Aeolian Sand Ripples: Experimental Study of Fully Developed States

We report an experimental investigation of aeolian sand ripples, performed both in a wind tunnel and on stoss slopes of dunes. Starting from a flat bed, we can identify three regimes: appearance of an initial wavelength, coarsening of the pattern, and finally saturation of the ripples. We show that both initial and final wavelengths, as well as the propagative speed of the ripples, are linear functions of the wind velocity. Investigating the evolution of an initially corrugated bed, we exhibit nonlinear stable solutions for a finite range of wavelengths, which demonstrates the existence of a saturation in amplitude. These results contradict most of the models.

Figure 1

Experimental setup both in the field and in the wind tunnel. (a) The profile $h(x)$ is given by the inclined laser sheet. (b) Autocorrelation function $C(\lambda ,t)=⟨h(x,t)h(x+\lambda ,t)⟩-⟨h(x,t){⟩}^2$ of the profile. The position of the first peak gives the mean wavelength $\lambda$. The amplitude is defined by $A(t)=2\sqrt{2C(0,t)}$. (c) Method for engraving periodic profiles (the lateral bars are removed once the pattern is engraved).

Figure 2

Evolution of an initially flat bed. (a) Pictures at different times for field experiments $u^{*}=1.3u_{\mathrm{th}}$. (b) Spatiotemporal diagram in the wind tunnel for $u^{*}=1.4u_{\mathrm{th}}$. Time evolution of (c) wavelength $\lambda (t)$ and (d) amplitude $A(t)$ from a flat bed for different values of the shear velocity: $u^{*}=1.3u_{\mathrm{th}}$ (△), $u^{*}=1.4u_{\mathrm{th}}$ (▲), $u^{*}=1.8u_{\mathrm{th}}$ (○), $u^{*}=2.3u_{\mathrm{th}}$ (●). Inset: time log scale.

Figure 3

Evolution of an initially corrugated bed. Pictures from the field for $u^{*}=1.3u_{\mathrm{th}}$ and initial wavelength (a) $\lambda =5\mathrm{cm}$; (b) $\lambda =13.5\mathrm{cm}$; (c) $\lambda =30\mathrm{cm}$. Spatiotemporal diagram in the wind tunnel for $u^{*}=1.3u_{\mathrm{th}}$ and (d) $\lambda =5\mathrm{cm}$; (e) $\lambda =9.3\mathrm{cm}$; (f) $\lambda =19.5\mathrm{cm}$.

Figure 4

Stability diagram of ripples of initial wavelength $\lambda$ and amplitude $A$ for $u^{*}=1.3u_{\mathrm{th}}$. Outside the locking zone (○), the pattern destabilizes by generation of harmonics (right) or subharmonics (left). Starting in the central region (■), $\lambda$ stays constant and $A$ readapts to reach a stable steady solution (●). Very large amplitudes cannot be imposed as avalanche processes take place. Hatched region is beyond experimental access.

Figure 5

(a) $A$ as a function of $\lambda$ for different wind velocities in the wind tunnel (●) and in the field (○). (b) Initial (■) and final (●) wavelength (wind tunnel data) and field final wavelength (○) as a function of the imposed flow velocity $u_{*}$. (c) Propagation velocity of developed ripples as a function of the wind speed for free evolving ripples in the wind tunnel (●) and in the field (○). Data represented by $+$ (resp. $\times$) come from 12 [13 ], for grains of size $d\sim 310\mu \mathrm{m}$ ($150\mu \mathrm{m}$).