Direct Numerical Simulation of the Formation of Subaqueous Sediment Patterns: Evolution Beyond the Initial Formation
Aman G. Kidanemariam and Markus Uhlmann
Computational Fluid Dynamics group, Institute for Hydrodynamics, Karlsruhe Institute of Technology (KIT), Germany
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HPC Platform used:
This project has investigated the problem of sediment transport and subaqueous pattern formation by means of high-fidelity direct numerical simulations which resolve all the relevant scales of the flow and the sediment bed. In order to realistically capture the phenomenon, sufficiently large computational domains with up to several billion grid nodes are adopted, while the sediment bed is represented by up to a million mobile spherical particles. The numerical method employed features an immersed boundary technique for the treatment of the moving fluid-solid interfaces and a soft-sphere model to realistically treat the inter-particle contacts. The study provides, first and foremost, a unique set of spatially and temporally resolved information on the flow field and the motion of individual particles which make up the sediment bed. Furthermore, based on the rigorous analysis of the generated data, the fluid flow and particle motion over the evolving patterns are studied in great detail, providing novel insight into the different mechanisms involved in the processes of sediment pattern formation.
Subaqueous sediment bedforms, besides being simply fascinating, have important implications in many fields of science and engineering. For instance, bedforms greatly influence the rate of sediment transport as well as the stability of hydraulic structures in a given river. Thus, fundamental understanding of the mechanisms behind their formation as well as predicting their characteristics is crucial. However, this task is very challenging due to the complex interaction between the sediment bed and the driving turbulent flow. Most of previous studies on pattern formation have typically considered the Reynolds averaged Navier-Stokes equations (RANS) to represented the turbulent flow while the sediment-bed evolution is described by the sediment continuity equation. A coupled hydro-morphodynamic problem is then theoretically or numerically solved in order to investigate the instability and evolution of the sediment bed and its interaction with the background flow. However, these models still suffer from a large degree of prediction unreliability when compared to experimental measurements and field observations.
In this project (which extends the simulations and analysis of the precursor project pr58do), researchers of the Institute for Hydrodynamics of the Karlsruhe Institute of Technology (KIT) have addressed the problem of sediment pattern formation from a first principle approach. The researchers have performed novel Navier-Stokes-based direct numerical simulations of the phenomenon in a channel flow configuration considering a very large number of freely-moving particles to represent the sediment bed [1, 2, 3]. The peculiarity of the simulations which have been performed lies on the fact that all the relevant scales of the turbulent flow, even in the near-field around each individual sediment grain, are resolved. Note that the largest simulation carried out is the first of its kind to pass the one-million fully resolved particle simulation milestone and has accommodated a series of self-formed ripple units as seen in figure 1.
For the purpose of performing the above mentioned simulations, the researchers have employed a self-developed parallel fluid solver, which features an immersed boundary technique for the treatment of the moving fluid-solid interfaces and a soft-sphere-based DEM solver to realistically treat inter-particle interactions [4, 5].
The study has provided, first and foremost, a unique set of spatially and temporally resolved information on the flow field and the motion of individual particles which make up the sediment bed. Furthermore, based on the rigorous analysis of the generated data, the fluid flow and particle motion over the evolving patterns have been studied in great detail, providing novel insight into the different mechanisms involved in the process of sediment pattern formation.
Figure 1 demonstrates the coupled interaction between the turbulent flow and the evolving sediment bed in which enhanced turbulence activity is evidenced in the region downstream of the dune crests. Moreover, the footprint of the complex structure of the turbulent flow over such evolving bedforms at the free-surface (simulated as a non-deformable free-slip boundary) is clearly observable in that figure. These features are closely linked to the erupting surface boils and upwelling/downwelling motions which have been reported in field and laboratory measurements of such flows. Another interesting aspect of the sediment bed evolution which has been addressed in this project concerns the determination of the lower threshold of the amplified pattern wavelength of an unstable bed. This task has been accomplished by carrying out a number of simulations in which the computational box dimension is successively varied (cf. figure 2). It is found that, for the considered parameter point, there indeed exists a threshold length (75–100 particle diameters) below which the bed remains macroscopically flat.
 A. Kidanemariam and M. Uhlmann. “Direct numerical simulation of pattern formation insubaqueous sediment”. In: J. Fluid Mech. 750 (July 2014), R2. doi: 10.1017/jfm.2014.284.
 A. G. Kidanemariam. “The formation of patterns in subaqueous sediment”. PhD thesis. Karlsruhe Institute of Technology, 2015. doi: 10.5445/KSP/1000054986.
 A. G. Kidanemariam and M. Uhlmann. “Formation of sediment patterns in channel flow: minimal unstable systems and their temporal evolution”. In: J. Fluid Mech. 818 (May 2017), pp. 716–743. doi: 10.1017/jfm.2017.147.
 M. Uhlmann. “An immersed boundary method with direct forcing for the simulation of particulate flows”. In: J. Comput. Phys. 209.2 (Nov. 2005), pp. 448–476. doi: 10.1016/j.jcp.2005.03.017.
 A. G. Kidanemariam and M. Uhlmann. “Interface-resolved direct numerical simulation of the erosion of a sediment bed sheared by laminar channel flow”. In: Int. J. Multiph. Flow 67 (Dec. 2014), pp. 174–188. doi: 10.1016/j.ijmultiphaseflow.2014.08.008.
Prof. Dr. Markus Uhlmann
Joint Head of Institute for Hydromechanics
Head of the Computational Fluid Dynamics group
Karlsruhe Institute of Technology (KIT)
Kaiserstraße 12, D-76131 Karlsruhe (Germany)
e-mail: markus.uhlmann [@] kit.edu