Nicholas, S (2022).
*High fidelity simulation of turbulent flows
over filamentous surfaces*.
(Unpublished Doctoral thesis, City, University of London)

## Abstract

Detailed analysis of turbulent shear flows that develop over filamentous surfaces has been carried out, in the context of an open channel flow at moderate bulk Reynolds number (i.e., Reb = UbH /ν , H being the open channel height and Ub the bulk velocity). The various filamentous surfaces found in nature present large variations in the geometrical configurations and the mechanical properties since they fulfil many biological tasks simultaneously. Thus, the number of free parameters that characterise a specific type of filamentous layer, or a specific type of canopy, is quite large (e.g. density ratios, fiexibility, sizes, levels of submersion, arrangement, active or passive motions, . . . ). To unravel the physical mechanisms of these flows by incorporating all these geometrical parameters into a comprehensive parametric investigation is an almost impossible task. This motivated Nepf (2012) to classify the overall behaviour of the flow by solely considering the geometrical features of the canopy. By reviewing a number of previous research work on canopy flows, she suggested using the solidity (λ) to classify the various flow behaviours observed in the case of submerged canopies. The magnitude of λ, enabled the identification of two asymptotic regimes: sparse and dense. The turbulent flow that develops above sparse canopy regimes is treated as a boundary layer that develops over a rough wall. On the other hand, the profound drag imposed by the filaments in the context of a dense regime yields a couple of inflection points in the mean velocity profile. These points allow the establishment of two separate shear layers within the canopy: an inner region (very close to the canopy bed), an outer region (which extends above the canopy edge), and an overlap region that exists in between these layers, which has been often described as a "mixing layer" (Finnigan, 2000). While the physical characterisation of the two asymptotic regimes is fairly understood, the transitional conditions remain an open question since the physical characteristics unique to the sparse and dense scenarios coexist in the transitional regime.

Although various publications have appeared in previous literature, they are either based on experimental work or oversimplified simulations. In this context, the current thesis provides an accurate and detailed characterisation of canopy flows via a fully resolved, numerical approach that is capable of tackling rigid, filamentous canopies made of cylindrical stems mounted normally to an impermeable wall. In particular, the simulation directly tackles the region occupied by the canopy, imposing the zero-velocity condition on every single stem by means of an immersed boundary method (Pinelli et al., 2010), thus mitigating the problems associated with canopy modelling. The outer flow is dealt with a large-eddy formulation that adopts a state-of-the-art grid independent closure for the unresolved scales of motion (Piomelli et al., 2015).

In the first part of the thesis, the regime transition of canopy flows is investigated. We have selected two-layer configurations characterised by filament spacing ratios such that the geometrical features of the two layers allow us to classify them as canopies in the transitional regime. In particular, the solidity was modified solely by decreasing the average distance between the adjacent filaments. This results in configurations that reside below and above the transitional threshold of λ ' 0.15. This enabled us to untangle the physical character of the flow in a transitional regime by analysing the relative positions of the inflection points and virtual origin (abstract origin seen from the external flow), which conditions the transition between the two asymptotic regimes. The coherent structures that emerge at the onset of the regime transition are also explored. Finally, the scaling argument for the mean flow quantities presented in the context of sparse and dense canopies is extended to the transitional regime. Following these observations, we embarked on a parametric study to investigate the influence of the average distance between adjacent filaments (or equally, the stem number density) on the different hydrodynamic regimes. A total of five canopy configurations have been selected for the study. All of them share the same frontal projected height, while the in-plane solid fraction of the canopy has been systematically varied to match the sparse, dense, and transitional canopy flow regimes. In particular, the configurations with the smallest and largest ∆S are representative of the sparse and dense regimes, respectively, while the intermediate cases nominally belong to the transitional regime. The mean filament spacing is generally considered the most important length scale of the canopy as it discriminates the scales of the outer flow that can penetrate into the canopy and controls the overall interactions between the inner and outer flows. The positional variation of the features of the mean velocity profile enabled us to propose a conceptual model, that describes the transition occurring between a sparse and a dense regime. Lastly, the coherent structures that emerge at the onset of different regimes are also compared, highlighting the role played by ∆S in controlling the interaction between the inner and outer flows.

In the second part of the thesis, a series of numerical investigations were conducted to study the effect of the filament’s inclination on turbulent shear flows developing above a canopy. Inspired by the ability of a naturally occurring canopy to modulate the local permeability, we consider a filamentous layer that is inclined along the streamwise direction. The resulting canopy is composed of rigid, cylindrical filaments, flush mounted onto the impermeable bottom wall of an open channel. The filaments, are characterised by a complex topology that mimics the mean streamlined posture of a typically reconfiguring aquatic vegetation (Nepf, 2012). The inclination angle θ ◦ of the canopy has been varied, whilst maintaining a constant in-plane solid fraction ∆S/H = π /48 and filament length h/H = 0.1. In all the resulting configurations, it is indeed the angle of inclination that dictates the solidity λ of the canopy, leading to the establishment of different flow regimes (i.e., sparse or dense). We have considered a total of six configurations such that θ systematically spans θ ∈ [0, 90], with the lowest corresponding to the fully dense regime. It is found that a simple inclination yields a substantially different flow behaviour when compared with perpendicular, which is amplified at the onset of extreme angles, promoting new hydrodynamic regimes.

Publication Type: | Thesis (Doctoral) |
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Subjects: | T Technology > TA Engineering (General). Civil engineering (General) |

Departments: | School of Science & Technology > Engineering School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses |