  Three-dimensional sand ripples can be observed under steady liquid flows in
both nature and industry. Some examples are the ripples observed on the bed of
rivers and in petroleum pipelines conveying sand. Although of importance, the
formation of these patterns is not completely understood. There are theoretical
and experimental evidence that aquatic ripples grow from two-dimensional bed
instabilities, so that a straight vortex is formed just downstream of their
crests. The proposition of Raudkivi (2006), that three-dimensionality has its
origin in a vortex instability, is employed here. This paper presents a linear
stability analysis of the downstream vortex in order to obtain the transverse
scales of three-dimensional ripples. The obtained wavelength is compared with
experimentally observed ripples.
