Long-wave Runup

UNDER CONSTRUCTION

Overview

The goal of this verification test to asses the model performance in simulating nonlinear runup/rundown over a plane slopt. Carrier et al. (2003) presented an analytical solution to the nonlinear shallow water equations over a plane slope for several initial wave forms. Here the analytical solution for a the initial wave form given by leading-depression N-wave is used.

Initial Condition

The bed has a constant slope of 1/10 with the initial shoreline located at x=0. Figure 1 shows the initial water level (is given by a leading depression N-wave (characteristic of the waves caused by submarine landslides). The initial current velocity is equal to zero everywhere.

Figure 1. Initial water level

Model Setup

The computational grid has a 3 m resolution for x<300 and increases to 10 m with an aspect ratio of 1.05. The general model parameters used in the simulation are shown in Table 1.

Table 1. Model Parameters

Parameter	Value
Time step	0.1 s
Ramp period	0.0 s
Drying depth	0.01 m
Wall friction	Off
Mixing terms	Off
Manning's coefficient	0.0

Results

Figure 2 shows a comparison of computed and analytical water surface elevations near the shoreline at 4 different time steps. The goodness of fit statistics are shown in Table 2.

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Figure 2. Comparison of calculated and analytical water levels for different time steps.

Table 2. Goodness of Fit Statistics

Time, s	RRMSE, %	RMAE, %	R^2	Bias, m
160	3.7	3.8	0.999	-0.012
175	6.5	5.9	0.997	-0.113
220	4.6	5.4	1.000	-0.066

• For a definition of the goodness of fit statistics see Goodness of fit statistics.

A comparison of the calculated and analytical shoreline position are shown in Figure 3.

Figure 3. Time series comparison of calculated and analytical shoreline position.

References

• Carrier, G., Wu, T.T., and Yeh, H. (2003). "Tsunami runup and draw-down on a plane beach", Journal of Fluid Mechanics, 475, 79-99.

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