In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher t...In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher than 4 was not feasible in the past with the original GN equations. The GN equations for shallow water waves were simplified here, which make the application of high level （higher than 4） equations feasible. The linear dispersion relationships of the first seven levels were presented. The accuracy of dispersion relationships increased as the level increased. Level 7 GN equations are capable of simulating waves out to wave number times depth kd 〈 26. Numerical simulation of nonlinear water waves was performed by use of Level 5 and 7 GN equations, which will be presented in the next paper.展开更多
In this paper,a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode(BDRM)theory is presented.According to the BDRM theory,the contribution of the beam displacement and the t...In this paper,a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode(BDRM)theory is presented.According to the BDRM theory,the contribution of the beam displacement and the time delay to the group velocity can be easily considered in a shallow water waveguide.A more accurate dispersion formula is derived by using the cycle distance formula to calculate the group velocity of normal modes.The derived dispersion formula can be applied to the homogeneous shallow water waveguide.Theoretically,the formula is related to the phase of the reflection coefficient and suitable for various bottom models.Furthermore,based on the derived dispersion relation,the modified warping operator is developed to obtain linear modal structures.For the Pekeris model,the formulae for the phase of the reflection coefficient are derived in this work.By taking account of the effect of the bottom attenuation on the reflection coefficient,the formula for the phase of the reflection coefficient including the bottom attenuation is obtained for the Pekeris model with a lossy bottom.Performance and accuracy of different formulae are evaluated and compared.The numerical simulations indicate that the derived dispersion formulae and the modified warping operator are more accurate.展开更多
基金Supported by the Special Fund for Basic Scientific Research of Central Colleges Harbin Engineering University(Harbin)the National Natural Science Foundation of China+1 种基金Doctor Subject Foundation of the Ministry of Education of Chinathe"111"project(B07019)
文摘In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher than 4 was not feasible in the past with the original GN equations. The GN equations for shallow water waves were simplified here, which make the application of high level （higher than 4） equations feasible. The linear dispersion relationships of the first seven levels were presented. The accuracy of dispersion relationships increased as the level increased. Level 7 GN equations are capable of simulating waves out to wave number times depth kd 〈 26. Numerical simulation of nonlinear water waves was performed by use of Level 5 and 7 GN equations, which will be presented in the next paper.
基金supported by the National Natural Science Foundation of China(Grant Nos.11174312 and 11074269)
文摘In this paper,a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode(BDRM)theory is presented.According to the BDRM theory,the contribution of the beam displacement and the time delay to the group velocity can be easily considered in a shallow water waveguide.A more accurate dispersion formula is derived by using the cycle distance formula to calculate the group velocity of normal modes.The derived dispersion formula can be applied to the homogeneous shallow water waveguide.Theoretically,the formula is related to the phase of the reflection coefficient and suitable for various bottom models.Furthermore,based on the derived dispersion relation,the modified warping operator is developed to obtain linear modal structures.For the Pekeris model,the formulae for the phase of the reflection coefficient are derived in this work.By taking account of the effect of the bottom attenuation on the reflection coefficient,the formula for the phase of the reflection coefficient including the bottom attenuation is obtained for the Pekeris model with a lossy bottom.Performance and accuracy of different formulae are evaluated and compared.The numerical simulations indicate that the derived dispersion formulae and the modified warping operator are more accurate.
