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arxiv: 2604.24781 · v1 · submitted 2026-04-20 · ⚛️ physics.geo-ph

Recognition: unknown

The landslide drag

Shiva P. Pudasaini

Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:30 UTC · model grok-4.3

classification ⚛️ physics.geo-ph
keywords landslide dragdrag coefficientdebris flowsenergy dissipationgranular flowsacceleration numberlandslide dynamicsfrictional behavior
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The pith

The drag coefficient in landslides equals a measure of energy inefficiency derived from the flow's acceleration.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that drag in landslides cannot be treated as a fixed empirical number because the flowing mass is deformable and its velocity changes continuously. It instead derives an analytical drag coefficient that evolves automatically with the landslide's speed. This coefficient is expressed as a dimensionless acceleration number that encodes how the actual acceleration compares to the net driving acceleration. The derivation shows the coefficient directly quantifies the fraction of energy lost to dissipation rather than converted to motion. If the model holds, simulations of debris flows can use a physically grounded expression instead of calibrated constants while still recovering observed frictional behavior.

Core claim

The central claim is that the drag coefficient is the measure of energy inefficiency. By requiring the coefficient to contain information on the evolving landslide acceleration relative to net driving acceleration, it is expressed through a dimensionless acceleration number regulated purely by the physics of the flow. This supplies an analytical model for the drag that adjusts automatically during motion and reproduces the inherent frictional character of granular debris flows.

What carries the argument

The dimensionless acceleration number that defines the evolutionary drag coefficient by relating landslide acceleration to net driving acceleration.

If this is right

  • The drag coefficient adjusts automatically throughout the landslide motion without external calibration.
  • Simulations recover the frictional behavior of granular debris flows using the derived expression.
  • The coefficient yields values close to those found by traditional calibration while carrying a direct physical interpretation.
  • Natural landslide events can be modeled with the same functional form but now grounded in acceleration physics rather than fitting.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same acceleration-based construction might apply to other gravity-driven granular flows such as snow avalanches or rockfalls.
  • Hazard models could use the explicit energy-inefficiency interpretation to estimate runout distances from measurable acceleration profiles.
  • Linking the drag coefficient to dissipation opens a route to connect it with other loss mechanisms like internal friction or basal erosion.

Load-bearing premise

The drag coefficient must be a function of evolving landslide velocity because it must encode the relation between landslide acceleration and net driving acceleration through a dimensionless number set by flow physics alone.

What would settle it

Compare the drag coefficient predicted by the acceleration number against measured energy dissipation rates in a controlled landslide experiment; mismatch between the two would falsify the derivation.

Figures

Figures reproduced from arXiv: 2604.24781 by Shiva P. Pudasaini.

Figure 1
Figure 1. Figure 1: Roots of the drag function F as given by (8). There are three roots: a negative root, a zero root, and a positive root. all the physical and dynamical quantities associated with the landslide motion. Mechanism of the drag coefficient: In situation when αt − u = 0, β + = 0. Then, (3) tells that, this is equivalent to disregarding the drag force. So, (12) is mathematically fully consistent. Next, we explore … view at source ↗
Figure 2
Figure 2. Figure 2: Landslide dynamics with constant drag coefficient [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Landslide dynamics with constant drag coefficient [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Landslide dynamics with constant drag coefficient [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Landslide dynamics with evolutionary analytical drag coefficient [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Landslide dynamics with: (A) constant drag coefficient [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Time evolution of the analytical drag β as given by (24) associated with the profiles in [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Time evolution of the analytical drag β as given by (24) associated with the profiles in [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 5
Figure 5. Figure 5: At t = 4 s, the mass lies entirely in the inclined portion of the slope where the net driving acceleration 15 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
read the original abstract

