WAVE CURRENT FORCE COEFFICIENTS ON INCLINED CYLINDER AND A NEW ESTIMATION METHOD

Based on the review of present force coefficients estimation methods, a new method in the frequency domain, revised cross-spectrum estimation method, is presented in this paper. Some experiments on the wave-current force on inclined cylinders are also described and the wave current force coefficients are estimated by the revised cross-spectrum estimation method. From the results, it is found that the wave and current directions have some regular effect on the coefficients. According to the results, some empirical formulas are obtained for converting the wave-current force coefficients on inclined cylinders into a unified coefficient. Comparisons show that the unified coefficients are in good agreement with other results.

Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients

By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.

Experimental Research on Wave Transmission over Submerged Rubble-Mound Breakwaters

This paper discusses some previous, and presents some new experimental results on wave transmission over submerged breakwaters. The objective of this study is to evaluate wave transmission coefficient and develop a two-dimensional （2D） model as an improvement to the existing wave transmission coefficient models. Factors which affect wave transmission over stbmerged breakwaters are discussed through a series of laboratory experiments. Basic recommendations for evaluation and design of submerged rubble-monud breakwaters are presented. From the test results, a calculation formula of wave transmission coefficient is proposed.

Approximate Calculation of Oblique Wave Transmission from A Single-Row of Rectangular Piles

Transmissions of oblique incident wave from a row of rectangular piles are analyzed theoretically. The incident angle of plane wave is taken as g = 90° , there then is the transmission coefficient ｜T｜ = 1 （This is a paradox）. In this paper, by means of the approximate relation between the transmitted and incident wave angle found from the shape of a slit, the paradoxical phenomenon is removed. On the basis of the continuality of the pressure and flux and the analysis of flow resistance at the row of rectangular piles, formulas of reflection and transmission coefficients are obtained. The transmission and reflection coefficients predicted by the present model quite agree with those of laboratory experiments in previous references

Research on Partial Coefficients for Design of Quarter-circular Caisson Breakwater

The quarter-circular caisson breakwater （QCB） is a new type of breakwater, and it can be applied in deepwater. The stability of QCB under wave force action can be enhanced, and the rubble mound engineering can be less than that of semi-circular breakwaters in deepwater. In order to study the wave force distribution acting on the QCB, to find wave force formula for this type of breakwater, firstly in this paper, the distribution characteristics of the horizontal force, the downward vertical force and the uplift force on the breakwater were gotten based on physical model wave flume experiments and on the analysis of the wave pressure experimental data. Based on a series of physical model tests acted by irregular waves, a kind of calculation method, which was modified by Goda formula, was proposed to carry out the wave force on the QCB. Secondly, the reliability method with correlated variables was adopted to analyze the QCB, considering the high correlation between wave forces or moments. Utilizing the observed wave data in engineering field, the reliability index and failure probability of QCB were obtained. Finally, a factor Q=0.9 is given to modify the zero pressure height above SWL of QCB, and wave force partial coefficient 1.34 to the design expressions of QCB for anti-sliding, as well as 1.67 for anti-overturning, were presented.

Hydrodynamic Coefficient Investigation on a Partial Permeable Stepped Breakwater Under Regular Waves

Traditional breakwater takes the advantage of high protection performance and has been widely used.However,it contributes to high wave reflection in the seaside direction and poor water exchange capacity between open seawater and an inside harbor.Consequently,a partially permeable stepped breakwater(PPSB)is proposed to ensure safety and good water exchange capacity for an inside harbor,and a 3-D computational fluid dynamics(CFD)mathematical model was used to investigate the hydrodynamic coefficients using Reynolds-Averaged Navier-Stokes equations,Re-Normalization Group(RNG)k-εequations,and the VOF technique.A series of experiments are conducted to measure the wave heights for validating the mathematical model,and a series of dimensionless parameters considering wave and PPSB effects were presented to assess their relationships with hydrodynamic coefficients,respectively.With the increase in the reciprocal value of PPSB slope,incident wave steepness and permeable ratio below still water level(SWL),the wave reflection coefficient decreases.The wave transmission coefficient decreases with an increase in the reciprocal value of the PPSB slope and incident wave steepness;however,it increases with the increase in the permeable ratio below SWL.With increases in the reciprocal value of the PPSB slope,permeable ratio below SWL and incident wave steepness for relatively high wave period scenarios,the wave energy dissipation coefficient increases;however,it decreases slightly with increases in the incident wave steepness for the smallest wave period scenarios.Furthermore,simple prediction formulas are conducted for predicting the hydrodynamic coefficients and they are well validated with the related data.

