This study investigates the hydrodynamic performance of a submerged two layer horizontal plate breakwater. The plate thickness is considered as non-zero in the study. In the context of linear potential theory, an anal...This study investigates the hydrodynamic performance of a submerged two layer horizontal plate breakwater. The plate thickness is considered as non-zero in the study. In the context of linear potential theory, an analytical solution for interaction of water waves with the plates is obtained using the matched eigenfunction expansion method. The solution consists of a symmetric part and an antisymmetric part. Its validity is confirmed by comparing the numerical results of reflection and transmission coefficients for limiting cases with previous predictions. Numerical examples are given to examine the major factors that affect the reflection and transmission coefficients of the plates. Some useful results are presented for engineering design.展开更多
Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset（AVO） analysis and inversion in exploration geophysics.However,the weak properties contrast hypothesi...Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset（AVO） analysis and inversion in exploration geophysics.However,the weak properties contrast hypothesis of those linearized approximate equations leads to big errors when the two media across the interface vary dramatically.To extend the application of AVO analysis and inversion to high contrast between the properties of the two layers,we derive a novel nonlinearized high-contrast approximation of the PP-wave reflection coefficient,which establishes the direct relationship between PPwave reflection coefficient and P-wave velocities,S-wave velocities and densities across the interface.（A PP wave is a reflected compressional wave from an incident compressional wave（P-wave）.） This novel approximation is derived from the exact reflection coefficient equation with Taylor expansion for the incident angle.Model tests demonstrate that,compared with the reflection coefficients of the linearized approximations,the reflection coefficients of the novel nonlinearized approximate equation agree with those of the exact PP equation better for a high contrast interface with a moderate incident angle.Furthermore,we introduce a nonlinear direct inversion method utilizing the novel reflection coefficient equation as forward solver,to implement the direct inversion for the six parameters including P-wave velocities,S-wave velocities,and densities in the upper and lower layers across the interface.This nonlinear inversion algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way.Three examples verified the feasibility and suitability of this novel approximation for a high contrast interface,and we still could estimate the six parameters across the interface reasonably when the parameters in both media across the interface vary about 50%.展开更多
The factors affecting the reflection and transmission coefficient of the ionosphere have been analyzed.These factors include wave frequency,incident angle,geomagnetic inclination,electron density and collision frequen...The factors affecting the reflection and transmission coefficient of the ionosphere have been analyzed.These factors include wave frequency,incident angle,geomagnetic inclination,electron density and collision frequency in the ionosphere.The ionosphere refractive index is also analyzed.The ionosphere above 70 km is considered to be homogeneous and anisotropic,and the reflection and transmission coefficient matrix is calculated using matrix method.Simultaneously the Booker quartic equation is solved to get the refractive index in the ionosphere.The results show that when the wave frequency is higher,it is easier to penetrate into the ionosphere from its bottom boundary and the propagation attenuation in the ionosphere is smaller.TE（traverse electric） wave and TM（traverse magnetic） wave can both penetrate into the ionosphere with a small incident angle,while TE wave can hardly transmit into the ionosphere when the incident angle is large.The transmission coefficient decreases as the geomagnetic inclination increases.TE and TM wave cannot penetrate into the ionosphere at magnetic equator.When the electron collision frequency is higher,it is easier for VLF wave to penetrate into the ionosphere and the attenuation of ordinary wave is weaker,which may be caused by the energy transportation between the waves and the particles.The ordinary（O） wave experiences severer attenuation than extraordinary（X） wave,and X wave is a penetration mode whereas O wave is a non-penetration mode in the ionosphere.All the results indicate that VLF wave with higher frequency is easier to penetrate into the ionosphere and to be recorded by the satellites at high latitude.It is hard for ULF and the lower frequency VLF wave to transmit into the ionosphere directly for the severe reflection and attenuation.It may transmit into the ionosphere with a small incident angle due to the nonlinear effect,for example,the interaction between the waves and the particles or cross modulation,and then propagate along the whistle duct with sma展开更多
The volume of fluid (VOF) method is presented to determine the reflection coefficient of and the total horizontal wave force on perforated caisson breakwaters. The present numerical model is compared with a linear ana...The volume of fluid (VOF) method is presented to determine the reflection coefficient of and the total horizontal wave force on perforated caisson breakwaters. The present numerical model is compared with a linear analytic solution obtained by Sahoo et al. (2000). Also this model is verified with the authors′ laboratory data. It is found that the numerical model is in good agreement with the regression equations obtained from the experimental data. The present numerical method is further discussed to relate porosity, the relative wave absorbing chamber depth, the reflection coefficient of perforated caissons and the total horizontal force on them.展开更多
The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is applicable to both regular and irregular trains; of waves. The wave data series measured with two wave ga...The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is applicable to both regular and irregular trains; of waves. The wave data series measured with two wave gauges in the experiments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily obtained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient. The reflection performance of the physical model can be estimated exactly without calculation of wave height and phase difference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conducted and compared with Goda's method and satisfactory results are obtained.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.50739004, 50609001)the Natural Science Foundation of Shandong Province (Grant No.Q2008F01)the specialized Research Fund for the Doctoral Program of High Education (Grant No. 200804231006)
文摘This study investigates the hydrodynamic performance of a submerged two layer horizontal plate breakwater. The plate thickness is considered as non-zero in the study. In the context of linear potential theory, an analytical solution for interaction of water waves with the plates is obtained using the matched eigenfunction expansion method. The solution consists of a symmetric part and an antisymmetric part. Its validity is confirmed by comparing the numerical results of reflection and transmission coefficients for limiting cases with previous predictions. Numerical examples are given to examine the major factors that affect the reflection and transmission coefficients of the plates. Some useful results are presented for engineering design.
