A two-layer depth-averaged model for both the dilute and the concentrated parts of pyroclastic currents

Pyroclastic currents are very destructive and their complex behavior makes the related hazards difficult to predict. A new numerical model has been developed to simulate the emplacement of both the concentrated and the dilute parts of pyroclastic currents using two coupled depth-averaged approaches. Interaction laws allow the concentrated current (pyroclastic flow) to generate a dilute current (pyroclastic surge) and, inversely, the dilute current to form a concentrated current or a deposit. The density of the concentrated current is assumed to be constant during emplacement, whereas the density of the dilute current changes depending on the particle supply from the concentrated current and the mass lost through sedimentation. The model is explored theoretically using simplified geometries as proxies for natural source conditions and topographies. It reproduces the relationships observed in the field between the surge genesis and the topography: the increase in surge production in constricted valleys, the decoupling between the concentrated and the dilute currents, and the formation of surge-derived concentrated flows. The strong nonlinear link between the surge genesis and the velocity of the concentrated flow beneath it could explain the sudden occurrence of powerful and destructive surges and the difficulty of predicting this occurrence. A companion paper compares the results of the model with the field data for the eruption of Merapi in 2010 and demonstrates that the approach is able to reproduce the natural emplacement of the concentrated and the dilute pyroclastic currents studied with good accuracy. Plain Language Summary Pyroclastic currents are composed of hot gas and rock fragments. They are very dangerous and their complex behavior makes the related hazards difficult to predict. They are generally formed of two distinct parts: (1) a basal flow that carries ashes and large blocks (up to cubic meters), which is very destructive but follows existing valleys; (2) a dilute part, called pyroclastic surge, that carries ashes in hot turbulent gases. This part is less destructive for infrastructures but it is less confined by the topography, escapes easily from the valleys, and is very dangerous for the inhabitants. A new numerical model has been developed to simulate their emplacement. It reproduces the relationships observed in the field between the surge genesis and the topography. The strong nonlinear link between the surge genesis and the velocity of the flow beneath it could explain the sudden occurrence of powerful and destructive surges and the difficulty of predicting this occurrence. This new model gives promising perspectives for the understanding of pyroclastic current emplacements and for future estimation of related hazards and impacts on the population, the infrastructure, and the environment.