AbstractMost existing tsunami propagation models consider the ocean to be an incompressible, homogenous medium. Recently, it has been shown that a number of physical features can slow the propagation speed of tsunami waves, including wave frequency dispersion, ocean bottom elasticity, water compressibility and thermal or salinity stratification. These physical effects are secondary to the leading order, shallow water or long wave behavior, but still play a quantifiable role in tsunami arrival time, especially at far distant locations. In this work, we have performed analytical and numerical investigations and have shown that consideration of those effects can actually improve the prediction of arrival time at distant stations, compared to incompressible forms of wave equations. We derive a modified Mild Slope Equation for Weakly Compressible fluid following the method proposed by Sammarco et al. (2013) and Abdolali et al. (2015) using linearized wave theory, and then describe comparable extensions to the Boussinesq model of Kirby et al. (2013). Both models account for water compressibility and compression of static water column to simulate tsunami waves. The mild slope model is formulated in plane Cartesian coordinates and is thus limited to medium propagation distances, while the Boussinesq model is formulated in spherical polar coordinates and is suitable for ocean scale simulations.
Sammarco, Cecioni, Bellotti, Abdolali (2013) Depthintegrated equation for large-scale modelling of lowfrequency hydroacoustic waves. Journal of Fluid Mechanics, 722, R6
Abdolali, A., Kirby, J. T. and Bellotti, G., 2015, Depthintegrated equation for hydro-acoustic waves with bottom damping, Journal of Fluid Mechanics, 766, R1 doi:10.1017/jfm.2015.37
Abdolali, Kirby (2017) Role of Compressibility on Tsunami Propagation, Journal of Geophysical Research: Ocean, 122. https://doi.org/10.1002/2017JC013054
Kirby, Shi, Tehranirad, Harris, Grilli (2013) Dispersive tsunami waves in the ocean: model equations and sensitivity to dispersion and Coriolis effects. Ocean Modelling, 62, 39-55
Tappin, Grilli, Harris, Geller, Masterlark, Kirby, Shi, Ma, Thingbaijam, Mai (2014). Did a submarine landslide contribute to the 2011 Tohoku tsunami? Marine Geology, 357, 344-361