Macroscopic Turbulence Models and Their Application in Turbulent Vegetated Flows
Publication: Journal of Hydraulic Engineering
Volume 137, Issue 3
Abstract
Turbulent flow in porous media, terrestrial and aquatic canopies, and urbanlike roughness is usually investigated using the macroscopic approach, which is based on the volume average theory (VAT). Two different methodologies have been developed in the past leading to different equations for both the mean and the turbulence quantities: time-averaging the volume-averaged equations and volume-averaging the time-averaged equations. In this study four models of the volume-averaging methodology are applied for modeling the flow in open channels with submerged vegetation. The vegetation is considered rigid, simulated as cylindrical roughness in a staggered or nonstaggered arrangement. Three of the models are of the type and one is of the Reynolds stress type. The latter has been applied using a modified ε equation to account for the extra dissipation attributable to vegetation. Numerical results for both mean and turbulence flow characteristics are compared against available experimental measurements for dense canopies under shallow and deep flow conditions. In addition, relevant characteristics (displacement thickness, canopy shear layer parameter, mixing length, penetration length scale, and etc.) are calculated for both computed and experimental data for assessing the performance of the models.
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References
Abdelrhman, M. A. (2003). “Effects of eelgrass Zostera Marina canopies on flow attributable transport.” Mar. Ecol. Prog. Ser., 248, 67–83.
Antohe, B. V., and Lage, J. L. (1997). “A general two-equation macroscopic turbulence model for incompressible flow in porous media.” Int. J. Heat Mass Transf., 40, 3013–3024.
Ayotte, K. W., Finnigan, J. F., and Raupach, M. R. (1999). “A second-order closure for neutrally stratified vegetative canopy flow.” Bound.-Lay. Meteorol., 90(2), 189–216.
Carollo, F. G., Ferro, V., and Termini, D. (2002). “Flow velocity measurement in vegetated channels.” J. Hydraul. Eng., 128(7), 664–673.
Chan, H. C., Leu, J. M., Lai, C. J., and Jia, Y. (2007). “Turbulent flow over a channel with fluid-saturated porous bed.” J. Hydraul. Eng., 133(6), 610–617.
Choi, S. U., and Kang, H. S. (2004). “Reynolds stress modelling of vegetated open-channel flows.” J. Hydraul. Res., 42(1), 3–11.
Cui, S., and Neary, V. S. (2008). “LES investigation of effects of submerged vegetation on turbulent flows.” J. Hydraul. Res., 46(3), 307–316.
De Lemos, M. J. S. (2006). Turbulence in porous media. Modelling and applications, Elsevier, Amsterdam.
De Lemos, M. J. S. (2009). “Turbulent flow around fluid-porous interfaces computed with a diffusion-jump model for and ε transport equations.” Transp. Porous Media, 78(3), 331–346.
Dunn, C., López, F., and García, M. H. (1996). “Mean flow and turbulence in a laboratory channel with simulated vegetation.” Civil engineering studies, Hydraulic engineering series, No. 51.
Finnigan, J. (2000). “Turbulence in plant canopies.” Annu. Rev. Fluid Mech., 32, 519–571.
FLUENT Inc. (2001). Fluent 6.0 Documentation. Lebanon, NH.
Foudhill, H., Brunet, Y., and Caltagirone, J.-P. (2005). “A fine-scale model for atmospheric flow over heterogeneous landscapes.” Environ. Fluid Mech., 5(3), 247–265.
Ghisalberti, M., and Nepf, H. (2009). “Shallow flows over a permeable medium: The hydrodynamics of submerged aquatic canopies.” Transp. Porous Media, 78(3), 385–402.
Ghisalberti, M. (2009). “Obstructed shear flows: Similarities across systems and scales.” J. Fluid Mech., 641, 51–61.
Harman, I. N., and Finnigan, J. J. (2007). “A simple unified theory for flow in the canopy and roughness sublayer.” Bound.-Lay. Meteorol., 123, 339–363.
Huthoff, F., Augustijn, D. C. M., and Hulscher, S. J. M. H. (2006). “Depth-averaged flow in presence of submerged cylindrical elements.” River Flow 2006, Taylor & Francis, London, 575–582.
Huthoff, F., and Augustijn, D. (2006). “Hydraulic resistance of vegetation: Predictions of average flow velocities based on a rigid-cylinders analogy.” Project No. U2/430.9/4268, Final Project Rep., Planungsmanagement fur Auen.
Järvelä, J. (2002). “Flow resistance of flexible and stiff vegetation: A flume study with natural plants.” J. Hydrol. (Amsterdam), 269(1–2), 44–54.
Launder, B. E., Reece, G. T., and Rodi, W. (1975). “The development of a Reynolds stress turbulent closure.” J. Fluid Mech., 68(3), 537–566.
Li, C. W., and Yan, K. (2007). “Numerical investigation of wave-current-vegetation interaction.” J. Hydraul. Eng., 133(7), 794–803.
Lien, F.-S., Yee, E., and Wilson, J. D. (2005). “Numerical modeling of the turbulent flow developing within and over a 3-D building array, Part II: A mathematical foundation for a distributed drag force approach.” Bound.-Lay. Meteorol., 114, 245–285.
