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The role of the in-plane solidity on canopy flows
- Shane Nicholas, Alessandro Monti, Mohammad Omidyeganeh, Alfredo Pinelli
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- Journal:
- Journal of Fluid Mechanics / Volume 975 / 25 November 2023
- Published online by Cambridge University Press:
- 21 November 2023, A37
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Turbulent open channel flows developing above submerged canopies made of slender cylinders mounted perpendicular to the channel bed are known to be largely governed by the solidity parameter $\lambda =dh/\Delta S^2$ ($d$ and $h$ being the diameter and height of the filament, and $\Delta S$ the average spacing between filaments). When the filaments are sufficiently slender, the ratio between the height of the stems and the spacing sets the hydrodynamic regime developing inside and outside the canopy. This ratio also establishes the conditions leading to the transition from a dense to a sparse canopy flow regime (Nepf, Annu. Rev. Fluid Mech., vol. 44, 2012, pp. 123–142). In a previous, companion numerical investigation, Monti et al. (J. Fluid Mech., vol. 891, 2020, A9) used large eddy simulation (LES) to study the influence of the canopy height on the onset of the different regimes without modifying the average spacing $\Delta S$ between the stems. In that LES study, we were looking at the complementary situation in which the height of the stems is constant while the filaments’ number density of the canopy is changed. It was found that for low values of $\lambda$ (i.e. sparse or moderately dense canopies: $\lambda \lessapprox 0.26$), the flows sharing the value of the solidity obtained by either varying $h$ or $\Delta S$ are very similar. Differently, for higher values of $\lambda$ (i.e. in denser canopies), the effects of $h$ and $\Delta S$ start to diverge although sharing the same nominal value of $\lambda$. In this paper, we analyse the different physical mechanisms that come into play for dense configurations obtained by varying either $\Delta S$ or $h$. In particular, we focus on the most relevant length scales and carry out a detailed analysis of the flows using a triple decomposition approach. We show that the inner region of dense canopy flows, characterised by tall stems, is dominated by wall-normal sweeps delivering high momentum in the wall vicinity. Here, the impenetrability condition of the bed redistributes the available momentum in the wall-parallel directions re-energising an otherwise stagnating flow. Differently, in densely packed canopies, the penetration of the outer jet and the momentum transfer from the external flow are limited by the decreasing value of the wall-parallel permeabilities leading to different behaviours, including a reduction of the total drag offered by the canopy.
On the solidity parameter in canopy flows
- Alessandro Monti, Shane Nicholas, Mohammad Omidyeganeh, Alfredo Pinelli, Marco E. Rosti
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- Journal:
- Journal of Fluid Mechanics / Volume 945 / 25 August 2022
- Published online by Cambridge University Press:
- 18 July 2022, A17
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We have performed high-fidelity simulations of turbulent open-channel flows over submerged rigid canopies made of cylindrical filaments of fixed length $l=0.25H$ ($H$ being the domain depth) mounted on the wall with angle of inclination $\theta$. The inclination is the free parameter that sets the density of the canopy by varying its frontal area. The density of the canopy, based on the solidity parameter $\lambda$, is a widely accepted criterion defining the ongoing canopy flow regime, with low values ($\lambda \ll 0.1$) indicating the sparse regime, and higher values ($\lambda > 0.1$) the dense regime. All the numerical predictions have been obtained considering the same nominal bulk Reynolds number (i.e. $Re_b=U_b H/\nu = 6000$). We consider nine configurations of canopies, with $\theta$ varying symmetrically around $0^{\circ }$ in the range $\theta \in [\pm 78.5^{\circ }$], where positive angles define canopies inclined in the flow direction (with the grain) and $\theta =0^{\circ }$ corresponds to the wall-normally mounted canopy. The study compares canopies with identical solidity obtained inclining the filaments in opposite angles, and assesses the efficacy of the solidity as a representative parameter. It is found that when the canopy is inclined, the actual flow regime differs substantially from the one of a straight canopy that shares the same solidity, indicating that criteria based solely on this parameter are not robust. Finally, a new phenomenological model describing the interaction between the coherent structures populating the canopy region and the outer flow is given.
On the genesis of different regimes in canopy flows: a numerical investigation
- Alessandro Monti, Mohammad Omidyeganeh, Bruno Eckhardt, Alfredo Pinelli
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- Journal:
- Journal of Fluid Mechanics / Volume 891 / 25 May 2020
- Published online by Cambridge University Press:
- 20 March 2020, A9
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We have performed fully resolved simulations of turbulent flows over various submerged rigid canopies covering the wall of an open channel. All the numerical predictions have been obtained considering the same nominal bulk Reynolds number (i.e. $Re_{b}=U_{b}H/\unicode[STIX]{x1D708}=6000$, $H$ being the channel depth and $U_{b}$ the bulk velocity). The computations directly tackle the region occupied by the canopy by imposing the zero-velocity condition on every single stem, while the outer flow is dealt with a highly resolved large-eddy simulation. Four canopy configurations have been considered. All of them share the same in-plane solid fraction while the canopy to channel height ratios have been selected to be $h/H=(0.05,0.1,0.25,0.4)$. The lowest and the highest values lead to flow conditions approaching the two asymptotic states that in the literature are usually termed the sparse and dense regimes (see Nepf (Annu. Rev. Fluid Mech., vol. 44, 2012, pp. 123–142)). The other two $h/H$ selected ratios are representative of transitional regimes, a generic category that incorporates all the non-asymptotic states. While the interaction of a turbulent flow with a filamentous canopy in the two asymptotic conditions is relatively well understood, not much is known on the transitional flows and on the physical mechanisms that are responsible for the variations of flow regimes when the canopy solidity is changed. The effects of the latter on the flow developing in the intra-canopy region, on the outer flow and on their mutual interactions have been numerically explored and are reported in this work. By systematically varying the canopy height, we have unravelled the main character of the different regimes that are generated by the interplay between the outer flow structures, the emerging instabilities driven by the canopy drag and the interstitial flow between the canopy stems. The key role played by the relative positions of the inflection points of the mean velocity profile and the location of the virtual wall origin (as seen from the outer flow) is put forward and used to define a new condition to infer the canopy flow regime when the solidity is changed. Finally, the presence and the effects of an instability occurring close to the bed, nearby the interior inflectional point of the mean velocity profile is highlighted together with its consequences on the flow structure within the canopy region. To the best of our knowledge, this is the first time that the emergence of close-to-the-bed coherent structures induced by the inner inflection point is reported in the literature.
Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 2. Flow structures
- Mohammad Omidyeganeh, Ugo Piomelli
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- Journal:
- Journal of Fluid Mechanics / Volume 734 / 10 November 2013
- Published online by Cambridge University Press:
- 15 October 2013, pp. 509-534
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We performed large-eddy simulations of the flow over a series of three-dimensional (3D) dunes at laboratory scale. The bedform three-dimensionality was imposed by shifting a standard two-dimensional (2D) dune shape in the streamwise direction according to a sine wave. The turbulence statistics were discussed in Part 1 of this article (Omidyeganeh & Piomelli, J. Fluid Mech., vol. 721, 2013, pp. 454–483). Coherent flow structures and their statistics are discussed concentrating on two cases with the same crestline amplitudes and wavelengths but different crestline alignments: in-phase and staggered. The present paper shows that the induced large-scale mean streamwise vortices are the primary factor that alters the features of the instantaneous flow structures. Wall turbulence is insensitive to the crestline alignment; alternating high- and low-speed streaks appear in the internal boundary layer developing on the stoss side, whereas over the node plane (the plane normal to the spanwise direction at the node of the crestline), they are inclined towards the lobe plane (the plane normal to the spanwise direction at the most downstream point of the crestline) due to the mean spanwise pressure gradient. Spanwise vortices (rollers) generated by Kelvin–Helmholtz instability in the separated shear layer appear regularly over the lobe with much larger length scale than those over the saddle (the plane normal to the spanwise direction at the most upstream point of the crestline). Rollers over the lobe may extend to the saddle plane and affect the reattachment features; their shedding is more frequent than in 2D geometries. Vortices shed from the separated shear layer in the lobe plane undergo a three-dimensional instability while being advected downstream, and rise toward the free surface. They develop into a horseshoe shape (similar to the 2D case) and affect the whole channel depth, whereas those generated near the saddle are advected downstream and toward the bed. When the tip of such a horseshoe reaches the free surface, the ejection of flow at the surface causes ‘boils’ (upwelling events on the surface). Strong boil events are observed on the surface of the lobe planes of 3D dunes more frequently than in the saddle planes. They also appear more frequently than in the corresponding 2D geometry. The crestline alignment of the dune alters the dynamics of the flow structures, in that they appear in the lobe plane and are advected towards the saddle plane of the next dune, where they are dissipated. Boil events occur at a higher frequency in the staggered alignment, but with less intensity than in the in-phase alignment.
Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 1. Turbulence statistics
- Mohammad Omidyeganeh, Ugo Piomelli
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- Journal:
- Journal of Fluid Mechanics / Volume 721 / 25 April 2013
- Published online by Cambridge University Press:
- 13 March 2013, pp. 454-483
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We performed large-eddy simulations of flow over a series of three-dimensional dunes at laboratory scale (Reynolds number based on the average channel depth and streamwise velocity was 18 900) using the Lagrangian dynamic eddy-viscosity subgrid-scale model. The bedform three-dimensionality was imposed by shifting a standard two-dimensional dune shape in the streamwise direction according to a sine wave. The statistics of the flow are discussed in 10 cases with in-phase and staggered crestlines, different deformation amplitudes and wavelengths. The results are validated qualitatively against experiments. The three-dimensional separation of flow at the crestline alters the distribution of wall pressure, which in turn may cause secondary flow across the stream, which directs low-momentum fluid, near the bed, toward the lobe (the most downstream point on the crestline) and high-momentum fluid, near the top surface, toward the saddle (the most upstream point on the crestline). The mean flow is characterized by a pair of counter-rotating streamwise vortices, with core radius of the order of the flow depth. However, for wavelengths smaller than the flow depth, the secondary flow exists only near the bed and the mean flow away from the bed resembles the two-dimensional case. Staggering the crestlines alters the secondary motion; the fastest flow occurs between the lobe and the saddle planes, and two pairs of streamwise vortices appear (a strong one, centred about the lobe, and a weaker one, coming from the previous dune, centred around the saddle). The distribution of the wall stress and the focal points of separation and attachment on the bed are discussed. The sensitivity of the average reattachment length, depends on the induced secondary flow, the streamwise and spanwise components of the channel resistance (the skin friction and the form drag), and the contribution of the form drag to the total resistance are also studied. Three-dimensionality of the bed increases the drag in the channel; the form drag contributes more than in the two-dimensional case to the resistance, except for the staggered-crest case. Turbulent-kinetic energy is increased in the separated shear layer by the introduction of three-dimensionality, but its value normalized by the plane-averaged wall stress is lower than in the corresponding two-dimensional dunes. The upward flow on the stoss side and higher deceleration of flow on the lee side over the lobe plane lift and broaden the separated shear layer, respectively, affecting the turbulent kinetic energy.