The theory of nonlinear interfacial-internal wave propagation in three-layer fluid systems

Based on the small steepness parameter assumption, the three-layer incompressible, inviscid and irrotational fluid system of arbitrary depth is discussed by using the perturbation method, and a unified theory of nonlinear interfacial-internal wave propagation and the approximate nonlinear evolution equations (NEEs) for interfacial-internal elevations are given on the basis of the rigid upper boundary and the flat impermeable bottom. At last we also discuss on NEEs arising from various limiting cases of fluid depth. It is also noted that the theories obtained from the present work include the theoretical results derived by Yoshimasa Matsuno (1993) as special cases.