On the transfer of momentum from a granular landslide to a water wave

Abstract

The momentum flux from a landslide at impact in a water body is the driving force behind the generation of landslide tsunamis. Analysis of this problem is presented and used to derive idealized theoretical relationships for the maximum wave amplitude in the near-field zone. This is accomplished for momentum transfer using both hydrostatic and hydrodynamic assumptions. For rapidly evolving near-field waves with a supercritical densimetric Froude number, the maximum wave amplitude is also constrained according to the fluid continuity equation. Simplification of the hydrostatic momentum equation is also presented by considering fluid acceleration, resulting in an expression that is independent of length and time scales during wave generation. The results of the novel momentum-based equations are in agreement with laboratory data collected using high-speed digital cameras for granular landslides and previously published experimental data used to develop a semi-empirical equation. Furthermore, the results provide new insight on the range of applicability of theoretical and semi-empirical equations for predicting the maximum near-field wave amplitude of landslide-generated tsunamis.