A numerical study of submarine–landslide–generated waves and run–up

A mathematical model is derived to describe the generation and propagation of water waves by a submarine landslide. The model consists of a depth–integrated continuity equation and momentum equations, in which the ground movement is the forcing function. These equations include full nonlinear, but weak frequency–dispersion, effects. The model is capable of describing wave propagation from relatively deep water to shallow water. Simplified models for waves generated by small seafloor displacement or creeping ground movement are also presented. A numerical algorithm is developed for the general fully nonlinear model. Comparisons are made with a boundary integral equation method model, and a deep–water limit for the depth–integrated model is determined in terms of a characteristic side length of the submarine mass. The importance of nonlinearity and frequency dispersion in the wave–generation region and on the shoreline movement is discussed.

[1]  Franklin Liu,et al.  Modeling wave runup with depth-integrated equations , 2002 .

[2]  Philip Watts,et al.  The Sissano, Papua New Guinea tsunami of July 1998 — offshore evidence on the source mechanism , 2001 .

[3]  Ge Wei,et al.  A fully nonlinear Boussinesq model for surface waves. Part 2. Extension to O(kh)4 , 2000, Journal of Fluid Mechanics.

[4]  Stephan T. Grilli,et al.  PII: S0955-7997(99)00021-1 , 1999 .

[5]  K. Crook,et al.  Sediment slump likely caused 1998 Papua New Guinea tsunami , 1999 .

[6]  H. Schäffer,et al.  Higher–order Boussinesq–type equations for surface gravity waves: derivation and analysis , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[7]  Qin Chen,et al.  Funwave 1.0: Fully Nonlinear Boussinesq Wave Model - Documentation and User's Manual , 1998 .

[8]  Eric L. Geist,et al.  Local Tsunamis and Earthquake Source Parameters , 1998 .

[9]  C. Synolakis,et al.  Long-Wave Runup Models: Proceedings of the International Workshop , 1997 .

[10]  Philip Watts,et al.  Water waves generated by underwater landslides , 1997 .

[11]  C. Synolakis,et al.  Long-wave runup models : Friday Harbor, USA, 12-17 September 1995 , 1996 .

[12]  G. Wei,et al.  Time-Dependent Numerical Code for Extended Boussinesq Equations , 1995 .

[13]  G. Wei,et al.  A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves , 1995, Journal of Fluid Mechanics.

[14]  Philip L.-F. Liu,et al.  Modified Boussinesq equations and associated parabolic models for water wave propagation , 1995 .

[15]  P. Liu,et al.  MODEL EQUATIONS FOR WAVE PROPAGATIONS FROM DEEP TO SHALLOW WATER , 1995 .

[16]  Stephan T. Grilli,et al.  Shoaling of Solitary Waves on Plane Beaches , 1994 .

[17]  G. Pedersen,et al.  Numerical Simulations of Large Water Waves due to Landslides , 1993 .

[18]  O. Nwogu.  Alternative form of Boussinesq equations for nearshore wave propagation , 1993 .

[19]  S. Grilli.  Modeling of nonlinear wave motion in shallow water , 1993 .

[20]  P. A. Madsen,et al.  A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry , 1992 .

[21]  Meng H. Lean,et al.  Applications of boundary integral equation methods for two‐dimensional non‐linear water wave problems , 1992 .

[22]  P. Leblond,et al.  The coupling of a submarine slide and the surface waves which it generates , 1992 .

[23]  Stephan T. Grilli,et al.  An efficient boundary element method for nonlinear water waves , 1989 .

[24]  J. Bourgois,et al.  A large tsunamogenic landslide and debris flow along the Peru Trench , 1989 .

[25]  George T. Yates,et al.  Experiments and analyses of upstream-advancing solitary waves generated by moving disturbances , 1989, Journal of Fluid Mechanics.

[26]  W. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[27]  J. G. Moore,et al.  Deposit from a Giant Wave on the Island of Lanai, Hawaii , 1984, Science.

[28]  Lawrence K. Forbes,et al.  Free-surface flow over a semicircular obstruction , 1982, Journal of Fluid Mechanics.

[29]  A Numerical Model for Tsunami Generation and Propagation , 1980 .

[30]  H. L. Butler,et al.  Landslide Generated Water Wave Model , 1976 .

[31]  J. Hammack.  A note on tsunamis: their generation and propagation in an ocean of uniform depth , 1973, Journal of Fluid Mechanics.

[32]  D. Peregrine.  Long waves on a beach , 1967, Journal of Fluid Mechanics.