CAJ | 학술논문

为在数学模型中考虑渗透性介质对波浪传播的影响，在多孔介质流体运动方程中引入拖曳阻力和惯性力，引出Laplace方程和边界条件．对控制方程无因次化，并以自由表面处速度势和交界面上的速度势进行幂级展开，推导了以静止水平面上速度、交界面上速度和波面升高3个变量表达的Boussinesq方程．给出积分平均速度或任一水深处速度与以上2个速度之间的关系式，进而推导出另外2个Boussinesq方程，并通过引入高阶色散项对方程进行加强以拓展其适用水深．对方程进行了理论分析，将相速度及衰减率与解析解进行了比较，发现四阶色散性方程具有最佳精度．不考虑渗透影响时，在2％误差下，四阶方程可适用最大无因次水深达到5．82．该高阶Boussinesq方程不仅可用于研究渗透海床上波浪的传播变形，也适用非渗透海床上的深水波浪传播变形．
위재수학모형중고필삼투성개질대파랑전파적영향，재다공개질류체운동방정중인입타예조력화관성력，인출Laplace방정화변계조건．대공제방정무인차화，병이자유표면처속도세화교계면상적속도세진행멱급전개，추도료이정지수평면상속도、교계면상속도화파면승고3개변량표체적Boussinesq방정．급출적분평균속도혹임일수심처속도여이상2개속도지간적관계식，진이추도출령외2개Boussinesq방정，병통과인입고계색산항대방정진행가강이탁전기괄용수심．대방정진행료이론분석，장상속도급쇠감솔여해석해진행료비교，발현사계색산성방정구유최가정도．불고필삼투영향시，재2％오차하，사계방정가괄용최대무인차수심체도5．82．해고계Boussinesq방정불부가용우연구삼투해상상파랑적전파변형，야괄용비삼투해상상적심수파랑전파변형．
To consider the effect of porous media on wave propagation in mathematical model, the drag resistance force and inertial force of the porous media were included in the fluid motion, and the corresponding Laplace equa-tion and boundary conditions were given. First cancelling out the dimensions of control equations, and then starting from the velocity potentials in still water depth and in the interface to conduct exponential expansion, thus a Bouss-inesq model was derived with the expressions of three variables, including two velocities in still water depth and in the interface, and wave surface lifted height. The other two sets of Boussinesq equations were also derived, which were formulated using integrated mean velocities, or relational expression of the velocity in arbitrary water depth and the above-mentioned two velocities. The high-order dispersion term embodied in the newly derived equations for the purpose of expanding it to deeper water depth was theoretically analyzed, and phase speed and damping rate were compared against the analytical solutions. The fourth-order dispersive model was found to be the most accurate one. Neglecting the effect of porous seabed, the fourth-order Boussinesq model had a promising dispersive property and can be applicable to maximum water depth =5.82 within 2% error. The high-order Boussinesq model is thus expec-ted to be applicable to wave propagation not only over permeable seabed but also over deep water evolution over im-permeable seabed.