2015
DOI: 10.5194/nhess-15-671-2015
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Modelling rapid mass movements using the shallow water equations in Cartesian coordinates

Abstract: Abstract. We propose a new method to model rapid mass movements on complex topography using the shallow water equations in Cartesian coordinates. These equations are the widely used standard approximation for the flow of water in rivers and shallow lakes, but the main prerequisite for their application -an almost horizontal fluid table -is in general not satisfied for avalanches and debris flows in steep terrain. Therefore, we have developed appropriate correction terms for large topographic gradients. In this… Show more

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Cited by 31 publications
(38 citation statements)
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“…The boundary condition u · n b = 0 (28) ensures that the velocity of the fluid is surface-tangential, as assumed by the boundary layer approximation and the Savage-Hutter model. This constraint can be considered as an equation to determine basal pressure p b in every point of the surface.…”
Section: Topography Boundary Conditionmentioning
confidence: 99%
See 1 more Smart Citation
“…The boundary condition u · n b = 0 (28) ensures that the velocity of the fluid is surface-tangential, as assumed by the boundary layer approximation and the Savage-Hutter model. This constraint can be considered as an equation to determine basal pressure p b in every point of the surface.…”
Section: Topography Boundary Conditionmentioning
confidence: 99%
“…Therefore, further extensions have been proposed by introducing a superimposed shallow terrain [24], a twisted central flow path [25], and curvature effects on friction [12]. In addition, a description in Cartesian coordinates, similar to the Shallow Water Equations, has been investigated [26,27,28], taking into account the inclination with various correction terms.…”
Section: Introductionmentioning
confidence: 99%
“…Nevertheless, some of the mass flow models mentioned have been implemented in computational tools used for hazard mapping and zoning, such as DAN (Hungr et al, 1995); TITAN2D (Pitman et al, 2003b;Pitman and Le, 2005); SamosAT (Sampl and Zwinger, 2004); or RAMMS (Christen et al, 2010a, b). Hergarten and Robl (2015) developed a modelling tool relying on the open source flow solver GERRIS (Popinet, 2009).…”
Section: Introductionmentioning
confidence: 99%
“…Physically based dynamic models are used for in-detailed analyses of specific events or situations (e.g., Savage and Hutter, 1989;Takahashi et al, 1992;Iverson, 1997;Pudasaini and Hutter, 2007;Hungr, 2004, 2005;Pitman and Le, 2005;Christen et al, 2010a, b;Mergili et al, 2012b;Pudasaini, 2012;Hergarten and Robl, 2015;. Since the processes are complex in detail and the input parameters are uncertain, simplified conceptual models for the motion of mass flows are today used in combination with GIS (Geographic Information System).…”
Section: Introductionmentioning
confidence: 99%