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It is widely accepted that both ripples and dunes form in rivers by primarylinear instability, the wavelength of the former scaling on the grain size,that of the latter being controled by the water depth. We revisit here thisproblem, using the computation of the turbulent flow over a wavy bottomperformed in Part 1. The details of the different mechanisms controllingsediment transport are encoded into three quantities: the saturated flux, thesaturation length and the threshold shear stress. Theses quantities aremodelled in the case of erosion and momentum limited bed loads. This frameworkallows to give a clear picture of the instability in terms of dynamicalmechanisms. The relation between the wavelength at which ripples form and theflux saturation length is quantitatively derived. Inverting the problem,experimental data is used to determine the saturation length as a function ofgrain size and shear velocity. Finally, using the systematic expansion of theflow field with respect to the corrugation amplitude, we discuss the non-linearselection of ripple aspect ratio. Investingating the effect of a free surfaceon the linear instability, we show that the excitation of standing waves at thesurface has a stabilising effect, independently of the details of the flow andsediment transport models. Consequently, the shape of the dispersion relationis such that dunes can not result from a primary linear instability. We presentthe results of field experiments performed in the natural sandy Leyre river,which evidence the formation of ripples by a linear instability and theformation of dunes by a non-linear pattern coarsening limited by the freesurface. We show that mega-dunes form when the sand bed presentsheterogeneities such as a wide distribution of grain sizes.

Bedforms in a turbulent stream.Part 2: Formation of ripples by primary linear instability and of dunes by non-linear pattern coarsening