Direct numerical simulations of ripples in an oscillatory flow

TL;DR

This study uses direct numerical simulations to investigate the formation and growth of sea ripples caused by oscillatory flow, revealing the roles of flow recirculation, particle motion, and pressure gradients in ripple development.

Contribution

It provides detailed fluid and sediment insights into ripple formation using fully-resolved spherical grains, advancing understanding beyond laboratory observations.

Findings

Ripple wavelength is determined by steady recirculating cells.

Ripple amplitude grows exponentially, consistent with linear stability theories.

Sediment flow is driven by bed shear stress and pressure gradient depending on oscillation phase.

Abstract

Sea ripples are small-scale bedforms which originate from the interaction of an oscillatory flow with an erodible sand bed. The phenomenon of sea ripple formation is investigated by means of direct numerical simulation in which the sediment bed is represented by a large number of fully-resolved spherical grains. Two sets of parameter values are adopted which are motivated by laboratory experiments on the formation of laminar rolling-grain ripples. The knowledge on the origin of ripples is presently enriched by insights and by providing fluid- and sediment-related quantities that are difficult to obtain in the laboratory. Detailed analysis of flow and sediment bed evolution has confirmed that ripple wavelength is determined by the action of steady recirculating cells which tend to accumulate sediment grains into ripple crests. The ripple amplitude is observed to grow exponentially consistent with established linear stability analysis theories. Particles at the bed surface exhibit two kinds of motion depending on their position with respect to the recirculating cells: particles at ripple crests are significantly faster and show larger excursions than those lying on ripple troughs. In analogy with segregation phenomenon of polydisperse sediments the non-uniform distribution of the velocity field promotes the formation of ripples. The wider the gap between the excursion of fast and slow particles, the the larger the resulting growth rate of ripples. Finally, it is revealed that, in the absence of turbulence, the sediment flow rate is driven by both the bed shear stress and the wave-induced pressure gradient, the dominance of each depending on the phase of the oscillation period. In phases of maximum bed shear stress, the sediment flow rate correlates more with the Shields number while the pressure gradient tends to drive sediment bed motion during phases of minimum bed shear stress.