A two-species model of aeolian sand transport

doi:10.1017/S0022112004009073

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A two-species model of aeolian sand transport

Journal Article•DOI•

A two-species model of aeolian sand transport

10 Jul 2004-Journal of Fluid Mechanics (Cambridge University Press)-Vol. 510, pp 47-70

TL;DR: In this article, a model based on a discrete number of states is derived, which solves the problems of self-consistent and unstable solutions to the transport of sand by wind, which results from the equilibrium between the erosion of grains dragged by the flow and the resulting slow down of the wind velocity.

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Abstract: The transport of sand by wind results from the equilibrium between the erosion of grains dragged by the flow and the resulting slow down of the wind velocity. The dynamical mechanisms governing the saturation of the sand flux are investigated theoretically. We first demonstrate that previous models, based on the assumption that all the grains have the same trajectory, are either not self-consistent or lead to unstable solutions. A model based on a discrete number of states is derived, which solves these problems. Two well-defined species of grain appear, which correspond to saltons (high-energy grains) and reptons (grains ejected from the sand bed by the impact of saltons). They play specific roles: the negative feedback of the transport on the wind is limited to the reptation layer while most of the transport is due to saltation. The model is further simplified, benefiting from the existence of these two species and the dependencies of the threshold velocity, the saturated flux, the aerodynamic roughness and the saturation length are derived and compared to experimental measurements.

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Journal Article•DOI•

The physics of wind-blown sand and dust

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Jasper F. Kok¹, Eric J. R. Parteli, Timothy I. Michaels, Diana Bou Karam•Institutions (1)

Cornell University¹

20 Jan 2012-arXiv: Earth and Planetary Astrophysics

TL;DR: The physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices are reviewed.

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Abstract: The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols This article presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices We also discuss the physics of wind-blown sand and dune formation on Venus and Titan

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1,175 citations

Cites background from "A two-species model of aeolian sand..."

...As is evident from equations (2.10) and (2.14), the steady state impact speed at which the replacement capacity equals unity is not dependent on u∗ (Ungar and Haff 1987, Andreotti 2004, Kok 2010a, Durán et al 2011a)....
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...The particle concentration in transport limited saltation is in steady state when there is exactly one particle leaving the soil bed for each particle impacting it (Ungar and Haff 1987, Andreotti 2004, Kok 2010a)....
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...However, more recent studies have questioned the linear scaling of particle speeds with u∗ and thus the scaling of Q with u3∗ (Ungar and Haff 1987, Andreotti 2004, Kok 2010a, 2010b, Durán et al 2011a, Ho et al 2011, Pähtz et al 2012)....
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Journal Article•DOI•

The physics of wind-blown sand and dust

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Jasper F. Kok¹, Eric J. R. Parteli, Timothy I. Michaels, Diana Bou Karam•Institutions (1)

Cornell University¹

14 Sep 2012-Reports on Progress in Physics

TL;DR: In this article, an extensive review of the physics of wind-blown sand and dust on Earth and Mars is presented, including a review of aeolian saltation, the formation and development of sand dunes and ripples, dust aerosol emission, weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices.

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Abstract: The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This paper presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars. Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices. We also discuss the physics of wind-blown sand and dune formation on Venus and Titan.

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1,069 citations

Book•

Granular Media: Between Fluid and Solid

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Bruno Andreotti¹, Yoël Forterre, Olivier Pouliquen•Institutions (1)

École Normale Supérieure¹

01 Jun 2013

TL;DR: In this article, the granular solid: statics and elasticity of granular liquid and granular gases are discussed at the grain level, and the interaction between granular media, statics, elasticity and plasticity at the liquid level.

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Abstract: Foreword 1. Introduction 2. Interactions at the grain level 3. The granular solid: statics and elasticity 4. The granular solid: plasticity 5. Granular gases 6. The granular liquid 7. Immersed granular media 8. Erosion and sediment transport 9. Geomorphology References Index.

