The theory of three-layer density-stratified ideal fluids is examined with a view toward its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Viríssimo and Milewski are also discussed.

考察了三层密度分层理想流体的理论，以期将其推广到n-层案例。重点是结构特性，特别是对于刚性上盖约束的情况。我们证明了长波无色散极限是一个不接受黎曼不变量的拟线性方程组。我们为层平均一维模型配备了自然哈密顿结构，该结构是从 Benjamin 提出的完整二维方程的连续密度分层结构中通过适当的简化过程获得的。对于水平刚性边界之间的横向无界流体，重新审视关于水平总动量不守恒的悖论，并且表明导致它的压力不平衡可以通过相对于其两层对应物的三层设置而加剧. x的生成器n层设置中的平移对称性也由适当的哈密顿形式主义确定。还讨论了 Boussinesq 极限和 de Melo Viríssimo 和 Milewski 最近引入的一系列特殊解。