Research On The Effect Of Slowly Varying Topography On Waves' Transmission Based On Boussinesq Equations

This paper focused on the effect of slowly varying topography on regular wave.The model for wave propagating over a pitch of slowly varying topography had been set up by linear perturbation method on basis of Boussinesq equations, and then the theory solutions for both infinite sandbar topography and finite sandbar topography were derived through solving system of partial differential equations by integral-transform method, in addition, the solution for ordinary slowly topography was derived on basis of the solution for finite sandbar topography by replace the function of the ordinary slowly topography with Fourier series .Discussed the reflection and transmission effect on basis of the solutions for wave passing by the sandbar topography, and obtained the reflection coefficient formula when the Bragg reflect occurs. The value of prediction formula was compared with both the potential flow theory result and experiment observation data, and the result demonstrated that the Boussinesq equations of this paper is appropriate for describing the Bragg reflection within a certain relative water depth . what's more, the comparisons among several Boussinesq equations about their characters of depicting the Bragg reflection showed that the different equation is appropriate for different range of water depth.Derived the first order wave solution for regular wave propagation over rectangular channel and Studied the impact of relative wave length, the channel-width and channel depth on the transmission coefficient and the reflect coefficient, in addition, gave the reflection coefficient formula when the reflect wave resonance occurs. The results show when the channel-width is odd times of the incident wavelength the reflect effect is greatest, while when the channel width is equivalent to even times of the incident wave the reflect wave tends to zero.