MATHEMATICAL MODELING IN MITIGATING THE HAZARDOUS EFFECT OF TSUNAMI WAVES IN THE OCEAN A Priori Analysis and Timely On-Line Forecast

Governing equations including full non-linearity are derived from the Euler equations of mass and momentum continuities assuming a long wave approximation, negligible friction and interracial mixing. The linearized equations for two-layers are analytically solved using the Fourier transform. A numerical model is developed using the staggered leap-frog scheme for computation of water level and discharge in one dimensional propagation. Results of the numerical model are venfled by comparing with the analytical solution for different boundary conditions. Good agreements between analytical and numerical model are observed for the boundary conditions using the characteristics method to estimate the representative celerity at the previous time step. The stability condition is discussed and it was found that CFL stability condition considering fixed interface and top surface wave celebrities as the physical celerity is not directly applicable. A modified stability condition taking the maximum celerity among them, At< & / max(cl, C2), is proposed. The properties of two-layers long waves is discussed through numerical simulations with different values of u ( ratio of density of fluid in an upper layer to a lower one) and ~ (ratio of water depth in a lower layer to an upper one). It is suggested that as a increases amplification of top surface decreases and vice versa. Again as ~ increases amplification of a top surface also increases and vice versa.

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