On the patterns of oscillatory flow over a wavy bed

Oscillatory flow over sedimentary wavy beds is fundamental to understanding sediment transport and seabed evolution. However, the vortex dynamics and flow pattern transitions across varying flow conditions remain inadequately quantified. This study employs direct numerical simulation to investigate oscillatory flow over a fixed wavy bed at Reynolds number Re = 900, covering the Keulegan–Carpenter number range 0.25 ≤ KC ≤ 3.50 and distinguishing between two-dimensional (2D) and three-dimensional (3D) flows. Three distinct flow patterns are mapped out, including the roll pattern (R), roll plus jet pattern (RJ), and vortex ejection pattern (VE). The present results show that as KC increases, the formation of these patterns is driven by changes in the intensity, dominance, and interaction of vortices generated by boundary layer separation. In 2D model, all these patterns are periodic and repeat once per oscillatory cycle. Further analysis of steady streaming reveals that as KC increases, the period-averaged flow fields transition from a quadruple-loop system at KC = 0.25 to a double-loop system at KC = 3.50. During this transition, a new triple-loop system is observed, which leads to the significant drifting velocity above the wavy surface. The present study also demonstrates that the major 3D effect is to disrupt the periodicity of the flow, while its influence on flow patterns and velocity details remains limited within the investigated parameter range.