A non-linear numerical model for stratified tsunami waves and its application

A non-linear numerical model is developed for the computation of water level and discharge for the propagation of a unidirectional two-layered tsunami wave. Four governing equations, two for each layer, are derived from Euler’s equations of motion and continuity, assuming a long wave approximation, negligible friction and no interfacial mixing. A numerical model is developed using a staggered Leap-Frog scheme. The developed nonlinear model is compared with an existing validated linear model developed earlier by the author for different non-dimensional wave amplitudes. The significance of non-linear terms is discussed. It is found that for simulations of the interface wave amplitude, the effect of non-linear terms is not significant. However, for the simulation of the top surface, the effect of non-linear terms is significant for higher wave amplitudes, and insignificant for lower wave amplitudes. Developed non-linear numerical model is used for the case of a progressive internal wave in an inclined bay. It is found that the effect of an adverse bottom slipe towards the direction of wave propagation is to amplify the wave. This amplification depends on the steepness of slope as well as the ratio of densities of upper layer fluid to lower layer fluid (α). Amplification increases with slope. For higher values of α, amplification of the top and interface surface decreases, which is reasonable. It is also found that even for a 4 percent density difference between upper layer and lower layer, amplification of the top surface will be twenty times higher than amplification in the non-stratified case. The model can be applied confidently to simulate the basic features of different practical problems, similar to those investigated in this study.