During the two revisions, the authors have done great job to substantially improve this MS: in the concept, model structure, and in the application aspect of the model. Although computationally expensive, the full dimensional models and simulations are required for the better understanding of mass flow processes such as avalanches and debris flows, and their applications in proper planing and mitigation measures. The model is able to very well reproduce laboratory debris flow experiments considered here. So, the the modelling and simulation approach presented in the MS can be potentially applied in different mass flows. I suggest to improve the MS as suggest below which are mainly conceptual, editorial, and concerns also with the consistency of the presentation. With this, I recommend for the publication of this paper. No further revision is necessary.
Title:
based on --> with [could be better!]
P2:
L12-14: Thus depth-averaging is not necessary in many cases and complex three-dimensional flow structures can be simulated while accounting for the pressure- and shear-rate-dependent rheology. --> Thus, complex three-dimensional flow structures can be simulated while accounting for the pressure- and shear-rate-dependent rheology.
L18: moving fluid mass. --> moving mixture mass.
L23: Ref (requires references).
P3:
L11: several physical parameters. --> several physical parameters (see, e.g., Pudasaini, 2012).
L17-19: The currently available models also contain many parameters that must be fitted to site-specific field data, severely limiting their applicability to real-world problems and their usefulness for scientific hypothesis testing. --> The currently available models also contain many parameters that must be measured, or fitted to site-specific field data, limiting their applicability to real-world problems.
L20: Here, we provide a coarse but effective solution --> Here, we provide a mechanically largely simplified but, effective solution
P4:
L4-7: Remove, not relevant.
P5:
More appropriate terminology could be used, e.g., gradient --> gradient operator; consistency factor --> consistency index; affects slurry phase rheology --> in slurry phase rheology; internal friction angle approximated as angle of repose --> internal friction angle; would affect gravel phase rheology --> in gravel phase rheology, etc. The symbols could be better grouped into Greeks, etc.
P6:
L1: Be consistent with the use of Capital letters in the section headings.
L13-14: as applied by --> as proposed by
L15: Navier-Stokes equations. --> mass and momentum balance equations.
L17: Pudasaini (2012) and Bouchut et al. (2015)). --> Bouchut et al. (2015)). Whereas Pudasaini (2012) proposed a more comprehensive two-phase mass flow model that includes general drag, buoyancy, virtual mass, and enhanced non-Newtonian viscous stress in which the solid volume fraction evolves dynamically.
L17-18: We apply the numerically more efficient method of Iverson and Denlinger (2001) and treat the debris flow material as one mixture --> We apply the numerically more efficient method and treat the debris flow material as one mixture (Iverson and Denlinger, 2001; Pudasaini et al., 2005 NHESS)
L19: Navier-Stokes equations. --> Navier-Stokes-type equations.
L23: some --> general
L24-25: fine material). --> fine material and large water content).
P7:
L2: pressure-dependent --> pressure- and rate-dependent
L8: physics of flow --> physics of flow in terms of the interactions between phases such as drag, buoyancy, virtual mass, non-Newtonian viscous stress and evolving volume fraction of the solid phase (Pitman and Le, 2005; Pudasaini, 2012).
L22: The text is generally better from here on!
P8:
L15: per unit mass like gravity --> per unit mass [see later, it is also used for surface tension!]
L17: and the fluid --> and the fluid (see, e.g., Pudasaini, 2012)
P9:
L4: t denotes time: put it after (5).
L15: set to a negligible small value --> set to a small value
P10:
L9: [also see other instances] do not put '.' between variables, e.g., use \phi_1 \rho_1, etc.
P11:
L6: second term in (12) is zero from (3). So, remove the second term.
L11: The term --> With the continuity equation (3) the term;
is decomposed as --> is written as
L17: used for validation.: Refs required.
P13:
L15: in the past.: Refs. (e.g., Pudasaini, 2011, etc. )
L19: due to the large number of rheology parameters --> due to three rheology parameters
P14:
L3: is confined to the gravel phase --> is assumed to be in the gravel phase
L12: C --> C (a constant)
P15:
L12: g is the acceleration due to gravity,: remove [repeated]
P16:
L1-8: Please make clear what are the two remaining parameters out of \tau_{00}, k, and n.
L15: slope reduction --> slope reduction, diverging or converging flows, and interactions with obstacles (see, e.g., Pudasaini et al., 2005 PoF; Domnik et al., 2013)
P16-17:
Equations (24), (27): It appears that in the previous iterations of this MS, the authors are unnecessarily confused with the correct form of the stress closure. This can be see in these equations. In Domnik and Pudasaini (2012) and Domnik et al. (2013) due to the constant bulk density \rho was taken out from the momentum equation so the stress closure was throughly normalized by density. But, in the present MS, the effective bulk density \rho is changing (see, 10) that remains inside the differential operators in (5) and (14) so that the stress closure cannot be normalized by density. Therefore, to be consistent, please remove the density \rho from the denominators from (24) and (27), and accordingly also remove the phrases like 'normalized by density'.
