Governing equations for multi-layered tsunami waves

In order to develop generalized governing equations for multi-layered long wave system, a three layer system was considered. It was anticipated that equations for top layer and bottom layer will be independent on number of intermediate layer(s) and equation for intermediate layer will be generalized depending on number of intermediate layers. However, from derived equations, it is found that only top layer equations are independent of number of intermediate layers; equations for all other layers are dependent on number, extent and density of intermediate layer(s). Momentum and continuity equations for the top layer are exactly same as in the case of earlier developed governing equations for two layered system. Continuity equation for the bottom layer is also exactly same as in the case of two-layered system. Momentum equation for the bottom layer is dependent on extent and density of top layer as well as all intermediate layers. Continuity equation for intermediate layer is affected by levels of immediate bottom layer. Momentum equation for the intermediate layer is affected by extent and density of upper layer(s). Six governing equations, two for each layer are derived from Euler equations of motion and continuity, assuming long wave approximation, negligible friction and interfacial mixing. This paper depicts details derivations of the governing equations.