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Technical Papers
Feb 10, 2024

Linear and Weakly Nonlinear Instabilities of Sand Waves Caused by a Turbulent Flow

Authors: Subhasish Dey, M.ASCE https://orcid.org/0000-0001-9764-1346 [email protected], Rajesh K. Mahato https://orcid.org/0000-0002-0334-2693 [email protected], and Sk Zeeshan Ali, M.ASCE https://orcid.org/0000-0003-0763-7437 [email protected]Author Affiliations
Publication: Journal of Hydraulic Engineering
Volume 150, Issue 3
https://doi.org/10.1061/JHEND8.HYENG-13760
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Abstract

This study examines the instability of sand waves (dunes and antidunes) from both linear and weakly nonlinear perspectives. The linear and weakly nonlinear analyses use the standard linearization and the center manifold-projection technique, respectively. The mathematical framework includes the depth-averaged continuity and momentum equations, the advection–diffusion equation for suspended sediment concentration, and Exner’s equation for bed evolution. The streamline curvature is treated using the Boussinesq approximation. The model considers the departure of the pressure distribution from the hydrostatic law. Both modes of sediment transport, as bedload and as suspended load, are taken into consideration. The perturbations characterize the maximum growth rate for a selected wave number, called the resonant wave number, which is the most favorable wave number for the formation of sand waves. As the flow Froude number and the relative roughness number increase, the dimensionless resonant wave number decreases. The dimensionless amplitude of sand waves increases as the flow Froude number and the relative roughness number increase to achieve a maximum, and subsequently it decreases. The predicted wave number and amplitude of sand waves satisfactorily match the available experimental data.

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Data Availability Statement

All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request, including an Excel file of the tabular data presented in Figs. 2–7.

Acknowledgments

The first author acknowledges the JC Bose Fellowship Award [Funded by DST | Science and Engineering Research Board (SERB), Grant reference number JCB/2018/000004] in pursuing this work.

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Information & Authors

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Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 150 • Issue 3 • May 2024

Copyright

© 2024 American Society of Civil Engineers.

History

Received: Apr 23, 2023
Accepted: Oct 29, 2023
Published online: Feb 10, 2024
Published in print: May 1, 2024
Discussion open until: Jul 10, 2024

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ASCE Technical Topics:

  1. Coastal engineering
  2. Coasts, oceans, ports, and waterways engineering
  3. Continuum mechanics
  4. Dynamics (solid mechanics)
  5. Engineering fundamentals
  6. Engineering mechanics
  7. Flow (fluid dynamics)
  8. Fluid dynamics
  9. Fluid mechanics
  10. Geomechanics
  11. Geotechnical engineering
  12. Hydrologic engineering
  13. Hydrology
  14. Linear analysis
  15. Linear functions
  16. Mathematical functions
  17. Mathematics
  18. Nonlinear waves
  19. River engineering
  20. Sand (hydraulic)
  21. Sand waves
  22. Sandy soils
  23. Sediment
  24. Sediment transport
  25. Shores
  26. Soil mechanics
  27. Soils (by type)
  28. Solid mechanics
  29. Structural analysis
  30. Structural engineering
  31. Turbulent flow
  32. Water and water resources
  33. Waves (mechanics)

Authors

Affiliations

Subhasish Dey, M.ASCE https://orcid.org/0000-0001-9764-1346 [email protected]
Distinguished Professor and Head, Dept. of Civil and Infrastructure Engineering, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan 342030, India; Visiting Professor, Dept. of Hydraulic Engineering, State Key Laboratory of Hydro-Science and Engineering, Tsinghua Univ., Beijing 100084, China (corresponding author). ORCID: https://orcid.org/0000-0001-9764-1346. Email: [email protected]
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Rajesh K. Mahato https://orcid.org/0000-0002-0334-2693 [email protected]
Assistant Professor, Dept. of Civil Engineering, Maulana Azad National Institute of Technology Bhopal, Bhopal, Madhya Pradesh 462003, India. ORCID: https://orcid.org/0000-0002-0334-2693. Email: [email protected]
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Sk Zeeshan Ali, M.ASCE https://orcid.org/0000-0003-0763-7437 [email protected]
Assistant Professor, Dept. of Civil Engineering, Indian Institute of Technology Hyderabad, Hyderabad, Kandi, Telangana 502285, India. ORCID: https://orcid.org/0000-0003-0763-7437. Email: [email protected]
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