Saltat senex, as it is in the proverb; he does triumph in his felicity, admires the party!
"Epicoene" by Ben Jonson
It was posturing rather than saltation.
"Samoa, A Hundred Years Ago And Long Before" by George Turner
In the heat of noon, in the cool of the evening, day after day there was no rest for them, their saltation was without end.
"Folk-lore and Legends: German" by Anonymous
Phoebe minor, however, executed gleeful saltations in honour of his arrival.
"Love's Usuries" by Louis Creswicke
Mr. Durnford found this Saltator "pretty common" near Baradero, on low scrubby ground near water, and afterwards obtained it near Salta.
"Argentine Ornithology, Volume I (of 2)" by P. L. Sclater
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To initiate saltation some grains have to be entrained directly by the air.
A Continuum Saltation Model for Sand Dunes
Through this feedback mechanism the saltation dynamics reaches an equilibrium state, characterized by a saturated density ρs and an average velocity us of the saltating grains.
A Continuum Saltation Model for Sand Dunes
Here, ρ(x, t) and u(x, t) denote the density and velocity of the grains in the saltation layer, respectively.
A Continuum Saltation Model for Sand Dunes
At the top zm of the saltation layer, the air born shear stress τa has to be equal to the overall shear stress τ , τa (zm ) = τ .
A Continuum Saltation Model for Sand Dunes
Here, vef f is an effective wind velocity, which is the wind speed taken at a reference height z1 within the saltation layer.
A Continuum Saltation Model for Sand Dunes
Neglecting the effect of the saltating grains on the wind ﬁeld, we could use the logarithmic proﬁle at z1 to calculate the effective wind speed.
A Continuum Saltation Model for Sand Dunes
But saltating grains in the air change the air shear stress and the wind speed.
A Continuum Saltation Model for Sand Dunes
Furthermore, we have introduced two model parameters α and z1 determining the equilibrium state of the saltation layer, and the parameter γ that controls the relaxation to equilibrium.
A Continuum Saltation Model for Sand Dunes
Direct aerodynamic entrainment, i.e. the initiation of saltation, has been neglected in Eq.(32), but can easily be included by adding the erosion rate Γa of Eq.(20) to the right hand side.
A Continuum Saltation Model for Sand Dunes
The dominant mechanism to adapt the grain density in the saltation layer due to a change in external conditions is by the chain reaction process modeled in Eq.(17).
A Continuum Saltation Model for Sand Dunes
In the following sections we will ﬁrst discuss the fully saturated situation and later some dynamical properties of the saltation layer.
A Continuum Saltation Model for Sand Dunes
The full dynamics of the saltation layer must be evaluated numerically, whereas the saturated ﬂux — the stationary solution (∂ /∂ t = 0) for a constant external shear stress (τ (x, t) = τ ) and a homogeneous bed (∂ /∂ x = 0) — can be calculated analytically from Eq.(29) and (33).
A Continuum Saltation Model for Sand Dunes
For large wind speeds (u∗ ≫ u∗t ) the ﬂux is asymptotically proportional to u3 ∗ , which is in accord with the predictions of other saltation models [3, 21, 25].
A Continuum Saltation Model for Sand Dunes
As anticipated above, the value obtained for z1 , the reference height for momentum transfer, is well below zm , the mean height of the saltation tra jectories.
A Continuum Saltation Model for Sand Dunes
After the saturated case has been studied in the preceding section, we now investigate the dynamics of the saltation layer in order to get an estimate for the saturation time Ts and thus for the model parameter γ .
A Continuum Saltation Model for Sand Dunes
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