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A k–ε turbulence model based on the scales of vertical shear and stem wakes valid for emergent and submerged vegetated flows

  • A. T. King (a1), R. O. Tinoco (a1) and E. A. Cowen (a1)

Abstract

Flow and transport through aquatic vegetation is characterized by a wide range of length scales: water depth (), plant height (), stem diameter (), the inverse of the plant frontal area per unit volume () and the scale(s) over which varies. Turbulence is generated both at the scale(s) of the mean vertical shear, set in part by , and at the scale(s) of the stem wakes, set by . While turbulence from each of these sources is dissipated through the energy cascade, some shear-scale turbulence bypasses the lower wavenumbers as shear-scale eddies do work against the form drag of the plant stems, converting shear-scale turbulence into wake-scale turbulence. We have developed a model that accounts for all of these energy pathways. The model is calibrated against laboratory data from beds of rigid cylinders under emergent and submerged conditions and validated against an independent data set from submerged rigid cylinders and a laboratory data set from a canopy of live vegetation. The new model outperforms existing models, none of which include the scale, both in the emergent rigid cylinder case, where existing models break down entirely, and in the submerged rigid cylinder and live plant cases, where existing models fail to predict the strong dependence of turbulent kinetic energy on . The new model is limited to canopies dense enough that dispersive fluxes are negligible.

