Ray path of head waves with irregular interfaces

Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity.However,the path that the rays travel along in media with irregular interfaces is not clear.Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements（SEMO） that can accurately evaluate waves traveling along an irregular interface.Consequently,the head waves are separated from interface waves by a time window.Thus,their energy and arrival time changes can be analyzed independently.These analyses demonstrate that,contrary to the case for head waves propagating along a flat interface,there are two mechanisms for head waves traveling along an irregular interface：a refraction mechanism and transmission mechanism.That is,the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media.Such knowledge will be helpful in constructing a more accurate inversion method,such as head wave travel-time tomography,and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas,such as the Tibetan Plateau.

Experimental Researches on Reflective and Transmitting Performances of Quarter Circular Breakwater Under Regular and Irregular Waves

A series of regular and irregular wave experiments are conducted to study the reflective and transmitting performances of quarter circular breakwater （QCB） in comparison with those of semi-circular breakwater （SCB）. Based on regular wave tests, the reflection and transmission characteristics of QCB are analyzed and a few influencing factors are investigated. Then, the wave energy dissipation as wave passing over the breakwater is discussed based on the hydraulic coefficients of QCB and SCB. In irregular wave experiments, the reflection coefficients of QCB and their spectrums are studied. Finally, the comparisons between the experimental results and numerical simulations for QCB under regular and irregular wave conditions are presented.

Experimental Study on Local Scour Around A Large Circular Cylinder Under Irregular Waves

A series of physical model tests are conducted for local scour around a circular cylinder of a relatively large diameter (0 15< D/L <0.5) under the action of irregular waves. The laws of change of the topography around the cylinder are systematically studied. The effects of wave height, wave period, water depth, sediment grain size and cylinder diameter are taken into account. The mechanism of formation of the topography around the cylinder is analyzed. A detailed analysis is given to bed sediment grain size, and it is considered that the depth of scour around the cylinder under wave action is not inversely proportional to the sediment grain diameter. On such a basis, an equation is proposed for calculation of the maximum depth of scour around a cylinder as well as its position under the action of irregular waves.

Parametric Resonance Analyses for Spar Platform in Irregular Waves

The parametric instability of a spar platform in irregular waves is analyzed. Parametric resonance is a phenomenon that may occur when a mechanical system parameter varies over time. When it occurs, a spar platform will have excessive pitch motion and may capsize. Therefore, avoiding parametric resonance is an important design requirement. The traditional methodology includes only a prediction of the Mathieu stability with harmonic excitation in regular waves. However, real sea conditions are irregular, and it has been observed that parametric resonance also occurs in non-harmonic excitations. Thus, it is imperative to predict the parametric resonance of a spar platform in irregular waves. A Hill equation is derived in this work, which can be used to analyze the parametric resonance under multi-frequency excitations. The derived Hill equation for predicting the instability of a spar can include non-harmonic excitation and random phases. The stability charts for multi-frequency excitation in irregular waves are given and compared with that for single frequency excitation in regular waves. Simulations of the pitch dynamic responses are carried out to check the stability. Three-dimensional stability charts with various damping coefficients for irregular waves are also investigated. The results show that the stability property in irregular waves has notable differences compared with that in case of regular waves. In addition, using the Hill equation to obtain the stability chart is an effective method to predict the parametric instability of spar platforms. Moreover, some suggestions for designing spar platforms to avoid parametric resonance are presented, such as increasing the damping coefficient, using an appropriate RAO and increasing the metacentric height.

The reflection of regular and irregular waves by a partially perforated caisson breakwater on a step bed

This study examines the reflection of regular and irregular waves from a partially perforated caisson breakwater located on a step bed. The step bed is treated as an idealized rubble mound foundation. Based on the linear potential theory, an analytical solution is developed to calculate the reflection coefficient of the structure subjected to regular waves. The matched eigenfunction expansion method is used for the solution. The regular wave method is also extended to irregular waves using a linear transfer function. The calculated results obtained for limiting cases are exactly the same as corresponding results given by the previous researchers. The present predictions also agree well with experimental data in the published literatures. Numerical experiments are conducted to examine the variations of the reflection coefficient versus its main effect factors, and some interesting results are presented.