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433 citations

Journal Article•DOI•

On aeolian transport: Grain-scale interactions, dynamical mechanisms and scaling laws

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Orencio Durán¹, Philippe Claudin¹, Bruno Andreotti¹•Institutions (1)

Paris Diderot University¹

01 Dec 2011-Aeolian Research

TL;DR: In this paper, the authors discuss the physics of aeolian sediment transport from a physical point of view using aerodynamic theory and introduce the concepts saturated flux, saturation length, and relevant framework for the development of a continuum quantitative description of transport.

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274 citations

Cites background or methods from "A two-species model of aeolian sand..."

...A tentative explanation for the origin of this scaling can be found in the different behavior of saltating grains, which follow the wind, and grains in reptation, which are more sensitive to the bed slope (Howard, 1977; Andreotti, 2004; Hersen et al., 2004)....
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...with a proportionality factor of order 2 (Andreotti et al., 2002a; Andreotti, 2004)....
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...As shown in Andreotti (2004) and Durán and Herrmann (2006), the proper way to test the scaling behavior from this data is to rescale the flux and to plot qsat=u2 as a function of u⁄ (Fig....
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...However, close to the threshold, the focal point argument gives a much better approximation (Andreotti, 2004; Durán and Herrmann, 2006)....
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...In the case of a static granular bed composed of grains of size d, reported values of the hydrodynamic roughness are reasonably consistent: z0 ’ d/30 in Bagnold (1941), z0 ’ d/24 in Schlichting and Gersten (2000) and z0 ’ d/10 in Kamphuis (1974) and Andreotti (2004)....
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Journal Article•DOI•

A comprehensive numerical model of steady state saltation (COMSALT)

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Jasper F. Kok¹, Nilton O. Renno¹•Institutions (1)

University of Michigan¹

16 Sep 2009-Journal of Geophysical Research

TL;DR: In this article, the authors presented a comprehensive numerical model of steady state saltation (COMSALT) that can reproduce a wide range of measurements and can simulate saltation over mixed soils.

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Abstract: [1] The blowing of sand by wind, known as saltation, ejects dust aerosols into the atmosphere, creates sand dunes, and erodes geological features. We present a comprehensive numerical model of steady state saltation (COMSALT) that, in contrast to most previous studies, can reproduce a wide range of measurements and can simulate saltation over mixed soils. COMSALT calculates the motion of saltating particles due to gravity, fluid drag, particle spin, fluid shear, and turbulence and explicitly accounts for the retardation of the wind due to drag from saltating particles. Furthermore, we included a novel physically based parameterization of the ejection of surface particles by impacting saltating particles which matches experimental results. COMSALT is the first numerical saltation model to reproduce measurements of the wind shear velocity at the impact threshold (i.e., the lowest shear velocity for which saltation is possible) and of the aerodynamic roughness length in saltation. It also reproduces a range of other saltation processes, including profiles of the wind speed and particle mass flux, and the size distribution of saltating particles. As such, COMSALT is the first physically based numerical model to reproduce such a wide range of experimental data. Since we use a minimum of empirical relations, COMSALT can be easily adapted to study saltation under a variety of physical conditions, such as saltation on other planets, saltation under water, and saltating snow.

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273 citations

Cites background from "A two-species model of aeolian sand..."

...Since the average impact speed is independent of shear velocity [Ungar and Haff, 1987; Andreotti, 2004], as also found by our model simulations (Kok, manuscript in preparation, 2009), we expect particle speeds for different shear velocities to converge near the surface....
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...Dimensional analysis [Andreotti, 2004; Beladjine et al., 2007] and conservation of momentum suggests that the...
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...…McEwan and Willetts, 1991; Rice et al., 1996; Rioual et al., 2000; Oger et al., 2005; Beladjine et al., 2007], N Avimp: ð20Þ Dimensional analysis [Andreotti, 2004; Beladjine et al., 2007] and conservation of momentum suggests that the parameter A can be rewritten as A ¼ affiffiffiffiffiffi gD…...
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...Since the average impact speed is independent of shear velocity [Ungar and Haff, 1987; Andreotti, 2004], as also found by our model simulations (Kok, manuscript in preparation, 2009), we expect particle speeds for different shear...
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...splashing particles from the surface (haeji) does not depend on impact speed [Andreotti, 2004], the average speed of...
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References

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Book•

The Physics of Blown Sand and Desert Dunes

[...]

