A unified model of ripples and dunes in water and planetary environments


Subaqueous and aeolian bedforms are ubiquitous on Earth and other planetary environments. However, it is still unclear which hydrodynamic mechanisms lead to the observed variety of morphologies of self-organized natural patterns such as ripples, dunes or compound bedforms. Here we present simulations with a coupled hydrodynamic and sediment transport model that resolve the initial and mature stages of subaqueous and aeolian bedform evolution in the limit of large flow thickness. We identify two types of bedforms consistent with subaqueous ripples and dunes, and separated by a gap in wavelength. This gap is explained in terms of an anomalous hydrodynamic response in the structure of the inner boundary layer that leads to a shift of the position of the maximum shear stress from upstream to downstream of the crest. This anomaly gradually disappears when the bed becomes hydrodynamically rough. By also considering the effect of the spatial relaxation of sediment transport we provide a new unifying framework to compare ripples and dunes in planetary environments to their terrestrial counterparts.

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Fig. 1: Temporal evolution of simulated subaqueous bedforms.
Fig. 2: Hydrodynamic mechanisms and predictions for subaqueous bedforms.
Fig. 3: Effects of lsat the on bedform formation.
Fig. 4: Predictions for different planetary conditions and transport modes.
Fig. 5: Phase diagram of ripples and dunes.

Code availability

The code that integrates the model equations used for this study can be made available upon request from the authors.

Data availability

The authors declare that the data supporting the findings of this study are within the corresponding references and available from the authors upon request. Some of the data is also within the Supplementary Information file.


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O.D.V. and C.W. were funded through the DFG Research Center/Cluster of Excellence ‘The Ocean in the Earth System’.

Author information




O.D.V. and C.W. contributed to the conception of the work and the analysis of bedform data. O.D.V. performed the simulations. O.D.V, B.A. and P.C. contributed to the validation of the model, interpretation of the results and writing of the manuscript.

Corresponding author

Correspondence to Orencio Duran Vinent.

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Supplementary information

Supplementary Information

Supplementary methods, supplementary figures, supplementary references

Supplementary Movie 1

Temporal evolution of simulated subaqueous bedforms. Simulation for Rd=3 and u/ut=2.2, corresponding to stable ripples (Fig. 1a).

Supplementary Movie 2

Temporal evolution of simulated subaqueous bedforms. Simulation for Rd=10 and u/ut=2.5, corresponding to dunes with superimposed stable ripples (Fig. 1b)

Supplementary Movie 3

Temporal evolution of simulated subaqueous bedforms. Simulation for Rd=35 and u/ut=4.2, corresponding to dunes without ripples (Fig. 1c)

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Duran Vinent, O., Andreotti, B., Claudin, P. et al. A unified model of ripples and dunes in water and planetary environments. Nat. Geosci. 12, 345–350 (2019). https://doi.org/10.1038/s41561-019-0336-4

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