A two-species model of aeolian sand transport
Citations
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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1,069 citations
433 citations
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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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
3,315 citations
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....
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...…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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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....
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...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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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…...
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...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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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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