Ince-Strutt Stability Charts for Ship Parametric Roll Resonance in Irregular Waves

Ince-Strutt stability chart of ship parametric roll resonance in irregular waves is conducted and utilized for the exploration of the parametric roll resonance in irregular waves. Ship parametric roll resonance will lead to large amplitude roll motion and even wreck. Firstly, the equation describing the parametric roll resonance in irregular waves is derived according to Grim’s effective theory and the corresponding Ince-Strutt stability charts are obtained. Secondly, the differences of stability charts for the parametric roll resonance in irregular and regular waves are compared. Thirdly, wave phases and peak periods are taken into consideration to obtain a more realistic sea condition. The influence of random wave phases should be taken into consideration when the analyzed points are located near the instability boundary. Stability charts for different wave peak periods are various. Stability charts are helpful for the parameter determination in design stage to better adapt to sailing condition. Last, ship variables are analyzed according to stability charts by a statistical approach. The increase of the metacentric height will help improve ship stability.

Interaction of Irregular Waves with Vertical Breakwater and Characteristics of Secondary Wave Generated by Overtopping

This study investigated the interaction between irregular waves and vertical breakwater.The main goal was to determine the wave force on the breakwater for different depths,along with the evolution of the secondary wave generated by overtopping.The open source code DualSPHysics was used in the simulation.Wavelet transform was employed to remove the acoustic components from the weakly compressible smoothed particle hydrodynamics pressure solution.The results of the experiments and simulations showed that although the wave height at the low water level(case 2 was smaller than that at the high water level(case 1,the horizontal and uplifting force of case 2 was higher than that of case 1.In case 2,a large impact pressure occurred because of the plunging wave and wave breaking effects.As the water level was close to the breakwater top in case 1,the secondary wave generated by overtopping was studied.Results indicated that wave and breakwater interactions transfer wave energy from the leading wave component to higher harmonics.Two main harmonics were identified in the secondary wave.The first harmonic was the incident peak frequency,which was still the dominant component.During the wave propagation behind the breakwater,the frequencies of harmonics remained unchanged,but the amplitude of the first harmonic showed an obvious change.Under the same wave condition,the first and second harmonics did not change with depth.

Numerical simulation of the propagation of electromagnetic waves in ionospheric irregularities

The characteristics of high-frequency(HF)electromagnetic(EM)wave propagation can be affected when EM waves propagate in the ionosphere.When ionospheric irregularities appear in the ionosphere,they can have a serious impact on the propagation of HF EM waves.In this study,the propagation of HF EM waves in ionospheric irregularities was investigated by numerical simulation.First,a twodimensional model of plasma bubbles was used to produce ionospheric irregularities in the ionosphere.A ray-tracing method was then utilized to simulate the propagation of HF radio waves in these ionospheric irregularities.Results showed that the propagation of HF radio waves in the ionosphere was more complex in ionospheric irregularities than without ionospheric irregularities.In addition,corresponding ionograms were synthesized by radio rays propagated in the ionosphere with these irregularities.The synthesized ionograms were then compared with the experimental ionograms recorded by an ionosonde.Results showed that spread F could be simulated on the ionograms when ionospheric irregularities occurred in the ionosphere.This result was consistent with the ionosonde observations.

Reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core

The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction method. Numerical results of the present model are compared with the experimental data of different researchers. Numerical examples are given to examine the effect of rock fill on the reflection coefficient. The differences between regular and irregular waves are also investigated by means of theoretical and experimental results. It is found that the minimum reflection coefficient of irregular waves is larger than that of corresponding regular waves, but the contrary is the case for the maximum reflection coefficient.

