دانلود رایگان مقاله راه حل های تحلیلی برای تخمین سرعت انتشار سونامی

ABSTRACT

Recent studies suggest that the tsunami speed can be slowed down by around 1% due to Earth elasticity, water compressibility and density stratification. Analytical solutions of wave dispersion relationship, accounting for such effects, were found in previous studies. In this paper, we investigate the additional effects of water viscosity, ocean stratification due to temperature/salinity and numerical dispersion. Theoretical solutions are derived and checked with known solutions. All the formulas are then simplified for long tsunamis waves so that the propagation speed can be calculated explicitly. The simplified solutions are evaluated using realistic geophysical parameters. For a typical tsunami wavelength of ∼200km, the viscous effect is found to be negligible; ocean stratification due to temperature/salinity causes significant speed reduction because of the high density change rate, which has been ignored before. We also evaluate the numerical dispersion of tsunami simulations, which is shown to be potentially comparable to physical dispersion

6. Conclusions

In this study we derive the theoretical solutions of dispersion relationships accounting for the effects of water viscosity, ocean stratification due to temperature/salinity and numerical dispersion. We find that the water viscosity hardly affects the speed of tsunami waves, but the density stratification due to temperature/salinity is capable of slowing down the tsunami waves by the same order as the stratification due to gravitational compression, because such a stratification has a sudden change of density over a small depth. The numerical dispersion is comparable to the physical dispersion if the spatial grid size is around 5 arc min in the numerical simulation. It is noted that 5 arc min has been commonly used for global tsunami warning purposes. Therefore, we suggest that if the correction of Earth elasticity, water compressibility and density stratification due to compression (e.g., Allgeyer and Cummins, 2014; Watada, 2013; Watada et al., 2014) were deemed to be significant, the effects of stratification due to temperature/salinity and numerical dispersion should also be taken into account. In this study we also simplify the theoretical dispersion relationships so that the simplified formulas are explicit and easy to adopt. They are Eqs. (28), (36), (49), (65), (70) and (74). The simplifications are verified to be good approximations of the full dispersion relationships for typical tsunami wavelength of 50–1000 km (or wave period 260–5000 s). Since all the effects slow down the tsunami speeds by a small order (<1%), it is expected that the combination of them in a linear system is simply the linear summation, and the crossing terms of the coupling effects are one order even smaller. Using the typical physical parameters given in Section 4, for tsunami waves with wavelength of ∼200 km, the effects that cause significant speed reduction are wave dispersion (0.26%), Earth elasticity (0.24%), water compressibility (0.30%), density stratification due to compression (0.15%) and density stratification due to temperature/salinity (0.14%). The total reduction is around 1.1%.