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Abstract

A detailed analysis of turbulent flows in an open channel over rigid submerged canopies, at a moderate bulk Reynolds number (i.e. Reb = UbH=v = 6000, H being the open channel depth and Ub the bulk velocity) has been carried out. Untangling the physical behaviour of these flows can become an impossible task if all the parameters that govern their physics are kept into account, e.g. the density of the layer, the level of submersion of the canopy and the flexibility of the stems, just to mention few of them. Nepf (2012a), after reviewing a number of relevant previous research works on canopy flows in her annual review, suggests to classify the behaviour of the flow by considering the geometrical features of the filamentous layer only. In the case of submerged canopies, based on the solidity of the canopy, three particular regimes are identified: sparse, dense and transitional. While sparse canopies are treated as rough walls, the form drag yielded by the filaments in a dense canopy induces the onset of two inflection points in the mean velocity profile. These two inflection points divide the intra-canopy flow into separate regions: an inner region, very close to the bed, populated by stems generated wakes, an outer region that mainly extends above the canopy and is usually modelled as a flow over a porous/rough wall, and an overlap region (Poggi et al., 2004). The latter can be assumed to behave as a peculiar Couette flow (in the literature it has been also described as a mixing-layer region, see Finnigan, 2000) characterised by large fluctuations produced by the meandering of the flow in between the canopy elements. Finally, the transitional regime can be thought of as a dense regime with a higher penetration of the upper layer flow structures into the canopy, where they concentrate (Nepf, 2012a).
Although some phenomenological models for dense canopy regimes are proposed in the literature, they are either based on two dimensional or even local one-dimensional measurements (Ghisalberti and Nepf, 2004, Nepf, 2012a, Poggi et al., 2004, Raupach et al., 1996) or on numerical simulations that adopt simpli- fied canopy models (Bailey and Stoll, 2013, 2016, Finnigan et al., 2009, Watanabe, 2004). In this context, the present thesis provides an accurate and detailed characterisation of canopy flows through a fully resolved, numerical approach tackling rigid, filamentous canopies made of cylindrical stems mounted normally to an impermeable wall. Firstly, a transitional-dense regime has been considered. Specifically, the first part of the thesis provides a novel and detailed insight that includes a new phenomenological model that also covers the character of the flow within the canopy. Moreover, an original scaling for the mean flow quantities is also proposed. The new approach allows highlighting important similarities and simplify the analysis.
In the second part of the thesis, a parametric study aimed to investigate the relation between the height of the canopy (i.e. its solidity) and the flow regimes is performed. Specifically, four canopy configurations have been considered. All of them share the same in-plane solid fraction while the canopy to open channel height ratio, h=H, has been selected within the range h=H = [0:05; 0:4]. The lowest and the highest values are representative of a quasi- sparse and a dense canopy regime, respectively. The other two h=H ratios nominally belong to the transitional regime values. The systematic variation of the height of the filamentous layer allowed us to unravel the main features characterising the different regimes. Particular attention has been paid to the relative locations of the two inflection points of the mean velocity profile and the virtual wall origin (origin seen from the outer flow located in the canopy layer). In view of the relative variations of their distance from the wall and the canopy tip, we propose to adopt the crossing between the internal inflection point and the virtual origin as a condition to infer the transition between canopy flow regimes when the solidity is varied. The structures of the different regimes have been also compared, highlighting the role played by the increasing solidity of the canopy as a natural splitter between the logarithmic structures of the outer flow and the coherent structures located inside the canopy. The wall-normal permeability of the canopy is identified as the main vehicle to transfer momentum through the different canopy layers, playing an important role in shaping the structures of the flow within the filamentous layer. Finally, a new scaling that adapts the flow conditions to the sparsity of the canopy is proposed.
All the results presented in the thesis have been obtained through fully resolved simulations. To the best of our knowledge, this is the first time that a 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, thus overcoming the problem of the canopy modelling. Conversely, 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, Rouhi et al., 2016).

Keywords: canopy flow, scaling, large coherent structures, large-eddy simulation, immersed boundary method.

Publication Type:	Thesis (Doctoral)
Subjects:	T Technology > TA Engineering (General). Civil engineering (General) T Technology > TL Motor vehicles. Aeronautics. Astronautics
Departments:	Doctoral Theses School of Science & Technology School of Science & Technology > Engineering

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