Numerical Models of Pyroclastic Flows and Turbidity Currents
Pyroclastic flows are amongst the most devastating and lethal volcanic events for populations close to volcanoes, primarily because of their extreme mobility; they can reach speeds of hundred of kilometres per hour and can travel as much as 100km or more from the source vent. The image to the right shows an eruption column from Soufriere Volcano, Montserrat, collapsing to form a pyroclastic flow. Much of the physics involved in turbidity current propagation is similar to that of pyroclastic flows in that they are both particle-bearing gravity currents. However turbidity currents are cold and the density difference between the particles and carrying fluid is much smaller than in a pyroclastic flow. The aim of these projects has been to produce more realistic numerical models of the propagation of these flows.
Dr Gustavo Cordoba has focussed on modelling the propagation of turbidity currents. He has generated a finite element model of the dilute companion cloud as well as a box model and has used these to explore the effect of the aspect ratio of the initial collapse and different particle size combinations on runout and depositional characteristics. He has also studied the effect of different approaches to sedimentation and, specifically, the effect of incorporating a hindered settling velocity. He is applying his models to the July 2003 Montserrat turbidity current and the Marmoso Arenea formation as well as to hypothetical pyroclastic surges at Montserrat and Galeras volcanoes.
Dr Emma Doyle has developed a two layer model for the collapse and spreading of a granular column. This is to our knowledge the first model that incorporates both the overlying dilute companion cloud as well as the dense basal avalanche commonly associated with pyroclastic flows. The model builds upon that of Larrieu et al (2006) where the free fall collapse of the column and subsequent flow of material onto a plane is represented by a 'raining' mass source term into a thin flowing layer of constant density. These modified shallow water equations with Coulomb friction capture the free surface of the flows and key scaling laws for initial sand columns with aspect ratios up to a less than 10. However unrealistically high coefficients of friction of µ=0.9 are required to reproduce observed run-outs. Key scaling laws for high aspect ratio columns are also not captured. These problems are dealt with by extending the model to include an estimation for the interface between the static and flowing regions observed within granular collapses in the laboratory by Lube et al (2007). An empirical sedimentation term Ls and the instantaneous removal of a static deposit wedge, seen in the laboratory, are incorporated into the 'raining' shallow water model. The growing static deposit surface provides a basal topography for the flowing layer. For a constant empirical sedimentation rate of Ls=0.20m/s, a coefficient of friction of µ=0.4 simulates comparable run-outs to laboratory observations. The correct run-out dependence of a=2/3 for columns of aspect ratio a > 3 is also captured. Simulating this behaviour for values of a greater than 10 has not been possible with previous continuum models. In addition, this model captures the correct dependence of final run-out time upon a0.5. The application of this extends beyond observed and simulated collapses, to sedimenting highly concentrated debris flows, useful in the development of large mechanistic numerical models utilized in hazard assessment.
Those involved in this research are Gustavo Cordoba (Alban PhD Student 2004-2007) Emma Doyle (NERC-funded PhD Student 2003-2007), Dr Heidy Mader and Professor Steve Sparks.
Funded by Natural Environment Research Council, UK