Geometry of Wave-Formed Orbital Ripples in Coarse Sand

Resumen

Using new large-scale wave-flume experiments we examine the cross-section and planform geometry of wave-formed ripples in coarse sand (median grain size D50=430" role="presentation" style="position: relative;">??50=430D50=430 D 50 = 430 µm) under high-energy shoaling and plunging random waves. We find that the ripples remain orbital for the full range of encountered conditions, even for wave forcing when in finer sand the ripple length λr" role="presentation" style="position: relative;">?????r ? r is known to become independent of the near-bed orbital diameter ds" role="presentation" style="position: relative;">????ds d s (anorbital ripples). The proportionality between λr" role="presentation" style="position: relative;">?????r ? r and ds" role="presentation" style="position: relative;">????ds d s is not constant, but decreases from about 0.55 for ds/D50≈1400" role="presentation" style="position: relative;">????/??50?1400ds/D50?1400 d s / D 50 ? 1400 to about 0.27 for ds/D50≈11,500" role="presentation" style="position: relative;">????/??50?11,500ds/D50?11,500 d s / D 50 ? 11 , 500 . Analogously, ripple height ηr" role="presentation" style="position: relative;">?????r ? r increases with ds" role="presentation" style="position: relative;">????ds d s , but the constant of proportionally decreases from about 0.08 for ds/D50≈1400" role="presentation" style="position: relative;">????/??50?1400ds/D50?1400 d s / D 50 ? 1400 to about 0.02 for ds/D50>8000" role="presentation" style="position: relative;">????/??50>8000ds/D50>8000 d s / D 50 > 8000 . In contrast to earlier observations of coarse-grained two-dimensional wave ripples under mild wave conditions, the ripple planform changes with the wave Reynolds number from quasi two-dimensional vortex ripples, through oval mounds with ripples attached from different directions, to strongly subdued hummocky-type features. Finally, we combine our data with existing mild-wave coarse-grain ripple data to develop new equilibrium predictors for ripple length, height and steepness suitable for a wide range of wave conditions and a D50" role="presentation" style="position: relative;">??50D50 D 50 larger than about 300 µm.