P17:
L4: is a model parameter --> is a numerical parameter
L4-5: which we will keep constant, for reasons outlined in the following section: Remove [not necessary here].
L11-12: two parameters: the friction angle \delta, --> only one material parameter parameter, the friction angle \delta, that is measurable;
and the parameter m_y influencing the transition --> and the parameter m_y introduced for numerical purpose for the smooth transition
L17: and m_y = 0.2 s, but --> and say, m_y = 0.2 s. So, we choose m_y to be constant and equal to 0.2 s for all simulations. [from P18, L1].
L18: parts of the nearly --> However, we mention that parts of the nearly; face --> experience
P18:
L17: and gas phases --> and probably gas phases
L19: The only way to account for the inhomogeneous nature of debris flows is by --> The only way to account for the inhomogeneous nature of debris flows is by using the real two-phase mass flow model (e.g., Pudasaini, 2012).
L20-26: Remove [not relevant, mechanically, this is not the best way to deal with evolving phases].
P19:
L2-3: A two-way coupling to a Lagrangian particle simulation could deliver the necessary coupling physics. --> A two-way coupling of Lagrangian particles could deliver an alternative solution.
P19-20:
Improve Section 3.2, Section 3.3 and also the Introduction with the following relevant materials and information. These sections are very weak and must be largely re-written, including the following suggestion:
Observations in the laboratory and in nature show that the rapid flow regime is characterized by more or less uniform velocity profiles with depth and dominant sliding at the base, while in the deposition regime and, in particular, in the transition region from the rapid flow into the deposition zone shock-like structures form, and an overall depth flow changes into a surface boundary layer flow, which, further downstream, quickly slows down and eventually settles. This has been observed in the laboratory with granular PIV (particle image velocimetry) measurements for rapidly moving granular material that impinges the frontal rigid wall perpendicular to the bed leading to strong shearing through the flow depth (Pudasaini et al., 2007). In such a case, some of the material comes to a complete standstill. So, whereas the flow state in the rapid flow regime of the avalanche is reasonably approximated by a depth integrated dynamical model, an adequate treatment of the deposition regime and the regions in the vicinity of an obstacle requires better resolution without the reduction of the dimension.
The depth-averaged equations are restricted to smooth basal surfaces and smooth changes of the slopes. Those equations could not fully be applied when topography changes are large (large curvatures), in the vicinity of the flow obstacle interactions, during the depositions, for strongly converging and diverging flows, in flow initiations and also during the deposition processes. All these complex processes can typically be characterized by the dominant basal slip, followed by the strong shearing and weak shearing of the velocity field from sliding surface to the top free surface of flow. Therefore, in general, we need a physically complete description of the flow dynamics without reduction of the information through the flow depth (Domnik and Pudasaini, 2012). All the information of the physics of flow can be retained by developing a full-dimensional flow model and then directly solving the model equation without reducing the dimension. With a novel model Domnik and Pudasaini (2012) show that the Coulomb-viscoplastic sliding law reveals completely different flow dynamics and flow depth variations of the field quantities, mainly the velocity and full dynamic pressure, and also other derived quantities, such as the bottom shear-stress, and the mean shear-rate, compared to the commonly used no-slip boundary condition. They show that for Coulomb-viscoplastic sliding law observable shearing mainly takes place close to the sliding surface in agreement with observations but in contrast to the no-slip boundary condition.
Domnik et al. (2013) developed a full two-dimensional Coulomb-viscoplastic model and applied it for inclined channel flows of granular materials from initiation to deposition. A pressure-dependent yield strength is proposed to account for the frictional nature of granular materials. The interaction of the flow with the solid boundary is modelled by a pressure and rate-dependent Coulomb-viscoplastic sliding law. In regions where depth-averaging becomes inaccurate, like in the initiation and deposition regions and particularly, when the flow hits an obstacle or a defense structure, full-dimensional models must be used, because in these regions the momentum transfer must be considered in all directions. So, prediction of the velocity variations along the flow depth direction, and the full dynamical and internal pressure can only be obtained by full dimensional model equations (Domnik et al., 2013). These dynamical quantities can be adequately described by Coulomb-viscoplastic material with a pressure-dependent yield stress expressed in terms of the internal friction angle, the only material parameter in their model.
P22:
L16-17: It does not add up to 100\%. Please check!
P23:
L24: Due to the solver's --> Due to the used
P24:
L4-5: The model is still limited to small simulations.: Remove.
P28:
Improve the references with the new ones.
P36:
Put only 5-5 lines. Reduce 50 deg to 40 deg!
P40:
Figure caption: confusing. |
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