基金the sponsorship of the National 973 Program of China (2013CB228604)the National Grand Project for Science and Technology (2011ZX05030-004-002, 2011ZX05019-003 and 2011ZX05006-002) for funding this research+2 种基金the support of the Australian and Western Australian Governments and the North West Shelf Joint Venture Partnersthe Western Australian Energy Research Alliance (WA:ERA)Foundation from Geophysical Key Lab of SINOPEC (WTYJYWX2013-04-01)
文摘Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset（AVO） analysis and inversion in exploration geophysics.However,the weak properties contrast hypothesis of those linearized approximate equations leads to big errors when the two media across the interface vary dramatically.To extend the application of AVO analysis and inversion to high contrast between the properties of the two layers,we derive a novel nonlinearized high-contrast approximation of the PP-wave reflection coefficient,which establishes the direct relationship between PPwave reflection coefficient and P-wave velocities,S-wave velocities and densities across the interface.（A PP wave is a reflected compressional wave from an incident compressional wave（P-wave）.） This novel approximation is derived from the exact reflection coefficient equation with Taylor expansion for the incident angle.Model tests demonstrate that,compared with the reflection coefficients of the linearized approximations,the reflection coefficients of the novel nonlinearized approximate equation agree with those of the exact PP equation better for a high contrast interface with a moderate incident angle.Furthermore,we introduce a nonlinear direct inversion method utilizing the novel reflection coefficient equation as forward solver,to implement the direct inversion for the six parameters including P-wave velocities,S-wave velocities,and densities in the upper and lower layers across the interface.This nonlinear inversion algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way.Three examples verified the feasibility and suitability of this novel approximation for a high contrast interface,and we still could estimate the six parameters across the interface reasonably when the parameters in both media across the interface vary about 50%.
基金supported by Chinese National Science and Technology Support Pro-gram (2008BAC35B01)Basic Research Project from Institute of Earthquake Science,China Earthquake Ad-ministration (02092408)
文摘The factors affecting the reflection and transmission coefficient of the ionosphere have been analyzed.These factors include wave frequency,incident angle,geomagnetic inclination,electron density and collision frequency in the ionosphere.The ionosphere refractive index is also analyzed.The ionosphere above 70 km is considered to be homogeneous and anisotropic,and the reflection and transmission coefficient matrix is calculated using matrix method.Simultaneously the Booker quartic equation is solved to get the refractive index in the ionosphere.The results show that when the wave frequency is higher,it is easier to penetrate into the ionosphere from its bottom boundary and the propagation attenuation in the ionosphere is smaller.TE（traverse electric） wave and TM（traverse magnetic） wave can both penetrate into the ionosphere with a small incident angle,while TE wave can hardly transmit into the ionosphere when the incident angle is large.The transmission coefficient decreases as the geomagnetic inclination increases.TE and TM wave cannot penetrate into the ionosphere at magnetic equator.When the electron collision frequency is higher,it is easier for VLF wave to penetrate into the ionosphere and the attenuation of ordinary wave is weaker,which may be caused by the energy transportation between the waves and the particles.The ordinary（O） wave experiences severer attenuation than extraordinary（X） wave,and X wave is a penetration mode whereas O wave is a non-penetration mode in the ionosphere.All the results indicate that VLF wave with higher frequency is easier to penetrate into the ionosphere and to be recorded by the satellites at high latitude.It is hard for ULF and the lower frequency VLF wave to transmit into the ionosphere directly for the severe reflection and attenuation.It may transmit into the ionosphere with a small incident angle due to the nonlinear effect,for example,the interaction between the waves and the particles or cross modulation,and then propagate along the whistle duct with sma
文摘The volume of fluid (VOF) method is presented to determine the reflection coefficient of and the total horizontal wave force on perforated caisson breakwaters. The present numerical model is compared with a linear analytic solution obtained by Sahoo et al. (2000). Also this model is verified with the authors′ laboratory data. It is found that the numerical model is in good agreement with the regression equations obtained from the experimental data. The present numerical method is further discussed to relate porosity, the relative wave absorbing chamber depth, the reflection coefficient of perforated caissons and the total horizontal force on them.
基金This project was financially supported by the Trans-Century Training Program Fund for the Talent,Ministry of Education of China.
文摘The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is applicable to both regular and irregular trains; of waves. The wave data series measured with two wave gauges in the experiments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily obtained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient. The reflection performance of the physical model can be estimated exactly without calculation of wave height and phase difference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conducted and compared with Goda's method and satisfactory results are obtained.