Laboratory Study of the Nonlinear Transformation of Irregular Waves over A Mild Slope

This paper considers the nonlinear transformation of irregular waves propagating over a mild slope （1：40）. Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this purpose. The results indicate that the wave heights obey the Rayleigh distribution at the offshore location; however, in the shoaling region, the heights of the largest waves are underestimated by the theoretical distributions. In the surf zone, the wave heights can be approximated by the composite Weibull distribution. In addition, the nonlinear phase coupling within the irregular waves is investigated by the wavelet-based bicoherence. The bicoherence spectra reflect that the number of frequency modes participating in the phase coupling increases with the decreasing water depth, as does the degree of phase coupling. After the incipient breaking, even though the degree of phase coupling decreases, a great number of higher harmonic wave modes are also involved in nonlinear interactions. Moreover, the summed bicoherence indicates that the frequency mode related to the strongest local nonlinear interactions shifts to higher harmonics with the decreasing water depth.

Hydrodynamic Coefficients for Grouping Piles Under the Action of Irregular Waves

-The hydrodynamic coefficients for each of two piles and three piles in both side-by-side arrangement and tandem arrangement under the action of irregular waves are experimentally investigated. These coefficients vary with the KC number, the relative pile spacing, the number of piles and the pile location, and their relationships are presented in this paper. They can be used in Morison Equation and other equations to calculate directly the in-line wave forces and the transverse forces on each pile in array.

Computation of Diffraction of Irregular Waves Behind Double Jetty

The coefficient of deffraction of regular waves behind the double jetty has been computed in this paper at first by using the singularity distribution method. The model tests conducted for diffraction of irregular waves with a unidirectional frequency spectrum have confirmed good agreement between the data measured in experiments and the results computed by the singularity distribution method plus the linear superposition method for the energy of component waves in the directional frequency spectra. Therefore, this technique for component waves in the directional spectra has been further used to compute diffraction of irregular waves of multidirection, including the employment of a directional distribution function of the cos2 type, as well as the Bretschneider-Misuyann frequency spectrum.

Impact Pressure of Incident Regular Waves and Irregular Waves on the Subface of Open-Piled Structures

This paper presents the results of comparison of impact pressures on open-plied structures induced by regular waves and irregular waves in a laboratory channel. Regular waves with wave heights ranging from 0.1～0.2 m and periods ranging from 1.0～2.0 s are tested. The target spectrum for the irregular wave is JONSWAP spectrum. Irregular waves with significant wave heights in the range of 0.10～0.25 m and peak periods in the range of 1.0～2.0 s are tested. The relative clearance s/H 1/3(H) is between -0.1 and 0.4, s being the subface level of structure model above the still water level. Time series of impact pressure are analyzed to indicate whether the property of impact pressures induced by the regular wave significantly deviates from that by the irregular wave. The distribution of the impact pressure along the underside of the structure is compared for different types of incident waves. The effects of wave parameters, structure dimension and structure clearance on the impact pressure are also discussed.

Response Analysis of Tension-Based Tension Leg Platform Under Irregular Waves

Tension Leg Platform（TLP） is a hybrid structure used as oil drilling and production facility within water depths of 1200 m. The extension of this TLP concept to deeper waters is a challenge and warrants for some innovative design concepts. In this paper, a relatively new concept of TLP which is christened as Tension-Based Tension Leg Platform（TBTLP） and patented by Srinivasan（1998） has been chosen for study. Response analysis of TLP with one tension base under irregular waves for three different sea states has been performed using hydrodynamic tool ANSYS？ AQWA？. Results are reported in terms of RAOs, response spectrums for surge, heave and pitch degrees of freedom from which spectral statistics have been obtained. The statistics of TBTLP have been compared with TLPs（without tension base） for two different water depths to highlight the features of the new concept. The effect of viscous damping and loading effects on the RAOs are also investigated.