Lopez, F., and Garcia, M. H. (2001). “Mean flow and turbulence structure of open-channel flow through non-emergent vegetation.” J. Hydraul. Eng., 127(5), 392–402.
Luhar, M., Rominger, J., and Nepf, H. (2008). “Interaction between flow, transport and vegetation spatial structure.” Environ. Fluid Mech., 8, 423–439.
Masuoka, T., and Takatsu, Y. (1996). “Turbulence model for flow through porous media.” Int. J. Heat Mass Transfer, 39(13), 2803–2809.
Nakayama, A., and Kuwahara, F. A. (1999). “A macroscopic turbulence model for flow in a porous medium.” J. Fluids Eng., 121, 427–433.
Nepf, H. and Ghisalberti, M. (2008). “Flow and transport in channels with submerged vegetation.” Acta Geophysica Polonica, 56(3), 753–777.
Nepf, H., Ghisalberti, M., White, B., and Murphy, E. (2007). “Retention time and dispersion associated with submerged aquatic canopies.” Water Resour. Res., 43, W04422.
Nepf, H. M., and Vivoni, E. R. (2000). “Flow structure in depth-limited, vegetated flow.” J. Geophys. Res., 105(C12), 28547–28557.
Nikora, V. I., McEwan, I. K., McLean, S. R., Coleman, S. E., Pokrajac, D., and Walters, R. (2007). “Double-averaging concept for rough-bed open-channel and overland flows: Theoretical background.” J. Hydraul. Eng., 133(8), 873–883.
Ochoa-Tapia, J. A., and Whitaker, S. (1995). “Momentum transfer at the boundary between a porous medium and a homogeneous fluid. I. Theoritical development.” Int. J. Heat Mass Transfer, 38(14), 2635–2646.
Pedras, M. H. J., and de Lemos, M. J. S. (2001). “Macroscopic turbulence modelling for incompressible flow through undeformable porous media.” Int. J. Heat Mass Transfer, 44, 1081–1093.
Pinard, J. P., and Wilson, J. D. (2001). “First and second-order closure models for wind in a plant canopy.” J. Appl. Meteorol., 40, 1762–1768.
Pinson, F., Gregoire, O., and Simonin, O. (2006). “ macro-scale modeling of turbulence based on a two scale analysis in porous media.” Int. J. Heat Fluid Flow, 27, 955–966.
Poggi, D., Porporato, A., Ridolfi, L., Albertson, D.-J., and Katul, G.-G. (2004). “The effect of vegetation density on canopy sub-layer turbulence.” Bound.-Lay. Meteorol., 111, 565–587.
Prinos, P., Sofialidis, D., and Keramaris, E. (2003). “Flow characteristics over and within a porous bed.” J. Hydraul. Eng., 129(9), 720–734.
Raupach, M. R., and Shaw, R. H. (1982). “Averaging procedures for flow within vegetation canopies.” Bound.-Lay. Meteorol., 22, 79–90.
Raupach, M. (1994). “Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index.” Bound.-Lay. Meteorol., 71, 211–216.
Rodi, W. (1980). Turbulence models and their applications in hydraulics, IAHR/AIRH, Rotterdam, The Netherlands.
Silva, R. A., and de Lemos, M. J. S. (2003). “Turbulent flow in a channel occupied by a porous layer considering the stress jump at the interface.” Int. J. Heat Mass Transfer, 46, 5113–5121.
Slattery, J. C. (1999). Advanced transport phenomena, Cambridge Univ. Press, Cambridge, UK.
Sogachev, A., and Panverov, O. (2006). “Modification of two-equation models to account for plant drag.” Bound.-Lay. Meteorol., 121, 229–266.
Souliotis, D., and Prinos, P. (2006). “Vegetation turbulence: From RANS micro-computations to macro-analysis.” Proc. of the 7th Int. Conf. of Hydroscience and Engineering, ICHE, Philadelphia.
Souliotis, D., and Prinos, P. (2008). “Turbulence in vegetated flows: Volume-average analysis and modelling aspects.” Acta Geophysica Polonica, 56(3), 894–917.
Stephan, U., and Gutknecht, D. (2002). “Hydraulic resistance of submerged flexible vegetation.” J. Hydrol. (Amsterdam), 269, 27–43.
Stoesser, T., Salvador, G. U., Rodi, W., and Diplas, P. (2009). “Large eddy simulation turbulent flow through submerged vegetation.” Transp. Porous Media, 78(3), 347–365.
Uittenbogaard, R. (2003). “Modelling turbulence in vegetated aquatic flows.” Riparian forest vegetated channels workshop, Trento, Italy.
Valdes-Parada, F. J., Alvarez-Ramirez, J., Goyeau, B., and Ochoa-Tapia, J. A. (2009). “Computation of jump coefficients for momentum transfer between a porous medium and a fluid using a closed generalized transfer equation.” Transp. Porous Media, 78, 459–476.
Whitaker, S. (1999). The method of Volume Averaging, Kluwer, Dordrecht, The Netherlands.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 137 • Issue 3 • March 2011
Pages: 315 - 332
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Sep 2, 2009
Accepted: Jul 29, 2010
Published online: Aug 3, 2010
Published in print: Mar 1, 2011
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