesq model. For fast evolution of focusing wave groups, the model accurately captures the limiting extreme wave conditions. Particularly the predicted local wave steepness of a narrow-banded wave group is higher than that of a broad-banded wave group, supporting the importance of spectral bandwidth in determining the limiting wave condition in the previous study. Overall, the agreement between the model’s results and experimental data are excellent, demonstrating the capability of the model on resolving wave-wave interactions in the nonlinear deep-water wave groups.     

Microporodynamics of Bones: Prediction of the “Frenkel–Biot” Slow Compressional Wave

Understanding of ultrasonic wave propagation in bones is essential for further development of related techniques in clinical practice. As any other saturated porous medium, bone is characterized by different forms of longitudinal wave propagation, either undrained waves or fast and (Frenkel–Biot) slow compressional waves. We here study the wave propagation in the framework of poromicromechanics. A continuum micromechanics model allows for the prediction of the anisotropic poroelastic properties, Biot’s coefficients, and moduli, from tissue-specific composition data, on the basis of tissue-independent (“universal”) elastic properties of the elementary components of all bones. These poroelastic properties enter the governing equations for wave propagation in anisotropic porous media. They allow for the prediction of undrained, fast and slow waves, as is verified by comparison of model results with experimental findings.     

Control of Scour at Vertical Circular Piles under Waves and Current

An experimental study on the control of scour at vertical circular piles under monochromatic waves and a steady current is presented. The experiments on wave and steady currents were carried out under live-bed and clear-water regimes, respectively. In waves, splitter plate attached to the pile along the vertical plane of symmetry and threaded pile (helical wires or cables wrapped spirally on the pile to form threads) were found to be effective to reduce the scour depth. For the Keulegan–Carpenter numbers 6–100, the vortex shedding is the main mechanism of scour under waves. The splitter plate and threaded pile disrupt the vortex shedding. The average reduction of the scour depth by the splitter plate was 61.6%. For threaded piles, different combinations of cable and pile sizes were tested, and the best combination was found for a cable–pile diameter ratio equaling 0.75, in which average scour depth reduction was 51.1%. The average reductions of scour depths for other cable–pile diameter ratios of 0.33 and 0.5 were 43.2 and 48.1%, respectively. On the other hand, in a steady current, the threaded pile proved to be effective to control scour depth to a great extent. Cables wrapped spirally forming threads on the pile help to weaken the downflow and horseshoe vortex, which are the principal agents of scour under a steady current. The experimental results showed that the scour depth consistently decreases with an increase in cable diameter and the number of threads, and with a decrease in thread angle. The maximum reduction of scour depth observed was 46.3% by using a triple threaded pile having a thread angle of 15° and a cable–pile diameter ratio of 0.1. The proposed methods of controlling scour are easy to install and are economical.     

RANS∕Laplace Calculations of Nonlinear Waves Induced by Surface-Piercing Bodies

An interactive zonal numerical method has been developed for the prediction of free surface flows around surface-piercing bodies, including both viscous and nonlinear wave effects. In this study, a Laplace solver for potential flow body-wave problems is used in conjunction with a Reynolds-averaged Navier-Stokes (RANS) method for accurate resolution of viscous, nonlinear free surface flows around a vertical strut and a series 60 ship hull. The Laplace equation for potential flow is solved in the far field to provide the nonlinear waves generated by the body. The RANS method is used in the near field to resolve the turbulent boundary layers, wakes, and nonlinear waves around the body. Both the kinematic and dynamic boundary conditions are satisfied on the exact free surface to ensure accurate resolution of the divergent and transverse waves. The viscous-inviscid interaction between the potential flow and viscous flow regions is captured through a direct matching of the velocity and pressure fields in an overlapping RANS and potential flow computational region. The numerical results demonstrate the capability of an interactive RANS∕Laplace coupling method for accurate and efficient resolution of the body boundary layer, the viscous wake, and the nonlinear waves induced by surface-piercing bodies.     

Probabilistic Solutions to Nonlinear Random Ship Roll Motion

The probability density function (PDF) and the mean up-crossing rate of the responses for nonlinear ship roll oscillations excited by random sea waves are examined. The excitation of random sea waves is approximated as white noise. The ship roll motion is described by a nonlinear stochastic differential equation that includes a nonlinear wave drag force and a nonlinear restoring moment. The PDF and mean up-crossing rate solution of the nonlinear oscillator are investigated with a new approximate method that expressed the PDF as an exponential function with an exponent in the form of a polynomial in the response variable and its derivative. A special measure is taken such that the Fokker-Planck-Kolmogorov equation is satisfied in the weak sense of integration with the assumed PDF. Numerical examples and a comparison with Monte Carlo simulation are given to show the effectiveness of the method in the study of randomly excited nonlinear ship roll motion.     

Effective Soil Density for Propagation of Small Strain Shear Waves in Saturated Soil

This technical note defines an “effective soil density” that controls the velocity of small strain shear waves in saturated soil. Biot theory indicates that the ratio of effective density to saturated density will generally range from 0.75 to 1.0 and is a function of specific gravity of solids, porosity, hydraulic conductivity, and shear wave frequency. For many geotechnical applications, effective density will be equal to saturated density for low hydraulic conductivity soils (clays and silts) and may be less than saturated density for high hydraulic conductivity soils (clean sands and gravels). The findings are relevant to applications involving the propagation of small strain shear waves through saturated soil, and in particular for laboratory and field tests in which shear modulus is back-calculated from measured shear-wave velocity.     

Three-Dimensional Linear and Simplified Nonlinear Soil Response Methods Based on an Input Wave Field

We propose three-dimensional linear and simplified nonlinear soil response methods based on an input seismic wave field. An input wave field is employed to treat seismic surface waves excited by a deep structure in a shallow soil model. First, the linear method is applied to a hard- and a soft-soil site located in Mexico City, and soil responses excited by S-, surface-, and whole-wave fields reproduce the input waves fields well. Then, the linear method is applied to estimate soil responses for three large earthquakes at two soft-soil sites located in the reclaimed zone of Tokyo Bay, and again it works well. Finally, we attempt to perform nonlinear and liquefaction soil response analyses in the reclaimed zone, on the basis of an input wave field modified according to varied soil properties. The nonlinear method seems to provide reasonable nonlinear and liquefaction soil responses.     

Spectral Collocation Model for Solitary Wave Attenuation and Mass Transport over Viscous Mud

In this paper, wave attenuation and mass transport of a water-mud system due to a solitary wave on the free surface is modeled by using the Chebyshev-Chebyshev collocation spectral method for spatial discretization and a fourth-order multistage scheme for time integration. The governing equations are formulated in Lagrangian coordinates and perturbation equations for shallow water waves are derived. An iteration-by-subdomain technique is introduced to tackle the interface in the two-layer system. The numerical model is tested against available analytical solutions and good agreement has been found. Numerical simulations of the water-mud system with different layer thicknesses suggest that the accuracy of the existing boundary layer theory for fluid-mud interaction is limited when the mud layer is thin because the assumption of irrotational core may not be valid. Although the paper is focused on solitary waves and Newtonian fluid-mud, the methodology can be extended to oscillatory, nonlinear water waves over a non-Newtonian mud bottom.