Long waves in a high-density, stratified fluid: Theoretical and numerical analyses of a suspended-flow tsunami

High-density, suspended-flow tsunamis that entrain large amounts of sediment from the seabed, can trigger severe, cascading damage. However, the vertical distribution of fluid density in a transient tsunami is not well understood, so its influence on the tsunami dynamics is unclear. Herein, we obtain insights into the basic properties of long surface waves in a density-stratified, two-layer, inviscid fluid based on linear shallow-water wave theory, numerical solitary-wave solutions of strongly nonlinear and strongly dispersive wave equations, and numerical simulations using Smoothed Particle Hydrodynamics. The linear analytical solution shows that when the fluid beneath a shallow-water wave changes from one to two layers, the wave height may increase despite the increased depth-averaged density, and the flow velocity in the upper layer also increases. These changes are proportional to the density ratio between the upper and lower layers, and they are emphasized more in nonlinear wave fields (e.g., in solitary waves). Nevertheless, the relative phase velocity never exceeds that of the one-layer fluid, as in the linear analytical solution, regardless of the density stratification. The change in flow and phase velocities also play important roles in unsteady problems, accelerating the wave-breaking limit as the density ratio increases. Additionally, as the density ratio increases, both steady and unsteady long waves exhibit greater wave height amplification upon collision with a vertical wall. These results indicate the importance of the density distribution in evaluating the effects of suspended-flow tsunamis. • Basic properties of tsunamis in a high-density two-layer fluid are investigated. • Phase/upper-flow velocities become slower/faster with increasing density ratio. • The larger the density ratio, the earlier does wave breaking occur. • During propagation, stratification makes the tsunami height and flow speed larger. • The larger the density ratio, the greater the wave height in a head-on collision.