Wavelength selection and symmetry breaking in orbital wave ripples

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.National Science Foundation (U.S.) (Award EAR-1225865)National Science Foundation (U.S.) (Award EAR-1225879

WaveWatch_timeseries

Timeseries of wave data extracted from .grb2 files. Timeseries contain a 30-year wave climatology that has been generated with the NOAA WAVEWATCH III® using the Ardhuin et al (2010) physics package, 15 regular lat-lon grids, and the NCEP Climate Forecast System Reanalysis and Reforecast (CFSRR) homogeneous dataset of hourly high-resolution winds. Model setup: Propagation scheme: Higher-order schemes with Tolman (2002) averaging technique (PR3) Linear input: Cavaleri and Malanotte-Rizzoli with filter (LN1) Nonlinear interactions: Discrete interaction approximation (NL1) Bottom friction: JONSWAP bottom friction formulation (BT1) Depth induced breaking: Battjes-Janssen (DB1) Use Miche-style shallow water limiter in equation for maximum wave energy (MLIM) The model was run with the Ardhuin et al (2010) source term package (ST4) which includes the flux computation in the sources (FLX0, STAB0). Additionally, the model uses a third order propagation scheme (UQ), with no damping or scattering by sea ice (IC0, IS0), and no reflection (REF0). Partition output in NetCDF format. These provide bulk spectral estimates for each wave system. Available hourly for each individual grid (where there is data). Data can be consulted by usage of the next examples: with the next python example: https://polar.ncep.noaa.gov/waves/how_to_read_partition.py (Python), https://polar.ncep.noaa.gov/waves/how_to_read_partition.m (Matlab) See for more information: https://polar.ncep.noaa.gov/waves/hindcasts/nopp-phase2.php Contact person for this dataset is Jaap Nienhuis - [email protected]