Abstract
The derivation of flow and mass transfer models in canopy and porous media environments involves the spatial-averaging of the flow properties and their subscale equations. The averaging of the momentum equation generates the dispersive stress terms that represent the subscale spatial variations of the unresolved velocity field. While previous studies ignored the dispersive stresses in their flow models, recent evidence indicates that the dispersive stresses may be important. Here we focus our attention on the magnitude of the normal dispersive stresses in the entry region of a ‘forest patch’, where the in-canopy velocities are large and the longitudinal derivatives do not cancel out. Highly detailed particle image velocimetry measurements, at a temporal and spatial resolution of 5 Hz and 1.4 mm, are obtained inside and around a 1-m long model canopy which consists of transparent vertical cylinders 6 mm in diameter and 74.3 mm high (h). The cylinders are randomly distributed to form a relatively sparse forest patch with a leaf area density of 7.56 m−1 and a fluid volume fraction (porosity) of 0.965. We present results of the double averaged flow properties at three different regions of the forest patch; the upstream edge (x ≈ 0), the fully-developed interior region (x ≈ 10h) and the downstream edge (x ≈ 13h). We find that the normal dispersive stresses around the entry region of the forest patch are significantly larger than the normal Reynolds stresses. An order of magnitude analysis of the relevant terms in the momentum equation indicates that the longitudinal derivatives of the dispersive stresses are of the same order of magnitude as that of the drag force and similar to that of the horizontal convection term. The longitudinal derivatives of the Reynolds stresses are smaller, though cannot be ignored. Comparing these results with the characteristic profiles measured in the fully-developed region indicates that the dispersive stresses, which are generated at the forest patch entrance, decrease along an adjustment region while maintaining their profile shape. We find that the dispersive stresses influence the rate at which momentum penetrates into the canopy. These observations suggest that under certain flow conditions, dispersive stresses may dominate the momentum balance and therefore must be considered in future canopy and porous media flow models.
Similar content being viewed by others
References
Aberle J, Koll K, Dittrich A (2008) Form induced stresses over rough gravel-beds. Acta Geophys 56: 584–600
Atkinson MJ (1987) Rates of phosphate-uptake by coral-reef flat communities. Limnol Oceanogr 32: 426–435
Bear J (1972) Dynamics of fluids in porous media. American Elsevier, New York, 784 pp
Belcher SE, Jerram N, Hunt JCR (2003) Adjustment of a turbulent boundary layer to a canopy of roughness elements. J Fluid Mech 488: 369–398
Breugem WP (2004) The influence of wall permeability on laminar and turbulent flows. Theory and simulations. Ph.D. thesis, Delft University, The Netherlands
Breugem WP, Boersma BJ (2005) Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach. Phys Fluids 17:025103
Brunet Y, Finnigan JJ, Raupach MR (1994) A wind-tunnel study of air-flow in waving wheat—single-point velocity statistics. Boundary-Layer Meteorol 70: 95–132
Cameron SM, Nikora VI, Coleman SE (2008) Double-averaged velocity and stress distributions for hydraulically-smooth and transitionally-rough turbulent flows. Acta Geophys 56: 642–653
Campbell L, McEwan I, Nikora V, Pokrajac D, Gallagher M, Manes C (2005) Bed-load effects on hydrodynamics of rough-bed open-channel flows. J Hydraul Eng 131: 576–585
Chen XW, Chiew YM (2004) Velocity distribution of turbulent open-channel flow with bed suction. J Hydraul Eng 130: 140–148
Cheng H, Castro IP (2002) Near wall flow over urban-like roughness. Boundary-Layer Meteorol 104: 229–259
Coceal O, Thomas TG, Castro IP, Belcher SE (2006) Mean flow and turbulence statistics over groups of urban-like cubical obstacles. Boundary-Layer Meteorol 121: 491–519
Coceal O, Thomas TG, Belcher SE (2008) Spatially-averaged flow statistics within a canopy of large bluff bodies: results from direct numerical simulations. Acta Geophys 56: 862–875
Dai CF, Lin MC (1993) The effects of flow on feeding of 3 gorgonians from southern Taiwan. J Exp Mar Biol Ecol 173: 57–69
Ferreira RML, Ricardo AM, Franca MJ (2009) Discussion of “Laboratory investigation of mean drag in a random array of rigid, emergent cylinders” by Yukie Tanino and Heidi M. Nepf. J Hydraul Eng 135: 690–693
Finnigan J (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32: 519–571
Fischer HB, List EJ, Koh RCY, Imberger J, Brooks NA (1979) Mixing in inland and coastal waters. Academic Press, New York, 302 pp
Gurka R, Liberzon A, Hefetz D, Rubinstein D, Shavit U (1999) Computation of pressure distribution using PIV velocity data. In: 3rd International workshop on particle image velocimetry, pp 671–676
Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows: their structure and measurement. Oxford University Press, Oxford, 289 pp
Katul GG, Mahrt L, Poggi D, Sanz C (2004) One- and two-equation models for canopy turbulence. Boundary-Layer Meteorol 113: 81–109
Launiainen S, Vesala T, Mölder M, Mammarella I, Smolander S, Kolar P, Kolar P, Har P, Lindroth A, Katul GG (2007) Vertical variability and effect of stability on turbulence characteristics down to the floor of a pine forest. Tellus B 59: 919–936