The study on the bottom friction and the breaking coefficient for typhoon waves in radial sand ridges—the Lanshayang Channel as an example

Owing to the interactions among the complex terrain, bottom materials, and the complicate hydrodynam-ics, typhoon waves show special characteristics as big waves appeared at the high water level （HWL） and small waves emerged at low and middle water levels （LWL and MWL） in radial sand ridges （RSR）. It is as-sumed that the mud damping, sandy bed friction and wave breaking effects have a great influence on the typhoon wave propagation in this area. Under the low wave energy, a mud layer will form and transport into the shallow area, thus the mud damping effects dominate at the LWL and the MWL. And high Collins coef-ficient （c around 1） can be applied to computing the damping effects at the LWL and the MWL. But under the high wave energy, the bottom sediment will be stirred and suspended, and then the damping effects disappear at the HWL. Thus the varying Collins coefficient with the water level method （VCWL） is imple-mented into the SWAN to model the typhoon wave process in the Lanshayang Channel （LSYC） of the RSR, the observed wave data under “Winnie” （“9711”） typhoon was used as validation. The results show that the typhoon wave in the RSR area is able to be simulated by the VCWL method concisely, and a constant wave breaking coefficient （γ） equaling 0.78 is better for the RSR where wide tidal flats and gentle bed slopes exist.

An Alternative Method to Study Wave Scattering by Semi-infinite Inertial Surfaces

A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.

Experimental Study on Hydrodynamic Load Characteristics for A Typical Cross-Section of A Submerged Floating Tunnel

The typical cross-sectional form of a submerged floating tunnel plays a significant role in the dynamic response of the tunnel itself,which directly affects the overall design.In this work,a series of experiments involving wave action on a submerged floating tube cross section is reported to study its hydrodynamic load characteristics.Two typical cross section tube cylinders,circular and rectangular,are chosen.Experiments are carried out in a wave flume with waves of relatively low Keulegan-Carpenter(KC)numbers.Three relative depths of submergence of 0,0.25 and 0.5 are chosen.The measured wave forces in regular waves are used to analyze the horizontal force,vertical force and torque,and then the drag coefficient(Cd)and inertia coefficient(Cm)are derived.The results show that the drag coefficients at low KC numbers are large and decrease sharply with increasing KC number.The inertial coefficient Cm values in the vertical direction are about 70%larger than those in the horizontal direction.With an increase in aspect ratio(the ratio of the height to width of the structure),the ratio of inertia coefficient in the horizontal direction to that in the vertical direction increases remarkably.The inertia force coefficient is very sensitive to the submerged water depth and aspect ratio.The existing results may overestimate the actual force value.

Hydrodynamic Performance of A Floating Breakwater System Under the Terrain of Islands and Reefs: A 3D Experimental Study

With the acceleration of marine construction in China,the exploitation and utilization of resources from islands and reefs are necessary.To prevent and dissipate waves in the process of resource exploitation and utilization,a more effective method is to install floating breakwaters near the terrain of islands and reefs.The terrain around islands and reefs is complex,and waves undergo a series of changes due to the impact of the complex terrain in transmission.It is important to find a suitable location for floating breakwater systems on islands and reefs and investigate how the terrain affects the system’s hydrodynamic performance.This paper introduces a three-cylinder floating breakwater design.The breakwater system consists of 8 units connected by elastic structures and secured by a slack mooring system.To evaluate its effectiveness,a 3D model experiment was conducted in a wave basin.During the experiment,a model resembling the islands and reefs terrain was created on the basis of the water depth map of a specific region in the East China Sea.The transmission coefficients and motion responses of the three-cylinder floating breakwater system were then measured.This was done both in the middle of and behind the islands and reefs terrain.According to the experimental results,the three-cylinder floating breakwater system performs better in terms of hydrodynamics when it is placed behind the terrain of islands and reefs than in the middle of the same terrain.

