The three-dimensional flow is initiated over two-dimensional shaped ripples (vortexrnripple) through three-dimensional instability, possibly causing the formation of the so-calledrnbrick-pattern ripple by a spanwise convection of sediments in a three-dimensional vortexrnstructure. The transition from two- to three-dimensional wave boundary layer flows over ripplesrnunder a small amplitude wave, and the convection process of a passive scalar function arernpresented. The maximum spanwise velocity depends on Reynolds number, and the prominentrnspectrum peaks of the spanwise velocity arise at harmonic wave numbers of the basic wavernnumber of a two-dimensional ripple.
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