Lee X (2000) Air motion within and above forest vegetation in non-ideal conditions. For Ecol Manag 135: 3–18
Li ZJ, Lin JD, Miller DR (1990) Air-flow over and through a forest edge—a steady-state numerical-simulation. Boundary-Layer Meteorol 51: 179–197
Lien FS, Yee E, Wilson JD (2005) Numerical modelling of the turbulent flow developing within and over a 3-D building array, part II: a mathematical foundation for a distributed drag force approach. Boundary-Layer Meteorol 114: 245–285
Liu J, Chen JM, Black TA, Novak MD (1996) E-epsilon modelling of turbulent air flow downwind of a model forest edge. Boundary-Layer Meteorol 77: 21–44
Luhar M, Rominger J, Nepf H (2008) Interaction between flow, transport and vegetation spatial structure. Environ Fluid Mech 8: 423–439
Macdonald IF, Elsayed MS, Mow K, Dullien FAL (1979) Flow through porous-media—Ergun equation revisited. Ind Eng Chem Fundam 18: 199–208
Manes C, Pokrajac D, McEwan I (2007) Double-averaged open-channel flows with small relative submergence. J Hydraul Eng 133: 896–904
Manes C, Pokrajac D, Coceal O, McEwan I (2008) On the significance of form-induced stress in rough wall turbulent boundary layers. Acta Geophys 56: 845–861
Martilli A, Santiago JL (2007) CFD simulation of airflow over a regular array of cubes. Part II: Analysis of spatial average properties. Boundary-Layer Meteorol 122: 635–654
McLean SR, Nikora VI (2006) Characteristics of turbulent unidirectional flow over rough beds: double-averaging perspective with particular focus on sand dunes and gravel beds. Water Resour Res 42:W10409
Meroney RN (1968) Characteristics of wind and turbulence in and above model forests. J Appl Meteorol 7: 780–788
Morse AP, Gardiner BA, Marshall BJ (2002) Mechanisms controlling turbulence development across a forest edge. Boundary-Layer Meteorol 103: 227–251
Nepf HM (1999) Drag, turbulence, and diffusion in flow through emergent vegetation. Water Resour Res 35: 479–489
Novak MD, Warland JS, Orchansky AL, Ketler R, Green S (2000) Wind tunnel and field measurements of turbulent flow in forests. Part I: Uniformly thinned stands. Boundary-Layer Meteorol 95: 457–495
Patterson MR (1992) A mass-transfer explanation of metabolic scaling relations in some aquatic invertebrates and algae. Science 255: 1421–1423
Pietri L, Petroff A, Amielh M, Anselmet F (2009) Turbulence characteristics within sparse and dense canopies. Environ Fluid Mech 9: 297–320
Poggi D, Katul GG (2008) Micro- and macro-dispersive fluxes in canopy flows. Acta Geophys 56: 778–799
Poggi D, Katul GG, Albertson JD (2004a) A note on the contribution of dispersive fluxes to momentum transfer within canopies—research note. Boundary-Layer Meteorol 111: 615–621
Poggi D, Porporato A, Ridolfi L, Albertson JD, Katul GG (2004b) The effect of vegetation density on canopy sub-layer turbulence. Boundary-Layer Meteorol 111: 565–587
Pokrajac D, McEwan I, Nikora V (2008) Spatially averaged turbulent stress and its partitioning. Exp Fluids 45: 73–83
Pope SB (2000) Turbulent flows. Cambridge University Press, New York, 770 pp
Raupach MR (1994) Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index. Boundary-Layer Meteorol 71: 211–216
Raupach MR, Coppin PA, Legg BJ (1986) Experiments on scalar dispersion within a model-plant canopy. 1 The turbulence structure. Boundary-Layer Meteorol 35: 21–52
Reynolds RT, Castro IP (2008) Measurements in an urban-type boundary layer. Exp Fluids 45: 141–156
Righetti A, Armanini A (2002) Flow resistance in open channel flows with sparsely distributed bushes. J Hydrol 269: 55–64
Schlichting H (1968) Boundary layer theory. McGraw-Hill, New York, 747 pp
Shavit U, Lowe RJ, Steinbuck JV (2007) Intensity capping: a simple method to improve cross-correlation PIV results. Exp Fluids 42: 225–240
Sveen KJ (2004) An introduction to MatPIV v. 1.6.1. Mechanics and applied mathematics. Department of Mathematics, University of Oslo
Tanino Y, Nepf HM (2008) Laboratory investigation of mean drag in a random array of rigid, emergent cylinders. J Hydraul Eng 134: 34–41
Whitaker S (1999) The method of volume averaging. Kluwer, Dordrecht, 240 pp
Wilson JD, Flesch TK (1999) Wind and remnant tree sway in forest cutblocks. III. A windflow model to diagnose spatial variation. Agric For Meteorol 93: 259–282
Yang B, Raupach MR, Shaw RH, Tha K, Paw U, Morse AP (2006) Large-eddy simulation of turbulent flow across a forest edge. Part I: Flow statistics. Boundary-Layer Meteorol 120: 377–412
Yue WS, Parlange MB, Meneveau C, Zhu WH, van Hout R, Katz J (2007) Large-eddy simulation of plant canopy flows using plant-scale representation. Boundary-Layer Meteorol 124: 183–203
Yue W, Meneveau C, Parlange MB, Zhu W, Kang HS, Katz J (2008) Turbulent kinetic energy budgets in a model canopy: comparisons between LES and wind-tunnel experiments. Environ Fluid Mech 8: 73–95
Zhu WH, van Hout R, Katz J (2007) On the flow structure and turbulence during sweep and ejection events in a wind-tunnel model canopy. Boundary-Layer Meteorol 124: 205–233
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Moltchanov, S., Bohbot-Raviv, Y. & Shavit, U. Dispersive Stresses at the Canopy Upstream Edge. Boundary-Layer Meteorol 139, 333–351 (2011). https://doi.org/10.1007/s10546-010-9582-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10546-010-9582-0