Highly-resolved simulation of fluid-structure interaction in abstracted canopies inspired by aquatic vegetation

Introduction
The turbulent flow over and through modelled aquatic canopies similar to seagrass meadows is investigated using scale-resolving numerical simulations. The aim of the study is to reveal detailed information on the interaction between the flow and the flexi-ble structures constituting the canopy.

Methods
Simulations were carried out using the code PRIME developed at the Institute of Fluid Mechanics, TU Dresden. It solves the equations for incompressible fluids and couples them to the equations describing the motion of the blades. The collisions between the individual blades are represented by appropriate forces between the blades. Periodic boundaries were applied in the two horizontal directions to achieve the same conditions as in a patch that is part of a very long and wide canopy.
 

Results
The main results stem from a case consisting of 672 highly flexible ribbons, derived from the experimental investigation in [1]. The flow is turbulent, with a bulk Reynolds number of 20 000. The low high flexibility of the blades is reflected by an elevated Cauchy num-ber of 25 000. Contrary to cases with less flexible plants, as studied in [2], the move-ment of the ribbons, characterized by the motion of their tips, is very pronounced verti-cally, and even more so in the spanwise direction. The blades also twist frequently and exchange momentum by mutual collisions. Substantial interaction between the canopy and the flow was found, including an increase in drag by a factor of 12 compared to the same channel flow without vegetation. At the same time the motion of the blades is well correlated with the streamwise velocity, so that the patterns developing at the canopy–flow interface reflect the larger flow structures passing by. For these, a staggered pat-tern was seen to be prevalent. Conditional averages were collected to isolate events where the canopy is locally very shallow, and events where the blades are significantly more upright than on average. Thinning and thickening of the canopy is related to verti-cal flow over the edge of the canopy, so that this creates exchange between the portion of flow inside the canopy and the exterior.
Ongoing Work and perspectives
The present method offers a wide amount of future prospects. Ongoing simulations in-clude cases where the geometric properties of the blades are varied. Initial results show an impact on patterns forming in the canopy–flow interface. Another perspective is to consider canopy patches. A first such case was studied using streamwise patches and moderately stiff blades [3]. Finally, it is interesting to consider variants where the flow is modified, since the canopy–flow interface interacts with the outer flow. One such modifi-cation is a case with sidewalls where secondary flow features related to the geometry of the channel play a role. Corresponding simulations have been conducted and are being pursued [4].

References

[1] L. Guiot, D. Doppler, J. J. S. Jerome, B. Löhrer, J. Fröhlich, N. Rivière. (2022). Indi-vidual and collective plants motion in a submerged, staggered, flexible, artificial canopy. In River Flow 2022: CRC Press. DOI: 10.1201/9781003323037-105.
[2] S. Tschisgale, B. Löhrer, R. Meller, J. Fröhlich. (2021). Large eddy simulation of the fluid–structure interaction in an abstracted aquatic canopy consisting of flexible blades. Journal of Fluid Mechanics 916, A43. DOI: 10.1017/jfm.2020.858.
[3] B. Löhrer, J. Fröhlich. (2023). Large eddy simulation of the flow over a canopy with spanwise patches. Proceedings in Applied Mathematics and Mechanics 23, e202300256. DOI: 10.1002/pamm.202300256. 
[4] B. Löhrer, D. Doppler, S. Puijalon, N. Rivière, J. J. S. Jerome, J. Fröhlich. (2020). A first simulation of a model aquatic canopy at high Cauchy number. In Proceedings of the 10th Conference on Fluvial Hydraulics: CRC Press. DOI: 10.1201/b22619.