Bedform initiation

Two examples illustrating the development of a sequence of instabilities beginning from a slight artificial perturbation. The left image shows the planform view of an experiment to create ripples on a flat bed in water (flowing from top to bottom). No sand-transport occurred until a mound of sand was placed on the bed. The mound disturbed the flow, which produced another ripple immediately downstream, which in turn disturbed the flow, and so on downcurrent. The photograph is from Southard and Dingler (1971), digitally processed to remove perspective distortion.

The right image shows a computer simulation of spatial differences using the dripping handrail model of Crutchfield and Kaneko (1987), beginning with initial conditions (top of image) that were uniform except for a single pixel. In this simple computational example, conditions in each horizontal row of the image determine the structure in lower rows.

These images illustrate the process whereby upstream bedforms modify the local boundary layer, which in turn influences the downstream sediment transport field, thereby influencing the morphology of the next bedform downstream.

REFERENCES

J. P. Crutchfield and K. Kaneko, 1987, Phenomenology of spatio-temporal chaos: in Hao Bai-lin, ed., Directions in Chaos, World Scientific, Singapore, v. 1, p. 272-353.

D. M. Rubin, 1992, Use of forecasting signatures to help distinguish periodicity, randomness, and chaos in ripples and other spatial patterns: Chaos, v. 2, p. 525-535.

D. M. Rubin, 1995, Forecasting techniques, underlying physics, and applications: in Middleton, G.V., Plotnick, R.E., and Rubin, D.M., Nonlinear Dynamics and Fractals--New Numerical Techniques for Sedimentary Data, SEPM Short Course no. 36, chapter 5, p. 85-120.

J. B. Southard and J. R. Dingler, 1971, Flume study of ripple propagation behind mounds on flat sand beds: Sedimentology, v. 16, p. 251-263.

Related pages

• Using nonlinear forecasting to identify low-dimensional deterministic time series and spatial patterns.