A new Savage–Hutter type model for submarine avalanches and generated tsunami

Abstract

In this paper we present a new two-layer model of Savage-Hutter type to study submarine avalanches. A layer composed of fluidized granular material is assumed to flow within an upper layer composed of an inviscid fluid (e. g. water). The model is derived in a system of local coordinates following a non-erodible bottom and takes into account its curvature. We prove that the model verifies an entropy inequality, preserves water at rest for a sediment layer and their solutions can be seen as particular solutions of incompressible Euler equations under hydrostatic assumptions. Buoyancy effects and the centripetal acceleration of the grain movement due to the curvature of the bottom are considered in the definition of the Coulomb term. We propose a two-step Roe type solver to discretize the presented model. It exactly preserves water at rest and no movement of the sediment layer, when its angle is smaller than the angle of repose, and up to second order all stationary solutions. Finally, some numerical tests are performed by simulating submarine and sub-aerial avalanches as well as the generated tsunami.

Modeling Shallow Over-Saturated Mixtures on Arbitrary Rigid Topography

“…A similar approach can be found in the paper by Fernández-Nieto et al [6] for the description of a one-dimensional shallow flow of two immiscible layers.…”

“…In Sect. 6 we show that, when a shallow over-saturated mixture, with water as the fluid constituent, is at rest on a slightly curved basal topography, the modeling equations predict a horizontal free surface. We end with conclusions in Sect.…”

“…Slightly more general, Fernández-Nieto et al [6] treat the lower layer as a mixture of two constituents moving with the same velocity and according to the momentum balance equation of the mixture as a whole; doing so, the stresses of each mixture constituent could be accounted for in this momentum balance equation. All the cited papers consider the two layers as being immiscible.…”

Subaerial Landslide-Generated Waves: Numerical and Laboratory Simulations

“…These four LGW types consist of several waves with respectively a symmetrical wave profile, a longer wave through than the wave crest, one dominant wave crest, and one dominant wave containing a large amount of air in the wave front (Heller and Hager 2011). They also hold the smallest to the largest amounts of mass transports, respectively (Di Risio et al 2011). The laboratory investigations of Kamphuis and Bowering (1970) on SALGWs showed that the LGW characteristics were mainly a function of the slide volume and the Froude number of the slide upon impact with the water.…”

An equivalent fluid/equivalent medium approach for the numerical simulation of coastal landslides propagation: theory and case studies

“…Some models that analyse turbidity currents are available, and recently, a cellular automata model was also developed that is suitable for such a phenomenon (Salles et al, 2007). Only one numerical model that can simulate underwater granular flows (like rock and debris avalanches) with a Savage-Hutter type model (Fernández-Nieto et al, 2008) has been recently developed; nevertheless, this model has not been applied to real landslides yet.…”