R. A. Bagnold

01 Jan 1941

TL;DR: The physics of blown sand and desert dunes, The physics of windblown sand and sand dunes, this paper, and the physics of dunes in the Middle East and Africa.

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Abstract: The physics of blown sand and desert dunes , The physics of blown sand and desert dunes , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

...read moreread less

3,315 citations

Journal Article•DOI•

The Physics of Blown Sand and Desert Dunes

[...]

H. Heywood

01 Oct 1941-Nature

TL;DR: Bagnold as mentioned in this paper described his travels in the Egyptian and Libyan Deserts, and combined the results of experimental research in a wind tunnel with personal observations in the desert, and the explanations of many desert features vitally affecting such operations will interest a wide range of readers.

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Abstract: LIEUT.–COLONEL BAGNOLD is well kno for his scientific publications on desert sands and dunes, and for a book describing his travels in the Egyptian and Libyan Deserts. The present book combines these papers and much other original research into one comprehensive volume, which would, however, have possessed an added interest to readers if the introduction had included some reference to the author's work as a pioneer of motor travel in the desert. Descriptions of desert features in various parts of the world have been written by many travellers, but this book is unique in that the author has combined the results of experimental research in a wind tunnel with personal observations in the desert. The subject has a particularly topical value in connexion with the present war operations in the Libyan Desert, and the explanations of many desert features vitally affecting such operations will interest a wide range of readers. There is also scope for applying the researches to other kindred problems, such as the encroachment of desert sands over cultivated land, which is a serious menace in certain parts of the United States. The Physics of Blown Sand and Desert Dunes By R. A. Bagnold. Pp. xx + 266 + 16 plates. (London: Methuen and Co., Ltd., 1941.) 24s. net.

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1,575 citations

"A two-species model of aeolian sand..." refers background or methods or result in this paper

...…the saltation curtain should behave as an aerodynamic roughness z0 whose height is of the order of the layer thickness H ; but all the experiments (Bagnold 1941; Zingg 1953; Rasmussen, Iversen & Rautaheimo 1996) have shown that z0 is much smaller than H (few millimetres compared to tens of…...
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...As a conclusion, the one-species model by Owen (1964) and those of the same type (Bagnold 1941; Kawamura 1951; Kind 1976; Lettau & Lettau 1978; Sørensen 1991; Sauermann et al. 2001) are not self-consistent and thus have to be rejected....
[...]
...…Rasmussen 1999) using both wind tunnels and atmospheric flows on the field, numerically (Anderson & Haff 1988, 1991; Werner 1990) and theoretically (Bagnold 1941; Kawamura 1951; Owen 1964; Kind 1976; Lettau & Lettau 1978; Ungar & Haff 1987; Sørensen 1991; Sauermann, Kroy & Herrmann 2001), the…...
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...Introduction The morphogenesis and the dynamics of dunes is controlled by the transport of sand by the wind (Bagnold 1941). The shape of the dune determines the velocity field around it. In turn, the wind controls the sand flux and thus modifies the dune topography through the erosion/deposition process. The flux of sand which can be transported by a given wind is limited to an equilibrium value called the saturated flux, which increases with the wind strength. There has been a great effort to obtain experimentally (Chepil & Milne 1939; Bagnold 1941; Zingg 1953; Williams 1964; Svasek & Terwindt 1974; Nickling 1978; Jones & Willetts 1979; White 1979; Willetts, Rice & Swaine 1982; Greeley, Blumberg & Williams 1996; Iversen & Rasmussen 1999) using both wind tunnels and atmospheric flows on the field, numerically (Anderson & Haff 1988, 1991; Werner 1990) and theoretically (Bagnold 1941; Kawamura 1951; Owen 1964; Kind 1976; Lettau & Lettau 1978; Ungar & Haff 1987; Sørensen 1991; Sauermann, Kroy & Herrmann 2001), the relationship between the saturated flux over a flat sand bed and the shear velocity u∗. Apart from the work by Ungar & Haff (1987) which we shall turn to later, all the theoretical studies give similar results: the saturated flux q vanishes below a threshold value uth of the shear velocity and scales at large shear velocity like the Bagnold (1941) prediction,...
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...The morphogenesis and the dynamics of dunes is controlled by the transport of sand by the wind (Bagnold 1941)....
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Journal Article•DOI•