Applying accurate gradients of seismic wave reflection coefficients (SWRC) to the inversion of seismic wave velocities

Through solving the Zoeppritz's partial derivative equations, we have obtained accurate partial derivatives of reflected coefficients of seismic wave with respect to Pand S-wave velocities.With those partial derivatives, a multi-angle inversion is developed for seismic wave velocities.Numerical examples of different formation models show that if the number of iterations goes over 10, the relative error of inversion results is less than 1%, whether or not there is interference among the reflection waves.When we only have the reflected seismograms of P-wave, and only invert for velocities of P-wave, the multi-angle inversion is able to obtain a high computation precision.When we have the reflected seismograms of both P-wave and VS-wave, and simultaneously invert for the velocities of P-wave and VS-wave, the computation precisions of VS-wave velocities improves gradually with the increase of the number of angles, but the computation precision of P-wave velocities becomes worse.No matter whether the reflected seismic waves from the different reflection interface are coherent or non-coherent, this method is able to achieve a higher computation precision.Because it is based on the accurate solution of the gradient of SWRCs without any additional restriction, the multi-angle inversion method can be applied to seismic inversion of total angles.By removing the difficulties caused by simplified Zoeppritz formulas that the conventional AVO technology struggles with, the multiangle inversion method extended the application range of AVO technology and improved the computation precision and speed of inversion of seismic wave velocities.

Experimental Study of Mooring Type Effect on the Hydrodynamic Characteristics of VLFS

Mooring system is a significant part of very large offshore floating structures(VLFS).In this paper,a single module pontoon type VLFS model considering four mooring types is studied through physical model tests to determine the effects of mooring conditions on the hydroelastic response,mooring force,incident coefficient,reflection coefficient and energy dissipation coefficient.Eight mooring cables are symmetrically arranged on both sides of the model.The floating body model satisfies the similarity of stiffness and gravity,while the cable satisfies the similarity of elasticity and gravity.The results show that the effect of mooring type on mooring force is greater than that on hydroelastic response.Increasing the initial tension of the mooring cable will reduce the amplitude of the leeward of the VLFS model.The mooring angle of the mooring cable will affect the maximum mooring force and the initial tension of the mooring line will affect the wave period in which the maximum mooring force occurs.The transmission coefficient and wave energy dissipation coefficient will change regularly with different mooring types.These results may provide a reference to facilitate the mooring design of VLFS.

Study of Electromagnetism Compatibility of Bleeper Station

Transmitted power will decrease, cross-modulate distortion and inter-modulate distortion will be caused and antenna pattern will shift if transmitted antennas are fixed together. All these will lead to the alteration of area coverage. According to the basic theory of electromagnetism compatibility a computer model is established. We do some quantitative analysis of the problems above and give total number, arrangement mode and distance between antennas of bleeper station that operate at 150 MHz. The relation of these factors above are also given. All these are basis of the arrangement of antenna group of bleeper station.

Numerical Investigations on Hydrodynamic Performance of An Open Comb-Type Breakwater Under Medium Water Levels

The comb-type breakwater(CTB)has been proposed and investigated in recent years due to its advantages in terms of deep-water adaptability,material saving and water exchanges.All existing empirical formulae for CTBs have been so far restricted to the water level above the bottom of the superstructure,which mainly occurs under the high tides or storm tides.However,based on recent engineering applications and experimental observations,the most severe conditions for CTBs are more likely to occur under a medium water level,because impulsive wave pressure may occur due to interactions between waves and the special chamber in CTBs.Meanwhile,during the most of construction and operation periods,the CTBs are mainly working under the medium water levels,i.e.,water levels below the bottom of the superstructure.In this study,the effects of main influence parameters on the horizontal wave force coefficient and wave transmission coefficient for open CTBs(with partially immersed side plates)under medium water levels were investigated based on a 3D numerical wave flume and corresponding empirical formulae were proposed.It is indicated that the location of the side plate related to the main caisson has significant influence on the hydrodynamic performance of CTBs.In engineering applications,the location of the side plate can be designed at b/L≤0.15 or b/L≥0.3(where b is the distance between the side plate and the front face of the main caisson and L is the incident wave length)for efficiently lowering the horizontal wave force and wave transmission.The flow mechanism of impulsive wave force on CTBs was revealed based on synchronous analyses of flow fields and pressure distribution.Through appropriate design of the height of the superstructure according to H/hD≤1.0 or H/hD≥1.5(where H is the incident wave height and hD is the distance between the still water level and the bottom of the superstructure),the likely impulsive wave pressure on the side plate can also be diminished.

