Research On The New Algorithm Of MCC-FS Internal Wave Theory And Free Surface Effect

In this paper,based on the internationally popular strong nonlinear MCC internal wave theory(including MCC-RL internal wave theory under rigid cover approximation and MCC-FS internal wave theory considering free surface effect),the large amplitude internal solitary waves between two layers of fluid in shallow configuration and deep configuration are studied.At present,on the research of MCC internal wave theory,because the dispersion relation of MCC internal wave theory has not been studied,some researchers mistakenly believe that MCC internal wave theory can accurately describe the internal wave in deep configuration,and the original steady-state solution method for solving MCC-FS internal wave theory can not directly obtain the relevant information of velocity field.Therefore,firstly,the dispersion relation of MCC internal wave model is studied in this paper.Through the linearization analysis of MCC internal wave model,the linear dispersion relationship is obtained,and compared with the accurate linear dispersion relationship,the applicable range of MCC internal wave model is obtained.Secondly,this paper proposes a new steady-state solution algorithm for MCC-FS internal wave model,through which the internal wave profile,free surface wave profile and velocity field can be obtained at the same time.Finally,the applicability of MCC internal wave theory in the deep configuration is studied.The results show that,based on the linear dispersion relation of MCC internal wave theory,the effect of density ratio between the upper and lower layers is small,but the influence of depth ratio of upper and lower fluid is great.MCC internal wave theory is only applicable to internal solitary wave in shallow configuration,and it is difficult to accurately describe internal solitary wave in deep configuration.At the same time,considering the free surface effect,the wave profiles of the internal solitary wave becomes narrower and the wave speed is slower,which also has an impact on the velocity field.At the same time,the free surface will stimulate the upward convex solitary wave,and the amplitude of the solitary wave can not be ignored.