Saltation of uniform grains in air

[...]

P. R. Owen¹•Institutions (1)

Imperial College London¹

01 Oct 1964-Journal of Fluid Mechanics

TL;DR: In this paper, the interaction between a turbulent wind and the motion of uniform saltating grains of sand or soil, so massive as to fail to enter into suspension, is examined on the basis of two complementary hypotheses.

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Abstract: The interaction between a turbulent wind and the motion of uniform saltating grains of sand or soil, so massive as to fail to enter into suspension, is examined on the basis of two complementary hypotheses. The first asserts that the effect of the moving grains on the fluid outside the region to which saltation is confined is similar to that of solid roughness of height comparable with the depth of the saltation layer. The second requires the concentration of particles engaging in the saltation to adjust itself so that the shear stress exerted by the wind on the ground—different from that acting on the fluid outside the saltation layer by an amount accountable to the change in horizontal momentum suffered by the particles in their passage through the fluid—is just sufficient to maintain the sand-strewn surface in a mobile state.Existing experimental data on the wind profiles outside the saltation region and the horizontal flux of particles through it are shown to be consistent with these hypotheses.The second hypothesis implies a self-balancing mechanism for controlling the concentration of saltating particles. For if the concentration is too low the shear stress at the surface rises above the value required merely to secure mobility and more particles are encouraged to leave the surface; conversely, too large a concentration depresses the surface stress, and the consequent loss of surface mobility inhibits saltation and reduces th concentration of particles until equilibrium is restored.

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1,051 citations

"A two-species model of aeolian sand..." refers background or methods in this paper

...As a conclusion, the one-species model by Owen (1964) and those of the same type (Bagnold 1941; Kawamura 1951; Kind 1976; Lettau & Lettau 1978; Sørensen 1991; Sauermann et al. 2001) are not self-consistent and thus have to be rejected....
[...]
...The total flux q is scaling asymptotically as u(2)∗Tsal in Owen-like models and as u 2 ∗Trep for Ungar & Haff (1987). We find here an asymptotic scaling as u(2)∗Lsal/Neje....
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...In order to compare the result to the Owen (1964) model, z0 is rescaled by the typical saltation layer height u2∗/2g....
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...…tunnels and atmospheric flows on the field, numerically (Anderson & Haff 1988, 1991; Werner 1990) and theoretically (Bagnold 1941; Kawamura 1951; Owen 1964; Kind 1976; Lettau & Lettau 1978; Ungar & Haff 1987; Sørensen 1991; Sauermann, Kroy & Herrmann 2001), the relationship between the…...
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...To point out the paradox of the one-species models, we recall the basic assumptions and the predictions of the model established by Owen (1964) as it is the reference of the others....
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Journal Article•DOI•

Soil Transport by Winds on Mars

[...]