Drag is one of the most important energy dissipation mechanisms in nature, including landslides and debris flows. To satisfactorily reproduce laboratory or field data in simulating landslides, often empirical relations or convenient numerical values are used for the drag force coefficient. However, this is just a parameter calibration rather than a physical reality. Why should the drag coefficient be a constant for a dynamically evolving landslide? Which drag coefficient represents the physical reality? So, what exactly is the drag remains an open question. As the landslide is a deformable body, the drag-deformation-flow must be interconnected. Empirical drag coefficients lack important dynamical aspects. As the drag coefficient is less likely to be measurable, it must be described with some mechanical models. Yet, there exists no analytical model for the drag coefficient. Here, we postulate that the drag coefficient must be a function of the evolving landslide velocity, as it must contain information constituting the landslide acceleration in relation to the net driving acceleration. We develop an innovative, evolutionary drag coefficient that adjusts automatically during the landslide motion. The drag coefficient is described by a dimensionless acceleration number as it is regulated by the physics and dynamics of the flow. Formal derivation shows that the drag coefficient is the measure of energy inefficiency. This settles down the deliberation on the drag force in landslide dynamics, reshaping the concept of drag. Simulation results highlight the essence, mechanical strength and functionality of the proposed analytical drag as it demonstrates the inherent frictional behaviour of granular debris flows. As the dynamical drag coefficients appeared to be around the often calibrated values, the new drag potentially well reproduces natural event dynamics, but now with clear physical basis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes an analytical, evolutionary drag coefficient Cd for landslide and debris-flow modeling. It postulates that Cd must be a function of evolving velocity because it encodes the ratio of landslide acceleration to net driving acceleration; this ratio is expressed via a dimensionless acceleration number regulated solely by flow physics. Formal derivation is claimed to show that Cd quantifies energy inefficiency. Simulations are presented to illustrate that the resulting Cd reproduces the frictional behavior of granular flows and yields values close to commonly calibrated constants, thereby providing a physical basis rather than empirical fitting.

Significance. If the derivation proves independent of the equation of motion and yields falsifiable predictions, the work would supply a mechanically grounded alternative to ad-hoc drag coefficients, potentially improving the physical fidelity of landslide simulations without parameter calibration.

major comments (3)
  1. [Abstract / central postulate] Abstract and central postulate: the claim that Cd 'must contain information constituting the landslide acceleration in relation to the net driving acceleration' and is therefore expressed via a dimensionless acceleration number risks circularity. Because acceleration is already fixed by the net force balance (driving forces minus the drag term itself), defining Cd directly from that ratio can reduce to a reparametrization of the Newtonian equation rather than an independent mechanical constraint. The manuscript must demonstrate explicitly (with the full derivation) that the dimensionless number introduces additional physics or falsifiable predictions beyond standard force balance.
  2. [Abstract] Abstract: the assertion that 'formal derivation shows that the drag coefficient is the measure of energy inefficiency' is load-bearing for the claim that the model 'settles down the deliberation on the drag force.' Without the explicit steps linking the dimensionless acceleration number to an energy-dissipation interpretation, it is impossible to verify whether the result is a new physical insight or a restatement of existing dissipation terms.
  3. [Simulation results] Simulation results paragraph: the statement that 'dynamical drag coefficients appeared to be around the often calibrated values' and 'potentially well reproduces natural event dynamics' requires quantitative comparison (error metrics, sensitivity tests, or direct confrontation with field/laboratory data) to substantiate that the new Cd improves upon or equals empirical choices on physical grounds rather than by construction.
minor comments (1)
  1. [Abstract] The abstract contains several run-on sentences and undefined terms (e.g., 'dimensionless acceleration number' introduced without prior definition). Clarify notation and improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments highlight important points regarding the clarity of our derivations and the strength of the supporting evidence. We have revised the manuscript to expand the formal derivations, clarify the independence from the equation of motion, and add quantitative comparisons with data. Below we respond point by point.

read point-by-point responses

  1. Referee: [Abstract / central postulate] Abstract and central postulate: the claim that Cd 'must contain information constituting the landslide acceleration in relation to the net driving acceleration' and is therefore expressed via a dimensionless acceleration number risks circularity. Because acceleration is already fixed by the net force balance (driving forces minus the drag term itself), defining Cd directly from that ratio can reduce to a reparametrization of the Newtonian equation rather than an independent mechanical constraint. The manuscript must demonstrate explicitly (with the full derivation) that the dimensionless number introduces additional physics or falsifiable predictions beyond standard force balance.

    Authors: We agree that the original presentation risked appearing circular and have revised the manuscript to include the complete step-by-step derivation in a new dedicated subsection. The dimensionless acceleration number is obtained from the ratio of the landslide's actual acceleration (obtained from the time derivative of the observed or simulated velocity) to the net driving acceleration computed from gravity and basal friction alone, without presupposing the form of the drag term. This construction yields an independent constraint: the resulting Cd evolves with velocity according to an explicit functional form that predicts specific scaling relations (e.g., Cd decreasing as velocity increases toward a terminal value). These predictions are falsifiable against independent velocity-time series from laboratory or field events that were not used in the derivation. The revised text explicitly contrasts this with a pure reparametrization of Newton's second law. revision: yes

  2. Referee: [Abstract] Abstract: the assertion that 'formal derivation shows that the drag coefficient is the measure of energy inefficiency' is load-bearing for the claim that the model 'settles down the deliberation on the drag force.' Without the explicit steps linking the dimensionless acceleration number to an energy-dissipation interpretation, it is impossible to verify whether the result is a new physical insight or a restatement of existing dissipation terms.

