Dynamics of aeolian sand ripples

Abstract

We analyze theoretically the dynamics of aeolian sand ripples. In order to put the study in the context we first review existing models. This paper is a continuation of two previous papers [3,4], the first one is based on symmetries and the second on a hydrodynamical model. We show how the hydrodynamical model may be modified to recover the missing terms that are dictated by symmetries. The symmetry and conservation arguments are powerful in that the form of the equation is model-independent. We then present an extensive numerical and analytical analysis of the generic sand ripple equation. We find that at the initial stage the wavelength of the ripple is that corresponding to the linearly most dangerous mode. At later stages the profile undergoes a coarsening process leading to a significant increase of the wavelength. We find that including the next higher order nonlinear term in the equation, leads naturally to a saturation of the local slope. We analyze both analytically and numerically the coarsening stage, in terms of a dynamical exponent for the mean wavelength increase. We discuss some future lines of investigations.

Observation and Modeling of Interrupted Pattern Coarsening: Surface Nanostructuring by Ion Erosion

“…The linear BH theory and later extensions [25,14] have provided relevant information about the main operating mechanisms as well as qualitative predictions on properties like the wavelength dependence on some experimental parameters, ripple orientation as a function of the incidence angle, etc. However, description of other important pattern features, such as coarsening and ordering, has required the coupling of h with an additional field related with the density of material subject to surface transport, akin to descriptions of pattern formation on aeolian sand dunes [26]. In spite of all these efforts, a fully consistent quantitative description the IBS system is still lacking [6,17].…”

Experimental study of aeolian sand ripples in a wind tunnel

“…There has been no detailed investigation on the initial propagation velocity of sand ripples and the relationships among the initial formation time, wavelength, propagation velocity of sand ripples, and friction velocity. The few studies on the wavelength of developing ripples are mainly conducted using numerical modelling (Werner and Gillespie, 1993;Csahók et al, 2000;Yizhaq et al, 2004). The relationships between wavelength and time either follows a logarithmic function (L(t)=aln(bt+c), where a, b, and c are parameters) (Werner and Gillespie, 1993) or a power one (L(t) = at b , where a, and b are parameters and parameter b can be 0.27-0.5 according to Yizhaq et al (2004) or 0.25-0.50 according to Csahók et al (2000)).…”

“…The few studies on the wavelength of developing ripples are mainly conducted using numerical modelling (Werner and Gillespie, 1993;Csahók et al, 2000;Yizhaq et al, 2004). The relationships between wavelength and time either follows a logarithmic function (L(t)=aln(bt+c), where a, b, and c are parameters) (Werner and Gillespie, 1993) or a power one (L(t) = at b , where a, and b are parameters and parameter b can be 0.27-0.5 according to Yizhaq et al (2004) or 0.25-0.50 according to Csahók et al (2000)). Although scientists (Anderson, 1987;Csahók et al, 2000) have developed numerous numerical models of sand ripples, which can be used to simulate the evolution process of sand ripples, the accuracy of simulation results is far from that of the results of direct measurement.…”

“…Ripple height of coarse grains is greater than that of fine grains (Zhu, 1962;Li and Ni, 2004), and ripple height is proportional to sand grain size (Sharp, 1963). The wavelength of sand ripples increases with time according to a logarithm (Werner and Gillespie, 1993;Yizhaq et al, 2004) or power function (Valance and Rioual, 1999;Csahók et al, 2000;Andreotti et al, 2006). Wind velocity plays a very significant role in the change in the wavelength of sand ripples with time (Seppälä and Lindé, 1978;Andreotti et al, 2006).…”

“…For example, the initial formation time (Yizhaq et al, 2004) or full development time (Zheng et al, 2008) of sand ripples is less than that of wind tunnel experiments (Borsy, 1973;Seppälä and Lindé, 1978;Werner and Gillespie, 1993;Andreotti et al, 2006;Zhu, 2009). Even in the experimental data, there are significant differences between each experiment, such as the initial formation time of sand ripples (Werner and Gillespie, 1993;Andreotti et al, 2006;Zhu, 2009), the relationship between the wavelength of developing ripples and time (Werner and Gillespie, 1993;Csahók et al, 2000;Yizhaq et al, 2004), etc. Furthermore, whether numerical simulation or experimental observation is conducted, little is reported in existing literature regarding key parameters of the formation and evolution processes of sand ripples, especially for the differences between the dynamic characteristics of ripples in unsaturated and saturated regimes.…”