Wavelength selection of rolling-grain ripples in the laboratory.

We have performed an experimental study, at very high resolution, of the wavelength selection and the evolution of rolling-grain ripples. A clear distinction is made between the flat sand bed instability and the ripple coarsening. The observation of the initial wavelength for the rolling-grain ripples is only possible close to the threshold for movement which imposes a constraint on the parameters. Moreover, we have proposed a law for the selection of the unstable wavelength under the latter constraint. Our results suggest that the initial wavelength depends on the amplitude of oscillation, the grain diameter, and the Stokes layer. Besides, during the coarsening, we observe no self-similarity of the ripple shape and for few cases a logarithmic growth of the wavelength.