A numerical shallow-water model for gravity currents for a wide range of density differences

Abstract

Gravity currents with various contrasting densities play a role in mass transport in a number of geophysical situations. The ratio of the density of the current, ρ c , to the density of the ambient fluid, ρ a , can vary between 10 0 and 10 3 . In this paper, we present a numerical method of simulating gravity currents for a wide range of ρ c /ρ a using a shallow-water model. In the model, the effects of varying ρ c /ρ a are taken into account via the front condition (i.e., factors describing the balance between the driving pressure and the ambient resistance pressure at the flow front). Previously, two types of numerical models have been proposed to solve the front condition. These are referred to here as the Boundary Condition (BC) model and the Artificial Bed (AB) model. The front condition is calculated as a boundary condition at each time step in the BC model, whereas it is calculated by setting a thin artificial bed ahead of the front in the AB model. We assessed the BC and AB models by comparing their numerical results with the analytical results for a simple case of homogeneous currents. The results from the BC model agree well with the analytical results when ρ c /ρ a 10 2 , but the model tends to overestimate the speed of the front position when ρ c /ρ a 10 2 . In contrast, the AB model generates good approximations of the analytical results for ρ c /ρ a 10 2 , given a sufficiently small artificial bed thickness, but fails to reproduce the analytical results when ρ c /ρ a 10 2 . Therefore, we propose a numerical method in which the BC model is used for currents with ρ c /ρ a 10 2 and the AB model is used for currents with ρ c /ρ a 10 2 .

Physical modeling of the dam-break flow of sedimenting suspensions

“…The present analyzis of experiments performed in a horizontal channel indicates that this should lead to a good prediction of the total flow duration and of the deposit shape, provided that the front velocity is correct. In addition, numerical solving of shallow-water equations for an inviscid fluid in a similar geometry leads to a constant front velocity in agreement with experiments [25]. We are therefore confident that shallow water equations with the sink terms proposed here constitute a good tool to predict natural flows of hot dense volcanic ash in any geometry with smooth slope variations, as it is the case when such flows travel down valleys.…”

“…Despite the multiplication of sophisticated models able to reasonably compute the behaviour of turbulent dilute surges [16][17][18][19][20][21], simulations developed for dense pyroclastic flows still lack of a realistic description, in particular through the term of bottom friction employed to capture the deceleration and stop of the flows during their final course [22][23][24][25].…”

IMEX_SfloW2D 1.0: a depth-averaged numerical flow model for pyroclastic avalanches

“…Pyroclastic avalanches stop when either the slope is reduced or their momentum is dissipated by friction. This is opposite to a pyroclastic density current, a term deriving from the general concept of density current (Von Karman, 1940;Benjamin, 1968;Simpson, 1999), which is a flow moving under the dominant action of the hydrostatic pressure associated with its density contrast with respect to the atmosphere. Thick density currents are able to propagate inertially even on flat topographies, and the effect of friction is usually negligible.…”

Modelling pyroclastic density currents from a subplinian eruption at La Soufrière de Guadeloupe (West Indies, France)

“…A common approach to studying the subsequent PDC dynamics and their hazard is to adopt homogeneous mixture, depth-averaged models, which have the advantage of a fast numerical solution (e.g. Patra et al 2005;Shimizu et al 2017;de' Michieli Vitturi et al 2019). However, single-layer models always impose a dichotomy (and the need for a choice) between dominantly frictional (concentrated) or dominantly inertial (dilute) PDCs.…”