Theoretical and Computational Fluid Dynamics

, Volume 33, Issue 2, pp 161–180 | Cite as

Linear stability analysis of subaqueous bedforms using direct numerical simulations

  • N. ZgheibEmail author
  • S. Balachandar
Original Article


We present results on the formation of ripples from linear stability analysis. The analysis is coupled with direct numerical simulations of turbulent open-channel flow over a fixed sinusoidal bed. The presence of the sediment bed is accounted for using the immersed boundary method. The simulations are used to extract the bed shear stress and consequently the sediment transport rate. The approach is different from traditional linear stability analysis in the sense that the phase lag between the bed topology and the sediment flux is obtained from the three-dimensional turbulent simulations. The stability analysis is performed on the Exner equation, whose input, the sediment flux, is provided from the simulations. We ran 11 simulations at a fixed shear Reynolds number of 180, but for different sediment bed wavelengths. The analysis allows us to sweep a large range of physical and modelling parameters to predict their effects on linear growth. The Froude number appears to be the critical controlling parameter in the early linear development of ripples, in contrast with the dominant role of particle Reynolds number during the equilibrium stage. We also present results from a wave packet analysis using a one-dimensional Gaussian ridge.


Linear stability analysis Sediment-fluid interactions Direct numerical simulations Immersed boundary method 


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We are grateful to ExxonMobil Upstream Research Company for providing support through Grant Number EM09296.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of EngineeringLebanese American UniversityByblosLebanon
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA

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