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We investigate the formation of subaqueous transverse bedforms in turbulentopen channel flow by means of direct numerical simulations with fully-resolvedparticles. The main goal of the present analysis is to address the questionwhether the initial pattern wavelength scales with the particle diameter orwith the mean fluid height. A previous study (Kidanemariam and Uhlmann, J.Fluid Mech., vol. 818, 2017, pp. 716-743) has observed a lower bound for themost unstable pattern wavelength in the range 75-100 times the particlediameter, which was equivalent to 3-4 times the mean fluid height. In thecurrent paper, we vary the streamwise box length in terms of the particlediameter and of the mean fluid height independently in order to distinguishbetween the two possible scaling relations. For the chosen parameter range, theobtained results clearly exhibit a scaling of the initial pattern wavelengthwith the particle diameter, with a lower bound around a streamwise extent ofapproximately 80 particle diameters. In longer domains, on the other hand,patterns are observed at initial wavelengths in the range 150-180 times theparticle diameter, which is in good agreement with experimental measurements.Variations of the mean fluid height, on the other hand, seem to have nosignificant influence on the most unstable initial pattern wavelength.Furthermore, for the cases with the largest relative submergence, we observespanwise and streamwise sediment waves of similar amplitude to evolve andsuperimpose, leading to three-dimensional sediment patterns.

On the scaling of the instability of a flat sediment bed with respect to ripple-like patterns