Global existence of solutions of the critical semilinear wave equations with variable coefficients outside obstacles

In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coefficients case, we show that the energy cannot concentrate at any point (t, x) ∈ (0, ∞) ×Ω. For that purpose, following Ibrahim and Majdoub's paper in 2003, we use a geometric multiplier similar to the well-known Morawetz multiplier used in the constant coefficients case. We then use the comparison theorem from Riemannian geometry to estimate the error terms. Finally, using the Strichartz inequality as in Smith and Sogge's paper in 1995, we confirm the global existence.

Weighted L^2-Estimates of Solutions for Damped Wave Equations with Variable Coefficients

The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l < 1, ρ(x) is the distance function of the metric g = A^(-1)(x) on IR^n. The authors show that these weighted L^2-estimates are closely related to the geometrical properties of the metric g = A^(-1)(x).

The influence of perforated plates on wave transmission and hydrodynamic performance of pontoon floating breakwater

In this study, a perforated pontoon floating breakwater（FB） consisting of an impermeable plate and a perforated plate was designed to untangle the effect of a perforated plate on wave transmission and hydrodynamic performance of floating breakwater. A series of 2-D physical model experiments were conducted to measure the wave transmission coefficient, tension acting on the mooring line, and motion response of FB under a regular wave. The experimental results of the motion responses and mooring lines indicated that the new perforated plate was evidently effective. Furthermore, the study also discussed and analyzed the influence of the perforated plate on transmission coefficients. The experimental results showed that the new perforated plate did not lead to obvious improvement in the transmission performance

LABORATORY STUDIES ON WAVE FORCE OF COASTAL STRUCTURES MADE OF FLAT GEOTUBES

Flat geotubes are widely used for coastal structures such as seawalls, breakwaters and sightseeing groins, etc.. However, the understanding of the stable mechanism involved in the wave-structure interactions should be deepened, and one of the important work is to clarify the stress state of the structure under the wave action. In this article, wave force acting on coastal structures made of flat geotube is experimentally investigated. The required drag, inertia and lift coefficients are especially analyzed from the results of hydraulic model experiments specially designed for geotube structure. Several types of structures made of flat geotubes under wave action have been tested in order to understand the stress state of the geotube fixed to force transducer within different structures. Experimental results show that the wave-induced forces on the instrumented geotube are markedly influenced by wave elements. Meanwhile, the magnitude of horizontal force of adjoining geotube is different at the same time.

Wave Interaction with an Emerged Porous Media

In this paper,we study wave interaction with an emerged porous media.The governing equation is shallow water equations with a friction term of the linearized Dupuit-Forcheimer’s formula.From the continuity of surface and horizontal flux,we derived the wave reflection and transmission coefficient formulas.They are similar with the corresponding formulas of the submerged solid bar breakwater.We solve the equations numerically using finite volume method on a staggered grid.The numerical wave reduction in the porous media confirms the analytical wave transmission curve.

Suppression of seismic surface waves based on adaptive weighted super-virtual interferometry

For land seismic surveys, the surface waves are the dominant noises that mask the effective signals on seismograms.The conventional methods isolate surface waves from the effective signals by the differences in frequencies or apparent velocities,but may not perform well when these differences are not obvious. Since the original seismic interferometry can only predict inter-receiver surface waves, we propose the use of super-virtual interferometry(SVI), which is a totally data-driven method, to predict shot-to-receiver surface waves, since this method relieves the limitation that a real shot should collocate with one of the receivers for adaptive subtraction. We further develop the adaptive weighted SVI(AWSVI) to improve the prediction of dispersive surface waves, which may be generated from heterogeneous media at the near surface. Numerical examples demonstrate the effectiveness of AWSVI to predict dispersive surface waves and its applicability to the complex near surface. The application of AWSVI on the field data from a land survey in the east of China improves the suppression of the residual surface waves compared to the conventional methods.