Fluid Dynamical Control of Spacing and Symmetry Breaking in Orbital Wave Ripples

Sand ripples in coastal environments and the rock record are a ubiquitous signature of the interaction of flows, bed topography and sediment transport. A common class of ripples, orbital wave ripples, exhibits a well-known linear relationship between the wavelength of the ripple pattern and the amplitude of wave-generated oscillatory flow. Based on this relationship, the ripple wavelength is often used as a paleoenvironmental indicator; and the height and spacing of modern ripples are major controls on bed roughness. However, the mechanism that selects the observed ratio of ripple wavelength to flow amplitude has not been explained. Orbital wave ripples are sustained by zones of reversed flow on the lee side of the crest that moves sand upslope toward the crest. Using a lattice Boltzmann numerical flow model to simulate two-dimensional flow over a rippled bed, we demonstrate a coupling of flow and ripples that leads to the observed equilibrium: if the ratio between the orbital diameter (double the flow amplitude) and ripple wavelength is 0.65 - the equilibrium ratio observed in laboratory experiments and in the field - the maximum length of the separation zone downstream of a ripple crest is exactly equal to the ripple wavelength. Longer separation zones, with vortices advected further, will erode the neighboring crest. Shorter separation zones will not be able to erode the adjacent troughs. In addition to this equilibrium morphology, orbital wave ripples display characteristic patterns as they evolve in response to changes in wave conditions. Multiple experiments have shown that large-scale symmetry is lost during adjustment to a new equilibrium. When the wave orbital diameter is shortened sufficiently, two new crests appear in every trough. Of these two, one decays, while the other keeps growing. Interestingly, the same side (right or left) is observed to 'win' in every trough. When the orbital diameter is lengthened, a 'bulging' instability occurs, in which select ripple crests become increasingly sinuous before breaking up. The origins of these transient phenomena are not yet understood. We extracted side-looking 1D-profiles from field-scale laboratory experiments in a wave tank to study the incipient response of ripples to a step change in wave conditions, and used the numerical flow model to calculate stresses over the evolving bed. Combining these calculations with real-time video and time-lapse imagery, we tracked the hydrodynamic and morphodynamic evolution of individual ripples. When the wave orbital diameter is shortened, incipient secondary crests act as 'speed bumps,' shortening the separation zone and encouraging the growth of crests on the next flank. This feedback appears to be the mechanism that systematically favors incipient crests on the same side of each trough. When the orbital diameter is lengthened, the nearly straight crests of equilibrium ripples become unstable: crests migrate preferentially towards the nearest adjacent crest that is closer, which amplifies crest sinuosity and may lead to the observed bulging instability. Understanding the mechanisms of ripple adjustment provides insight into bedform dynamics and paleoenvironmental reconstructions, and should aid in the development of reduced-complexity morphodynamic models by providing a basis for parameterizing complicated flow effects.