Experimental and numerical study of Sharp’s shadow zone hypothesis on sand ripple wavelength

Experimental study of aeolian sand ripples in a wind tunnel

“…This trend in ripple height, i.e. increasing initially and then decreasing with the friction velocity, is consistent with previous research conducted by Ling et al (1998) and Walker (1981), but disagrees with those by Bagnold (1941), Sharp (1963), Seppälä and Lindé (1978), Ling et al (2003), Li and Ni (2004), Andreotti et al (2006), Durán et al (2014) and Schmerler et al (2016), which found a linear increase of ripple height with shear velocity. The possible reason for the decrease in ripple height at high wind velocities is the effect of the descending processes of wind velocities on ripple heights, which is largely dependent on the friction velocity.…”

“…Later studies, however, showed no direct relationship between these two (Sharp, 1963;Anderson and Haff, 1988;Kok et al, 2012;Lämmel et al, 2012;Yizhaq et al, 2014;Schmerler et al, 2016). Although the initial wavelength of the ripple is about six times the mean reptation length (Seppälä and Lindé, 1978;Anderson 1987), the simulation results failed to explain the dependence of wavelength on wind speed (Anderson 1987;Anderotti et al 2006;Schmerler et al, 2016). Recently, Schmerler et al (2016) solved the issue by assuming the wavelength of the sand ripples to be the sum of the length between the ripples' shadow zone and the impact zone and detected the increasing trend of sand ripple wavelength with friction velocity.…”

“…As early as in the 1940s, Bagnold (1941) found that the wavelength of sand ripples is positively correlated with the mean characteristic path of saltating sand grains, which increases with friction velocity. Later studies, however, showed no direct relationship between these two (Sharp, 1963;Anderson and Haff, 1988;Kok et al, 2012;Lämmel et al, 2012;Yizhaq et al, 2014;Schmerler et al, 2016). Although the initial wavelength of the ripple is about six times the mean reptation length (Seppälä and Lindé, 1978;Anderson 1987), the simulation results failed to explain the dependence of wavelength on wind speed (Anderson 1987;Anderotti et al 2006;Schmerler et al, 2016).…”

“…As a result of the varying ripple height, the surface roughness increases and the friction velocity changes as well. The wavelengths of sand ripples linearly increase with ripple height (Bagnold, 1941;Sharp, 1963;Seppälä and Lindé, 1978;Lin et al, 1998;Ling et al, 2003;Li and Ni, 2004;Luo et al, 2004;Andreotti et al, 2006;Durán et al, 2014;Schmerler et al, 2016). However, the propagation velocity is inversely proportional to the ripple height, since small ripples catch up to and merge with larger ones (Bagnold 1941;Sharp, 1963;Forrest and Haff, 1992;Landry and Werner, 1994;Hoyle and Woods, 1997).…”

“…The collision angle between sand grains and the bed increases with grain size (Jensen and Sørensen, 1986;Willetts and Rice, 1989;Rice et al, 1995;Fu et al, 2013) and decreases with wind velocity (Mitha et al, 1986;Cheng et al, 2009) as well as shadow zone length (Cooke and Warren, 1973). Furthermore, the latter increases with ripple wavelength (Schmerler et al, 2016), indicating that the wavelength of sand ripples decreases with collision angle (Hoyle and Woods, 1997). Thus, detailed experiments are necessary to improve the accuracy of numerical modelling.…”