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为了描述水波和强烈的环境流在非平整海底上的相互作用，运用无旋运动的Ｌａｇｒａｎａｇｉａｎ变分原理，对经典的Ｂｅｒｋｈｏｆｆ缓坡方程进行了改进．假定水流沿水深方向基本上保持均匀性，这正如潮流运动的特征．海底地形由慢变、快变两个分量叠加构成：慢变分量满足缓坡逼近假定，快变分量的波长与表面波波长为同一量级，但其振幅小于表面波的振幅．在以上假定条件下，得到了适用于非平整海底的推广型浅水方程和应用性更加广泛的波－流－非平整海底相互作用的一般缓坡方程，并且从理论上证明一般缓坡方程包含了以下３种著名的缓坡型方程：经典的 Ｂｅｒｋｈｏｆｆ缓坡方程；波－流相互作用的 Ｋｉｒｂｙ缓坡方程、 Ｄｉｎｇｅｍａｎｓ关于沙纹海底的缓坡方程．最后，通过与Ｂｒａｇｇ反射实验数据的比较，表明该模型可以准确地反映快变海底的典型地貌特征．
In order to describe the interaction of water waves and intense environmental flow on non-flat seafloor, the classical Berkhoff gentle slope equation is improved by Lagrangeagian variational principle of non-rotating motion. It is assumed that the water flow substantially maintains its uniformity along the depth of water, just as the tidal current is characterized. The submarine topography consists of superposition of slowly varying and fast changing components: the slowly variable component satisfies the assumption of gentle slope approximation that the wavelength of the fast component is the same magnitude as the surface wave but its amplitude is smaller than the amplitude of the surface wave. Under the above assumptions, the general gentle slope equation applicable to the generalized shallow-water equation of non-flat seafloor and the more general wave-flow-non-flat seafloor interaction is obtained and it is theoretically proved that the general mild-slope equation contains the following three The well-known gentle-slope equations: the classical Berkhoff gentle slope equation; the Kirby gentle slope equation for wave-flow interaction; and the Dingemans gentle slope equation for sandy sea floor. Finally, the comparison with experimental data of Bragg reflection shows that the model can accurately reflect the typical topographic features of fast changing seabed.