Amplitude equation and long-range interactions in underwater sand ripples in one dimension

Schnipper, Teis; Mertens, Keith; Ellegaard, C.; Bohr, Tomas

doi:10.1103/physreve.78.047301

Cited by 11 publications

(7 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Sekiguchi [2005] attributed this phenomenon to asymmetric drift in the wave orbital motion. However, later experiments by Schnipper et al [2008] showed similar patterns in symmetrical flow, indicating that a coupling between the topography and the flow must be responsible.…”

Section: Transient Ripple Adjustmentmentioning

confidence: 93%

“…For larger reductions in d, secondary crests accommodate shortening of the ripple wavelength [Lofquist, 1978], a process that involves several stages. A pair of new, small crests initially appears on the flanks of each ripple, one on either side of the original crest [Schnipper et al, 2008]. Very quickly thereafter, the trough flattens and the new crests, which by this time have formed their own small separation vortices, migrate toward the center of the trough [Marieu et al, 2008].…”

Section: Transient Ripple Adjustmentmentioning

confidence: 99%

“…However, later experiments by Schnipper et al . [] showed similar patterns in symmetrical flow, indicating that a coupling between the topography and the flow must be responsible.…”

Section: Introductionmentioning

confidence: 99%

“…In cases where the new equilibrium spacing would not sustain two new ripples in each trough, one crest grows and the other decays. For some reason, the same side wins in every trough throughout the ripple field: either all “right‐sided” or all “left‐sided” secondary crests grow (Figure a) [ Sekiguchi , ; Schnipper et al ., ]. Sekiguchi [] attributed this phenomenon to asymmetric drift in the wave orbital motion.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Wavelength selection and symmetry breaking in orbital wave ripples

et al. 2014

View full text Add to dashboard Cite

Sand ripples formed by waves have a uniform wavelength while at equilibrium and develop defects while adjusting to changes in the flow. These patterns arise from the interaction of the flow with the bed topography, but the specific mechanisms have not been fully explained. We use numerical flow models and laboratory wave tank experiments to explore the origins of these patterns. The wavelength of "orbital" wave ripples (λ) is directly proportional to the oscillating flow's orbital diameter (d), with many experimental and field studies finding λ/d ≈ 0.65. We demonstrate a coupling that selects this ratio: the maximum length of the flow separation zone downstream of a ripple crest equals λ when λ/d ≈ 0.65. We show that this condition maximizes the growth rate of ripples. Ripples adjusting to changed flow conditions develop defects that break the bed's symmetry. When d is shortened sufficiently, two new incipient crests appear in every trough, but only one grows into a full-sized crest. Experiments have shown that the same side (right or left) wins in every trough. We find that this occurs because incipient secondary crests slow the flow and encourage the growth of crests on the next flank. Experiments have also shown that when d is lengthened, ripple crests become increasingly sinuous and eventually break up. We find that this occurs because crests migrate preferentially toward the nearest adjacent crest, amplifying any initial sinuosity. Our results reveal the mechanisms that form common wave ripple patterns and highlight interactions among unsteady flows, sediment transport, and bed topography.

show abstract

Section: Transient Ripple Adjustmentmentioning

confidence: 93%

Section: Transient Ripple Adjustmentmentioning

confidence: 99%

“…However, later experiments by Schnipper et al . [] showed similar patterns in symmetrical flow, indicating that a coupling between the topography and the flow must be responsible.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Wavelength selection and symmetry breaking in orbital wave ripples

et al. 2014

View full text Add to dashboard Cite

show abstract

“…To our knowledge there have been two studies on the subject in a restricted, quasi-two-dimensional setup [10,11] and only one publication on the full problem [12], which is remarkable, since the merging of Faraday heaps is one of the clearest and most beautiful examples of coarsening in granular matter. It is not the only system in which the interplay of sand and the surrounding medium gives rise to patterns that coarsen over time: Other classic examples are underwater sand ripples at the beach [13][14][15][16][17][18] and wind-driven barchan dunes in the deserts on Earth and Mars [19][20][21][22][23][24][25], yet in those cases the coarsening process is never seen to run its full course. The growth of beach ripples and barchan dunes is limited by various factors and the coarsening process leads to the selection of a preferred length scale rather than to the formation of one big ripple or giant dune.…”

Section: Introductionmentioning

confidence: 99%

Scaling behavior of coarsening Faraday heaps

et al. 2015

View full text Add to dashboard Cite

When a layer of sand is vertically shaken, the surface spontaneously breaks up in a landscape of small conical "Faraday heaps," which merge into larger ones on an ever increasing time scale. We propose a model for the heap dynamics and show analytically that the mean lifetime of the transient state with N heaps scales as N(-2). When there is an abundance of sand, such that the vibrating plate always remains completely covered, this means that the average diameter of the heaps grows as t(1/2). Otherwise, when the sand is less plentiful and parts of the plate get depleted during the coarsening process, the average diameter of the heaps grows more slowly, namely as t(1/3). This result compares well with experimental observations.

show abstract