Bruce R. White¹•Institutions (1)

University of California, Davis¹

10 Aug 1979-Journal of Geophysical Research

TL;DR: In this paper, a semi-empirical formula is developed for estimating the total amount of surface material moving in eolian saltation, surface traction, and suspension on the surface of Mars, and the ratio of final particle speed to the particle threshold friction speed is found to be several times that of saltation on earth.

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Abstract: Results of low-pressure wind tunnel testing and theoretical considerations are used to estimate the eolian transport of surface material on Mars Saltation on Mars, equations of particle motion, computational results, and analytical determination of surface material movement are considered A semiempirical formula is developed for estimating the total amount of surface material moving in eolian saltation, surface traction, and suspension Numerical solutions of the equations of motion for particle trajectories on the surface of Mars are presented The ratio of final particle speed to the particle threshold friction speed is found to be several times that of saltation on earth

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449 citations

"A two-species model of aeolian sand..." refers background in this paper

...…obtain experimentally (Chepil & Milne 1939; Bagnold 1941; Zingg 1953; Williams 1964; Svasek & Terwindt 1974; Nickling 1978; Jones & Willetts 1979; White 1979; Willetts, Rice & Swaine 1982; Greeley, Blumberg & Williams 1996; Iversen & Rasmussen 1999) using both wind tunnels and atmospheric flows…...
[...]
...There has been a great effort to obtain experimentally (Chepil & Milne 1939; Bagnold 1941; Zingg 1953; Williams 1964; Svasek & Terwindt 1974; Nickling 1978; Jones & Willetts 1979; White 1979; Willetts, Rice & Swaine 1982; Greeley, Blumberg & Williams 1996; Iversen & Rasmussen 1999) using both wind tunnels and atmospheric flows on the field, numerically (Anderson & Haff 1988, 1991; Werner 1990) and theoretically (Bagnold 1941; Kawamura 1951; Owen 1964; Kind 1976; Lettau & Lettau 1978; Ungar & Haff 1987; Sørensen 1991; Sauermann, Kroy & Herrmann 2001), the relationship between the saturated flux over a flat sand bed and the shear velocity u∗....
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Book Chapter•DOI•

Wind modification and bed response during saltation of sand in air

[...]

Robert S. Anderson¹, Peter K. Haff²•Institutions (2)

University of California, Santa Cruz¹, Duke University²

01 Jan 1991

TL;DR: In this article, a model of eolian sediment transport was constructed, which is a special case of sand-sized mineral grains subjected to moderate winds: saltation, and the model consists of four compartments corresponding to aerodynamic entrainment, grain trajectories, grain-bed impacts, and momentum extraction from the wind.

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Abstract: A model of eolian sediment transport has been constructed, a special case of which is that corresponding to sand-sized mineral grains subjected to moderate winds: saltation. The model consists of four compartments corresponding to (1) aerodynamic entrainment, (2) grain trajectories, (3) grain-bed impacts, and (4) momentum extraction from the wind. Each sub-model encapsulates the physics of the process, and is constrained where necessary by experimental data. When combined, the full model allows simulation of eolian saltation from inception by aerodynamic entrainment to steady state.

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419 citations

"A two-species model of aeolian sand..." refers background or methods or result in this paper

...Later, we shall compare our results to the numerical computations by Anderson & Haff (1988, 1991) and Werner (1990) in which a probabilistic splash function is used....
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...This was done in the numerical simulations by Anderson & Haff (1988, 1991) and Werner (1990) where a continuous distribution of trajectories was investigated....
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...The first steps of the saturation process have been observed by Willetts, McEwan & Rice (1991) and studied numerically by Anderson & Haff (1988, 1991)....
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...The results by Werner (1988), Anderson & Haff (1988, 1991) and McEwan et al. (1992) and Rioual et al. (2000) are consistent with the assumption that a constant fraction of the impact momentum is transferred to the ejecta....
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...Following the numerical simulations by Werner (1988) and Anderson & Haff (1988, 1991), we will use the expression: preb = p∞ [ 1 − exp ( − vimp a √ gd )] ....
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