Single‐parameter model of vegetated aquatic flows

Battiato, Ilenia; Rubol, S.

doi:10.1002/2013wr015065

Cited by 37 publications

(51 citation statements)

References 36 publications

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“…Here we use the flow model proposed by Battiato [] and Battiato and Rubol [] as the analytical approximation of the mean velocity profile above and within the obstruction. In the following, we provide the flow model description for completeness.…”

Section: Turbulent Flow Over a Permeable Layermentioning

confidence: 99%

“…The methodology is appealing since it is flexible and computationally inexpensive in comparison to existing numerical models. The velocity profile we adopt is based on the two‐domain model proposed by Battiato and Rubol []. The proposed flow model treats the canopy layer as a porous medium [see Lowe et al ., ; Papke and Battiato , ; Battiato and Rubol , ] and is coupled to the advection‐dispersion equation with spatially variable coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…The paper is structured as follows: section 2 describes the flow model of Battiato and Rubol []. The transport formulation and the solution methodology are given in section 3. Results are analyzed in section 4. Conclusions are provided in section 5.…”

Section: Introductionmentioning

confidence: 99%

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Vertical dispersion in vegetated shear flows

Rubol

Battiato²,

Barros

2016

Water Resour. Res.

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Canopy layers control momentum and solute transport to and from the overlying water surface layer. These transfer mechanisms strongly dependent on canopy geometry, affect the amount of solute in the river, the hydrological retention and availability of dissolved solutes to organisms located in the vegetated layers, and are critical to improve water quality. In this work, we consider steady state transport in a vegetated channel under fully developed flow conditions. Under the hypothesis that the canopy layer can be described as an effective porous medium with prescribed properties, i.e., porosity and permeability, we model solute transport above and within the vegetated layer with an advection‐dispersion equation with a spatially variable dispersion coefficient (diffusivity). By means of the Generalized Integral Transform Technique, we derive a semianalytical solution for the concentration field in submerged vegetated aquatic systems. We show that canopy layer's permeability affects the asymmetry of the concentration profile, the effective vertical spreading behavior, and the magnitude of the peak concentration. Due to its analytical features, the model has a low computational cost. The proposed solution successfully reproduces previously published experimental data.

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Section: Turbulent Flow Over a Permeable Layermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vertical dispersion in vegetated shear flows

Rubol

Battiato²,

Barros

2016

Water Resour. Res.

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“…Despite a number of studies have experimentally or analytically demonstrated the impact of morphological and topological alteration on, e.g., solute dispersion and fouling at the system (macro-) scale (Maruf et al 2013b;Battiato et al 2010;Griffiths et al 2013;Battiato & Rubol 2014;Rubol et al 2016;Ling et al 2016Ling et al , 2018, ROMs systems are still primarily optimized by trail and error. This is due to the lack of quantitative understanding of the impact of morphological and/or topological modifications on membrane fouling at prescribed operating conditions.…”

Section: Introductionmentioning

confidence: 99%

Rough or wiggly? Membrane topology and morphology for fouling control

Ling

Battiato

2019

J. Fluid Mech.

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Reverse Osmosis Membrane (ROM) filtration systems are widely applied in wastewater recovery, seawater desalination, landfill water treatment, etc. During filtration, the system performance is dramatically affected by membrane fouling which causes a significant decrease in permeate flux as well as an increase in the energy input required to operate the system. Design and optimization of ROM filtration systems aim at reducing membrane fouling by studying the coupling between membrane structure, local flow field, local solute concentration and foulant adsorption patterns. Yet, current studies focus exclusively on oversimplified steady-state models that ignore any dynamic coupling between the fluid dynamics and the transport through the membrane, while membrane design still proceeds through trials and errors. In this work, we develop a model that couples the transient Navier-Stokes and the Advection-Diffusion-Equations, as well as an adsorptiondesorption equation for the foulant accumulation, and we validate it against unsteady measurements of permeate flux as well as steady-state spatial fouling patterns. Furthermore, we analytically show that, for a straight channel, a universal scaling relationship exists between the Sherwood and Bejam numbers, i.e. the dimensionless permeate flux through the membrane and the pressure drop along the channel, respectively. We then generalize this result to membranes subject to morphological and/or topological modifications, i.e., whose shape (wiggliness) or surface roughness is altered from the rectangular and flat reference case. We demonstrate that universal scaling behavior can be identified through the definition of a modified Reynolds number, Re , that accounts for the additional length scales introduced by the membrane modifications, and a membrane performance index, ξ, which represents an aggregate efficiency measure with respect to both clean permeate flux and energy input required to operate the system. Our numerical simulations demonstrate that 'wiggly' membranes outperforms 'rough' membranes for smaller values of Re , while the trend is reversed at higher Re . To the best of our knowledge, the proposed approach is the first able to quantitatively investigate, optimize and guide the design of both morphologically and topologically altered membranes under the same framework, while providing insights on the physical mechanisms controlling the overall system performance. † Email address for correspondence: ibattiat@stanford.edu arXiv:1809.00217v1 [physics.flu-dyn] 1 Sep 2018

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“…Emergent and submerged vegetation also affects solute transport by altering the distribution of the velocity and the mixing coefficient in the channel [Nepf, 2012;Shucksmith et al, 2010;Musner et al, 2014]. Battiato and Rubol [2014] and Rubol et al [2016] used a two-domain approach to model flow through and over submerged canopies, and derived a semianalytical solution for the concentration field in submerged vegetated systems under steady-state conditions. Day [1975] analyzed the behavior of the first two moments of the breakthrough curves from an extensive series of tracer experiments in small mountain streams and showed that the standard deviation of an initially concentrated mass increases linearly with distance instead of its square root, in contrast with Taylor's mixing model.…”

Section: Introductionmentioning

confidence: 99%

Non‐Fickian dispersion in open‐channel flow over a porous bed

Bottacin‐Busolin

2017

Water Resources Research

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Solute transport in rivers has been traditionally represented using one‐dimensional models assuming advection and Fickian dispersion along the main flow direction and transient storage in surface and subsurface dead zones. Experimental evidence from several stream tracer studies has shown that the longitudinal scaling of the moments of the breakthrough curves (BTCs) is inconsistent with classic 1‐D solute transport models. In this work, simulations of advection and diffusion in a 2‐D and 3‐D channel flow over a porous bed are presented assuming an exponentially attenuated profile of the transverse mixing coefficient in the porous medium, as suggested by recent experimental and numerical studies. It is shown that the longitudinal transport in the channel is superdiffusive, and the skewness of the concentration distributions can be almost constant over a broad temporal range, with no sign of approaching zero at large times. A sensitivity analysis shows that, at large times, longitudinal dispersion is controlled by the cross‐sectional profile of the in‐bed transverse mixing coefficient, and by the difference between the average velocity in the channel and in the porous bed. The normalized concentration distributions can be approximated by beta‐distributions with time‐dependent parameters, and relationships are derived between the scaling of the parameters under power‐law approximation and the scaling of the spatial and temporal moments. The results provide new insights into the physical mechanisms that control the anomalous scaling of the moments observed in field tracer studies and opens new possibilities for predictive and inverse modeling of transport processes in rivers and their catchments.

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Single‐parameter model of vegetated aquatic flows

Cited by 37 publications

References 36 publications

Vertical dispersion in vegetated shear flows

Vertical dispersion in vegetated shear flows

Rough or wiggly? Membrane topology and morphology for fouling control

Non‐Fickian dispersion in open‐channel flow over a porous bed

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