Nonlinear analytical solution for landslide generated tsunamis

Gutenberg (1939 Bull. Seismol. Soc. Am. 29, 517-526.) reported that “submarine landslides are to be considered at least as one of the chief causes, if not indeed the major cause of tsunamis.” Recent tsunami events caused by landslides, including 1998 Papua New Guinea tsunami (Synolakis et al. 2002 Proc. R. Soc. A 458, 763-789), renewed interest for landslide generated tsunamis. We attempt to identify propagation and runup characteristics of subaerial and submarine landslides analytically. We solve the forced -nonhomogeneous- nonlinear shallow-water wave equations so that sliding volume is incorporated into the governing equations as a forcing term. We first transform the governing equations into a single linear partial differential equation applying the so-called hodograph transformation as in Kanoglu and Synolakis (2006 Phys. Rev. Lett. 97, 148501). However, unlike without forcing case, it is not possible to transform the governing nonlinear equations into a single linear equation exactly. Therefore, we linearize the transform equation and follow the same methodology as in Liu, Lynett and Synolakis (2003 J. Fluid Mech. 478, 101-109), i.e., solve an initial value problem for a sliding Gaussian shape. We compare nonlinear solution results with the existing linear analytical and nonlinear numerical solutions of Liu, Lynett and Synolakis (2003).