  We investigate the formation of subaqueous transverse bedforms in turbulent
open channel flow by means of direct numerical simulations with fully-resolved
particles. The main goal of the present analysis is to address the question
whether the initial pattern wavelength scales with the particle diameter or
with 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 the
most unstable pattern wavelength in the range 75-100 times the particle
diameter, which was equivalent to 3-4 times the mean fluid height. In the
current paper, we vary the streamwise box length in terms of the particle
diameter and of the mean fluid height independently in order to distinguish
between the two possible scaling relations. For the chosen parameter range, the
obtained results clearly exhibit a scaling of the initial pattern wavelength
with the particle diameter, with a lower bound around a streamwise extent of
approximately 80 particle diameters. In longer domains, on the other hand,
patterns are observed at initial wavelengths in the range 150-180 times the
particle diameter, which is in good agreement with experimental measurements.
Variations of the mean fluid height, on the other hand, seem to have no
significant influence on the most unstable initial pattern wavelength.
Furthermore, for the cases with the largest relative submergence, we observe
spanwise and streamwise sediment waves of similar amplitude to evolve and
superimpose, leading to three-dimensional sediment patterns.
