TSUNAMI RESEARCH GROUP
Indian Ocean Tsunami of December 26, 2004.
Wave Dispersion Study
Numerical models: Non-Linear Shallow Water, nonlinear Boussinesq and Navier-Stokes and volume of fluid method.
Description: Here we present a numerical study which takes into account wave dispersion effects. The study has been carried out in the Indian Ocean to reproduce the initial stage of wave propagation of the tsunami event that occured on December 26, 2004. Three different numerical models are used: the nonlinear shallow water (NLSW) (nondispersive), the nonlinear Boussinesq (NLB), and the Navier-Stokes aided by the volume of fluid method to track the free surface (FNS-VOF). Numerical model results are compared against each other and some important differences are observed in the wave patterns, i.e., the development in time of the wave front is shown to be strongly connected to the dispersion effects.
Reference:
Horrillo J., Kowalik Z. and Shigihara Y. 2006 Wave Dispersion Study in the Indian Ocean-Tsunami
of December 26, 2004. Marine Geodesy, 29:, 149-166.
(Download PDF file, size: 3.32MB)
AMATEUR VIDEO -PATONG BEACH THAILAND-
dispersion effect?
Note: Although we can not assure that the approaching waves are result of dispersion effects, the amateur video clearly showed two consecutive waves, the last one rode over the flooding of the preceding one 13 sec later. The last wave encountered a higher sealevel (runup) still propagating landward. We can assume that subsequent waves as they runup over the flooded region impinge on structures with higher sea level and speed. Therefore, we can guess that dispersion consideration in numerical models is necessary for accurate prediction and hazard mitigation, since dispersion can produce significant differences in coastal runup. (Download. MOV file size: 18MB)
MODEL SETUP
Figure 1. Indian Ocean bathymetry, initial free surface deformation and location of wave transect.
MODEL COMPARISON
Wave propagation along Transect A-A
Note: Tsunami propagation along transect A-A as computed by three
different methods, namely: Nonlinear shallow water (NLSW), nonlinear Boussinesq (NLB) and
Full Navier-Stokes (FNS) method.
General features of the wave evolution agreed very well in all approaches.
However, some differences in reproducing the dispersion phenomena become more noticeable as time advances.
The wave dispersion is evident according to NLB and FNS results as a train of wave which comprises
multiple amplitudes and frequency components is formed immediately behind the leading wave.
Major wave features are well reproduced by the NLSW method with exception of the train of waves.
The leading NLSW wave is taller and shifted forward in space in relation to the dispersive solutions.
The nondispersive NLSW approach overpredicts by 28% the wave height at time 2 h 5 min.
A slight advance in time (2 min 15 s) of the NLSW leading wave crest is observed as well.
However, the wave front tip of the NLSW leading wave matches very well to its counterpart.
This reaffirms the use of NLSW as an accurate approximation for determining the tsunami arrival time.
The NLB train which follows the leading wave is shifted forward in time with
respect to FNS-VOF train. The shift increases in time as the wave diminishes in amplitude and length as shown
in the movie. Although the second, third and subsequent NLB model waves shift slightly forward in relation to the
FNS results, the NLB model predicts well the wave height, wave length and number of waves in the wave train.
(Download high resolution version. MOV file size: 4.53MB)
Modified 20 October 2007. Website questions or comments to Juan J. Horrillo.