The three-dimensional flow is initiated over two-dimensional shaped ripples (vortex ripple) through three-dimensional instability, possibly causing the formation of the so-called brick-pattern ripple by a spanwise convection of sediments in a three-dimensional vortex structure. The transition from two- to three-dimensional wave boundary layer flows over ripples under a small amplitude wave, and the convection process of a passive scalar function are presented. The maximum spanwise velocity depends on Reynolds number, and the prominent spectrum peaks of the spanwise velocity arise at harmonic wave numbers of the basic wave number of a two-dimensional ripple. The bellow animation shows evolution of the three-dimesnional instantaneous vorticities occuring over a two-dimensional ripple in one wave period.

Ref.
Watanabe, Y., Matsumoto, S., Saeki, H., Three-dimensional boundary layer
flow over ripples, Proceedings of Coastal Sediments (CD-ROM), (2003)