Fig. 11
From: A numerical shallow-water model for gravity currents for a wide range of density differences
Numerical results of a one-layer dense PDC model for the dam-break problem. The density ratio (ρ H/ρ a) is set to 600.6, and the AB model with ε=10−10 is applied. Given parameters: initial height h 0=0.2 m, initial length x 0=0.1 m, density of particles =1500 kg/m3; density of volcanic gas =1 kg/m3; and density of air =1 kg/m3. a Heights \(h_{\mathrm {H}}^{*}\) of the dense PDC with shear drag at t ∗=0.0, 0.2, 0.4, and 0.6 s. b Front positions of the dense PDC with shear drag (red solid curve) and Coulomb friction (blue solid curve). In (b), the numerical results are compared with the experimental results of an initially fluidized granular flow (black dashed curve) and water (gray solid curve) (Roche et al. 2008). The experimental result of the initially fluidized granular flow has three distinct regimes: (i) initial acceleration, (ii) constant velocity, and (iii) stopping (see Roche et al. 2008 for details). Note that during (i) and (ii), the initially fluidized granular flow behaves as water. The numerical result with shear drag reproduces the slope (i.e., the constant velocity) of (ii). The numerical result with Coulomb friction reproduces the features of (iii)