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

Hezi Yizhaq 1 ,4, Erez Schmerler2, Itzhak Katra2, Jasper Kok3, Haim Tsoar2
1Blaustein Institutes for Desert Research, Midreshet Ben-Gurion, Israel, 2Ben-Gurion University of the Negev, Beer Sheva, Israel, 3University of California, Los Angeles, USA, 44The Dead Sea and Arava Science Center, Tamar Regional Council, Israel

Despite advances in understanding processes of sand transport by saltation and reptation involved in formation of sand ripples, it is still unclear what mechanisms determine the linear dependence of ripple spacing on wind speed and their relative importance. In a pivotal study, Sharp (1963) proposed that this linear dependence arises from the scaling of the ripples' shadow zone - that part of the ripple devoid of particle impacts - with the wind speed. Here, we test this hypothesis by integrating wind tunnel experiments with numerical simulations of saltation using COMSALT. Specifically, we measured the effective shadow zone by using sand traps designed for this purpose and found a linear relationship between the shadow zone and the wind shear velocity for different grain size fractions, consistent with Sharp's hypothesis. However, contrary to what Sharp (1963) assumed, we found that the shadow zone is not completely screened from particle impacts, which numerical simulations indicate is due to the wide distribution of impact angles. Nonetheless, the shadow zone hypothesis can be one of the major mechanisms contributing to the linear increase of the ripple wavelength with wind speed at the nonlinear growth stage of the ripples where merging events between small ripples take place and the lee slope angle exceeds the mean impact angle. However, for the initial stage of ripple development, when the ripple dimension is small, other mechanisms can be dominant and control the initial wavelength, such as the recently suggested resonant saltation trajectory (Durán et al., 2014).
The mechanism which saturates the ripple growth is also not fully understood, although it could be related to the increase of shear stress at the ripple crest due to flow convergence preventing further ripple growth. If correct, this still leaves open the questions of why the ripple height also grows linearly with speed and why the larger ripples in the wind tunnel experiment were obtained with the fine fraction since the finer grains can be entrained more easily from the crest. One possible explanation is discussed that the shear velocity at the surface decreases with shear velocity to a value below the impact threshold, thus it cannot dislodge grains from the crest, despite that the shear velocity is higher above the saltation layer.

References
Durán, O., Claudin, P. and Andreotti, B. (2014). Direct numerical simulations of aeolian sand ripples. PNAS 111 (44) 15665-15668.
Sharp, R. P. 1963. Wind ripples. Journal of Geology 71: 617-636.