In this article dedicated to the modeling of vertical mass transfers between the biofilm and the bulk flow, we have, in the first instance, presented the methodology used, followed by the presentation of various results obtained through analyses conducted on velocity fields, different fluxes, and overall transfer coefficients. Due to numerical constraints (resolution of relevant spatial scales), we have restricted the analysis to low Schmidt numbers (Sc=0.1, Sc=1, and Sc=10) and a single roughness Reynolds number (Re*=150). The analysis of instantaneous concentration fields from various simulations revealed logarithmic concentration profiles above the canopy. In this zone, the concentration is relatively homogeneous for longer times. The analysis of results also showed that the contribution of molecular diffusion to the total flux depends on the Schmidt number. This contribution is negligible for Schmidt numbers Sc≥0.1, but nearly balances the turbulent flux for Sc=0.1. In the canopy, the local Sherwood number, given by the ratio of the total flux (within or above the canopy) to the molecular diffusion flux at the wall, also depends on the Schmidt number and varies significantly between the canopy and the region above. The exchange velocity, a purely hydrodynamic parameter, is independent of the Schmidt number and is on the order of 10% of in the present case. This study also reveals that nutrient absorption by organisms near the wall depends on the Schmidt number. Such absorption is facilitated by lower Schmidt numbers.
References
[1]
Font, R.A., Khamis, K., Milner, A.M., Smith, G.H.S. and Ledger, M.E. (2021) Low Flow and Heatwaves Alter Ecosystem Functioning in a Stream Mesocosm Experiment. Science of the Total Environment, 777, Article 146067. https://doi.org/10.1016/j.scitotenv.2021.146067
[2]
Koch, R., Kerling, D. and O’Brien, J.M. (2018) Effects of Chronic Elevated Nitrate Concentrations on the Structure and Function of River Biofilms. Freshwater Biology, 63, 1199-1210. https://doi.org/10.1111/fwb.13126
[3]
Boulêtreau, S., Salvo, E., Lyautey, E., Mastrorillo, S. and Garabetian, F. (2012) Temperature Dependence of Denitrification in Phototrophic River Biofilms. Science of the Total Environment, 416, 323-328. https://doi.org/10.1016/j.scitotenv.2011.11.066
[4]
Nepf, H.M. (2012) Flow and Transport in Regions with Aquatic Vegetation. Annual Review of Fluid Mechanics, 44, 123-142. https://doi.org/10.1146/annurev-fluid-120710-101048
[5]
Calmet, I. (1995) Analyse Par Simulation Des Grandes échelles Des Mouvements Turbulents et Du Transfert de Masse Sous Une Interface Plane. Ph.D. Thesis, Institut National Polytechnique de Toulouse. https://www.theses.fr/1995INPT110H
[6]
Nikora, V. (2007) Hydrodynamics of Aquatic Ecosystems: Spatial-Averaging Perspective. Acta Geophysica, 55, 3-10. https://doi.org/10.2478/s11600-006-0043-6
[7]
Nikora, V., Larned, S. and Biggs, B.J.F. (2003) Hydrodynamic Effects in Aquatic Ecosystems with a Focus on Periphyton. Recent Research Developments in Fluid Dynamics, 4, 41-70.
[8]
Larned, S., Nikora, V. and Walter, R. (2004) Mass-Transfert-Controlled Nitrogen and Phosphorus Uptake by Stream by Stream Periphyton: A Conceptual Model and Experimental Evidence. Limnology and Oceanography, 49, 1992-2000. https://doi.org/10.4319/lo.2004.49.6.1992
[9]
Coundoul, F., Bonometti, T., Graba, M., Sauvage, S., Sanchez Pérez, J.-M. and Moulin, F. (2015) Role of Local Flow Conditions in River Biofilm Colonization and Early Growth. River Research and Applications, 31, 350-367. https://doi.org/10.1002/rra.2746
[10]
Bonometti, T. and Magnaudet, J. (2007) An Interface-Capturing Method for Incompressible Two-Phase Flows. Validation and Application to Bubble Dynamics. International Journal of Multiphase Flow, 33, 109-133. https://doi.org/10.1016/j.ijmultiphaseflow.2006.07.003
[11]
Tougma, J.L.W. (2023) Method of Analytical Resolution of the Navier-Stokes Equations. Open Journal of Fluid Dynamics, 13, 226-231. https://doi.org/10.4236/ojfd.2023.135017
[12]
Badahmane, A. (2023) Linear System Solutions of the Navier-Stokes Equations with Application to Flow over a Backward-Facing Step. Open Journal of Fluid Dynamics, 13, 133-143. https://doi.org/10.4236/ojfd.2023.133011
[13]
Legendre, D. (1996) Quelques aspects des forces hydrodynamiques et des transferts de chaleur sur une bulle sphérique.
[14]
Yuki, Y., Takeuchi, S. and Kajishima, T. (2007) Efficient Immersed Boundary Method for Strong Interaction Problem of Arbitrary Shape Object with the Self-Induced Flow. Journal of Fluid Science and Technology, 2, 1-11. https://doi.org/10.1299/jfst.2.1
[15]
Kim, J. and Choi, H. (2004) An Immersed-Boundary Finite-Volume Method for Simulation of Heat Transfer in Complex Geometries. Journal of Mechanical Science and Technology, 18, 1026-1035. https://doi.org/10.1007/BF02990875
[16]
Eckert, E.R.G. and Soehngen, E. (1952) Distribution of Heat Transfer Coefficients Around Ciculair Cylinders in Crossflow at Reynolds Numbers from 20 to 500. Transactions of the American Society of Mechanical Engineers, 75, 343-347. https://doi.org/10.1115/1.4015778
[17]
Florens, E. (2010) Couche limite turbulente dans les écoulements à surface libre: Etude expérimentale d’effets de macro-rugosités. Ph.D. Thesis, Université Paul Sabatier, Toulouse III.
[18]
Coceal, O., Thomas, T.G., Castro, I.P. and Belcher, S.E. (2006) Mean Flow and Turbulence Statistics over Groups of Urban-Like Cubical Obstacles. Boundary-Layer Meteorology, 121, 491-519. https://doi.org/10.1007/s10546-006-9076-2