Numerical Investigation on the Generation and Propagation of Irregular Waves in A Two-Dimensional Wave Tank

The modeling of generation and subsequent propagation of irregular waves in a numerical wave flume is performed by mean of the boundary element method. Random waves are generated by a piston-type wave generator at one end of the flume with the Mitsuyasu-Bretschneider spectrum used as the target spectrum for the generation. An artificial absorbing beach is placed at the other end of the flume to minimize wave reflection. Surface fluctuations are described by use of the Lagrangian description, and finite difference is adopted for the approximation of time derivative. To monitor the developments of the waves, a number of pseudo wave gauges are installed along the tank. Through comparison of the spectra from those gauges with the target spectrum, satisfactory results can be obtained from the present numerical scheme.

TRANSVERSE FORCES AND RESULTANT FORCES ON ARRAY OF BI-PILE IN IRREGULAR WAVES

The total transverse forces on each of the two piles in the side-by-side arrangement and tandem arrangement are experimentally investigated in irregular waves and the total in-line wave forces are measured simultaneously. The statistical and spectral characteristics of the transverse forces are analyzed. The ratio of the transverse force on each pile in group to that on a single pile is defined as the transverse groupling-pile factor, KGL. Both the transverse coefficients CLG and KGL for each pile in array are varied with the relative pile distance and KC number and their relationships are presented in this paper. Also the ratio of the resultant wave froce of in-line force and transverse force to the in-line force and the vriation of the resultant coefficient are investigated.

Experimental Study on the Armor Grate Plate of Sloping Breakwater Under the Action of Irregular Waves

The irregular wave experiment on the stability of the Grate Plate was carried out in the light of the wind wave spectrum recently advanced by Prof. Wen Shengchang. The stability formulas of GP under the action of irregular waves were procured. Comparisons between the formulas obtained and those of GP under regular waves advanced by the first author in 1993 showed a coincident result.

Placement Effect on the Stability of Tetrapod Armor Unit on Breakwaters in Irregular Waves

Tetrapod, one of the well-known artificial concrete units, is frequently used as an armor unit on breakwaters. Two layers of tetrapod units are normmaly placed on the breakwaters with different placement methods. In this study, the stability of tetrapod units with two different regularly placement methods are investigated experimentally in irregular waves. Stability coefficients of tetrapod units for both placement methods are obtained. The important characteristic wave parameters of irregular waves causing the same damage ratio as those of the regular waves are also determined. It reveals that the average of one-tenth highest wave heights within the wave train （H1/lo） causes the similar damage as regular waves.

Dispersion equation of magnetoelastic shear waves in irregular monoclinic layer

This paper studies the propagation of horizontally polarized shear waves in an internal magnetoelastic monoclinic stratum with irregularity in lower interface. The stratum is sandwiched between two magnetoelastic monoclinic semi-infinite media. Dispersion equation is obtained in a closed form. In the absence of magnetic field and irregularity of the medium, the dispersion equation agrees with the equation of classical case in three layered media. The effects of magnetic field and size of irregularity on the phase velocity are depicted by means of graphs.

A Calculation Method for Incidence and Reflection of Irregular Waves Along Seawalls

Some researches have been made in this aspect. In the method by Walton Jr.(1992), incident waves are supposed to be the overlapping result of M component waves with different frequencies which may take different directions, the direction of incident waves should be available in advance, but in fact the direction of incident waves is not available. In our study, incident waves are supposed to be composed of M overlapping component waves with different frequencies, and different frequencies have different directions. Based on the irregular wave reflection theory, the calculation formulas of wave direction, complex amplitude of incident waves, and complex amplitude of reflected waves in surface which are composed of component waves are derived by means of discrete Fourier transform. Then, the frequency spectra of incident waves and reflected waves and the reflection coefficient of waves with corresponding frequencies are obtained. Verification of the method and the calculation results from in-situ measured data indicate that the method is reliable and highly accurate.