Propagation of distant tsunamis over slowly varying topography

Abstract

[1] A new two-dimensional finite difference numerical scheme is developed to simulate the propagation of distant tsunamis over slowly varying topography with improved dispersion effect of waves. The new scheme solves the shallow water equations on a uniform grid system. However, the actual computation is made on a hidden grid system whose grid size is adjustable according to the condition required to satisfy local dispersion relationships of waves for varying water depth. The present model is tested for the cases of two-dimensional propagation of an initial Gaussian hump over various uniform water depth regions. For a varying topography, a one-dimensional test is conducted. The tests show that accuracy of the numerical model is improved significantly over that of the conventional finite difference models. Finally, the present model is applied to the simulation of a historical tsunami event. The numerical result shows that the submerged rise and ridge play an important role of a waveguide for the tsunamis propagating over that topography.

Capturing Physical Dispersion Using a Nonlinear Shallow Water Model

“…In the first case, the grid size is selected according to Equation (1) which provides ∆x =1280 m, given h = 600 m (Figure 3a,b) and ∆x = 4287 m for h = 2100 m (Figure 3c,d). In the second case, the grid size is selected as ∆x = 2500 m according to [5]. Figure 3a,c (θ = 0 • ) show that when Equation (1) is satisfied, NAMI DANCE's solutions are closer to the analytical results of [27] and Yoon's model [5], while, in diagonal propagation (Figure 3b,d), Yoon's [5] solution leads to more accurate results.…”

“…The accuracy of the numerical solution of NLSWEs in NAMI DANCE is tested through simulation of a Gaussian hump tsunami as initial free surface [5,6] on a constant uniform bottom. In this section, the water surface displacement at certain time steps along horizontal, vertical and diagonal directions are computed and compared with the analytical solution of the linear BTEs [3,27].…”

“…Two different propagation axes (θ = 0 • and θ = 45 • ) as well as two different depths (h = 600 m and h = 2100 m) are investigated using a uniform bottom domain. The time step is not strongly influenced by a ratio for dispersion and hence, a constant value of ∆t = 6 s is used following the work of Yoon [5]. The grid size ∆x is constant according to Equation (1) and the memory capacity of the hardware/software.…”

“…This helped to control the inherent numerical dispersion errors of the scheme to cover the effects of physical frequency dispersion for the propagation of tsunami in bathymetries with constant water depth. Later, the approach was extended by Yoon [5] to a slowly varying bathymetry. He proposed a hidden grid system in which the local water depth determines the grid size for the capturing of dispersion effects.…”

“…A brief explanation of NAMI DANCE is presented in the next section. In this study, the ability of NAMI DANCE to capture dispersion effects is examined with several bathymetry profiles or case studies taken from the literature [5,6]. The bathymetry profiles are: (i) uniform bottom, (ii) slowly varying depth and (iii) submerged circular shoal.…”