    Authors: We have added the missing explicit steps in the revised Section 2. Starting from the mechanical energy equation for the landslide, the power dissipated by drag is expressed as the difference between the rate of change of kinetic plus potential energy and the work done by gravity and friction. Dividing this dissipation rate by the square of the velocity produces the drag coefficient as the factor quantifying the fraction of available mechanical energy that is irreversibly lost to internal deformation and turbulence. The dimensionless acceleration number appears naturally as the ratio that normalizes this inefficiency, thereby linking the kinematic description directly to the energy balance without merely restating existing terms. The revised manuscript now contains the full algebraic sequence from the energy equation to the final expression for Cd. revision: yes

  3. Referee: [Simulation results] Simulation results paragraph: the statement that 'dynamical drag coefficients appeared to be around the often calibrated values' and 'potentially well reproduces natural event dynamics' requires quantitative comparison (error metrics, sensitivity tests, or direct confrontation with field/laboratory data) to substantiate that the new Cd improves upon or equals empirical choices on physical grounds rather than by construction.

    Authors: We accept that the original simulation paragraph lacked sufficient quantitative support. The revised manuscript now includes direct comparisons against two well-documented events (one laboratory flume test and one field debris-flow case). We report root-mean-square errors in velocity and run-out distance for the evolutionary Cd versus constant Cd values commonly used in the literature. Sensitivity tests varying the initial acceleration number are also presented, together with the resulting range of Cd values. These additions demonstrate that the physically derived Cd yields errors comparable to or lower than calibrated constants while eliminating the need for event-specific tuning. revision: yes

Circularity Check

1 steps flagged

Postulate tying drag coefficient to acceleration ratio reduces to tautological reparametrization of net force balance

specific steps
  1. self definitional [Abstract (postulate and formal derivation paragraph)]
    "We postulate that the drag coefficient must be a function of the evolving landslide velocity, as it must contain information constituting the landslide acceleration in relation to the net driving acceleration. ... The drag coefficient is described by a dimensionless acceleration number as it is regulated by the physics and dynamics of the flow. Formal derivation shows that the drag coefficient is the measure of energy inefficiency."

    The postulate directly defines Cd to contain the acceleration-to-driving-acceleration ratio. Yet that ratio is computed from the net force equation in which acceleration = (driving forces - Cd term) / mass. Substituting the ratio back into Cd therefore makes the 'derived' evolutionary coefficient a re-expression of the input force balance rather than an independent physical model.

full rationale

The paper's core derivation begins with an explicit postulate that defines the drag coefficient Cd as necessarily encoding the ratio of landslide acceleration to net driving acceleration, then introduces a dimensionless acceleration number to 'derive' an evolutionary Cd that measures energy inefficiency. Because the acceleration in question is already fixed by the Newtonian force balance (driving forces minus the drag term containing Cd), the construction makes the claimed formal derivation equivalent to a rewriting of the original equation of motion. No independent mechanical constraint or external benchmark is introduced beyond this self-referential postulate, producing partial circularity consistent with the reader's score of 6. The remainder of the paper (simulation results, comparison to calibrated values) does not break the definitional loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on a postulate that the drag coefficient must encode acceleration information and on the introduction of a dimensionless acceleration number whose independent physical status is not demonstrated in the abstract.

axioms (1)
  • ad hoc to paper The drag coefficient must be a function of the evolving landslide velocity because it must contain information about the landslide acceleration relative to the net driving acceleration.
    This is the explicit postulate that launches the derivation; it is presented as necessary rather than derived from prior equations.
invented entities (1)
  • dimensionless acceleration number no independent evidence
    purpose: To regulate and describe the evolutionary drag coefficient during landslide motion.
    Introduced as the physical regulator of the drag; no independent falsifiable prediction or measurement is supplied in the abstract.

pith-pipeline@v0.9.0 · 5573 in / 1403 out tokens · 27539 ms · 2026-05-10T03:30:40.676123+00:00 · methodology

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