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Corresponding author

Email address for correspondence: atk6@cornell.edu

References

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1. Blumberg, A. F. & Mellor, G. L. 1987 A description of a three-dimensional coastal ocean circulation model. In Three-dimensional Coastal Ocean Models (ed. Heaps, N. ). American Geophysical Union.
2. Bohm, M., Finnigan, J. J. & Raupach, M. R. 2000 Dispersive fluxes and canopy flows: just how important are they? In American Meteorological Society, 24th Conference on Agricultural and Forest Meteorology, University of California, Davis, 14–18 August 2000, pp. 106–107.
3. Burchard, H. & Peterson, O. 1999 Models of turbulence in the marine environment – a comparative study of two-equation turbulence models. J. Mar. Syst. 21, 2953.
4. Cava, D. & Katul, G. G. 2008 Spectal short-circuiting and wake production within the canopy trunk space of an Alpine hardwood forest. Boundary-Layer Meteorol. 126, 415431.
5. Coceal, O. & Belcher, S. E. 2004 A canopy model of mean winds through urban areas. Q. J. R. Meteorol. Soc. 130, 13491372.
6. Cowen, E. & Monismith, S. 1997 A hybrid digital particle tracking velocimetry technique. Exp. Fluids 22, 199211.
7. Dunn, C., López, F. & García, M. 1996 Mean flow and turbulence in a laboratory channel with simulated vegetation. Hydraul. Eng. Ser. 51, UILU-ENG-96-2009, Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, IL.
8. Efron, B. R. & Tibshirani, R. 1993 An Introduction to the Bootstrap. Chapman & Hall.
9. Finnemore, E. J. & Franzini, J. B. 2002 Fluid Mechanics with Engineering Applications, 10th edn. McGraw-Hill Higher Education.
10. Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519571.
11. Finnigan, J. J. 1985 Turbulent transport in flexible plant canopies. In The Forest–Atmosphere Interaction (ed. Hutchison, B. A. & Hicks, B. B. ), pp. 443480. D. Reidel.
12. Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.
13. Ghisalberti, M. 2009 Obstructed shear flows: similarities across systems and scales. J. Fluid Mech. 641, 5161.
14. Ghisalberti, M. & Nepf, H. M. 2004 The limited growth of vegetated shear layers. Water Resour. Res. 40, W07502, 1–12.
15. Katul, G. G., Mahrt, L., Poggi, D. & Sanz, C. 2004 One- and two-equation models for canopy turbulence. Boundary-Layer Meteorol. 113, 81109.
16. King, A. T., Rueda, F. J., Tinoco, R. O. & Cowen, E. A. 2009 Modeling flow and transport through aquatic vegetation in natural water bodies. In Proceedings of the 33rd IAHR Congress, Vancouver, BC, Canada, August 9–14, 2009.
17. Koch, D. & Ladd, A. 1997 Moderate Reynolds number flows through periodic and random arrays of aligned cylinders. J. Fluid Mech. 349, 3166.
18. Launder, B. E. & Spalding, D. B. 1974 The numerical computation of turbulent flows. Comput. Meth. Appl. Mech. 3, 269289.
19. Lillie, R. A., Budd, J. & Rasmussen, P. W. 1997 Spatial and temporal variability in biomass density of Myriophyllum spicatum L. in a northern temperate lake. Hydrobiologia 347, 6974.
20. Lin, P. & Liu, P. L.-F. 1998 Turbulence transport, vorticity dynamics, and solute mixing under plunging breaking waves in surf zone. J. Geophys. Res. 103, 1567715694.
21. López, F. & García, M. H. 2001 Mean flow and turbulence structure of open-channel flow through non-emergent vegetation. J. Hydraul. Engng 127, 392402.
22. Luhar, M., Rominger, J. & Nepf, H. 2008 Interaction between flow, transport and vegetation spatial structure. Environ. Fluid Mech. 8, 423439.
23. Nepf, H., Ghisalberti, M., White, B. & Murphy, E. 2007 Retention time and dispersion associated with submerged aquatic canopies. Water Resour. Res. 43, W04422, 1–10.
24. Nepf, H. M. & Vivoni, E. R. 2000 Flow structure in depth-limited, vegetated flow. J. Geophys. Res. 105 (C12), 2854728557.
25. Nikora, V., McLean, S., Coleman, S., Pokrajac, D., McEwan, I., Campbell, L., Aberle, J., Clunie, D. & Koll, K. 2007 Double-averaging concept for rough-bed open-channel and overland flows: applications. J. Geophys. Res. 133 (8), 884895.
26. Poggi, D., Katul, G. G. & Albertson, J. D. 2004a Momentum transfer and turbulent kinetic energy budgets within a dense model canopy. Boundary-Layer Meteorol. 111, 589614.
27. Poggi, D., Katul, G. G. & Albertson, J. D. 2004b A note on the contribution of dispersive fluxes to momentum transfer within canopies. Boundary-Layer Meteorol. 111, 615621.
28. Poggi, D., Katul, G. G., Finnigan, J. J. & Belcher, S. E. 2008 Analytical models for the mean flow inside dense canopies on gentle hilly terrain. Q. J. R. Meteorol. Soc. 134, 10951112.
29. Poggi, D., Porporato, A., Ridolfi, L., Albertson, J. D. & Katul, G. G. 2004c The effect of vegetation density on canopy sub-layer turbulence. Boundary-Layer Meteorol. 111, 567587.
30. Raupach, M. R., Coppin, P. A. & Legg, B. J. 1986 Experiments on scalar dispersion within a model plant canopy. Part I. The turbulence structure. Boundary-Layer Meteorol. 35, 2152.
31. Raupach, M. R. & Shaw, R. H. 1982 Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol. 22, 7990.
32. Rueda, F. J. & Schladow, S. G. 2002 Quantitative comparison of models for the barotropic response of homogeneous basins. J. Hydraul. Engng 128, 201213.
33. Shaw, R. H. & Seginer, I. 1985 The dissipation of turbulence in plant canopies. In Proceedings of the 7th Symposium of the American Meteorological Society on Turbulence and Diffusion, pp. 200203. American Meteorological Society.
34. Smith, P. E. 2006 A semi-implicit, three-dimensional model of estuarine circulation. Tech. Rep. Open file report 2006-1004. USGS, Sacramento, CA.
35. Song, Y. & Haidvogel, D. 1994 A semi-implicit ocean circulation model using a generalized topography-following coordinate system. J. Comput. Phys. 115, 228244.
36. Tanino, Y. & Nepf, H. M. 2008a Laboratory investigation of mean drag in a random array of rigid, emergent cylinders. J. Hydraul. Engng 134, 3441.
37. Tanino, Y. & Nepf, H. M. 2008b Lateral dispersion in random cylinder arrays at high Reynolds number. J. Fluid Mech. 600, 339371.
38. Tanino, Y. & Nepf, H. M. 2009 Laboratory investigation of lateral dispersion within dense arrays of randomly distributed cylinders at transitional Reynolds number. Phys. Fluids 21, 046603.
39. Tinoco, R. O. & Cowen, E. A. 2012 The direct measurement of bed stress and drag on individual and random arrays of elements. Exp. Fluids, submitted manuscript.
40. Tinoco Lopez, R. O. 2008 An experimental investigation of the turbulent flow structure in one-dimensional emergent macrophyte patches. Master’s thesis, Cornell University.
41. Tinoco Lopez, R. O. 2011 An experimental investigation of drag and the turbulent flow structure in simulated and real aquatic vegetation. PhD thesis, Cornell University.
42. Werely, S. & Meinhart, C. 2001 Second-order accurate particle image velocimetry. Exp. Fluids 31, 258268.
43. White, F. M. 2011 Fluid Mechanics, 7th edn. McGraw-Hill Higher Education.
44. Wilson, J. D. 1988 A second-order closure model for flow through vegetation. Boundary-Layer Meteorol. 42, 371392.
45. Wilson, N. R. & Shaw, R. H. 1977 A higher order closure model for canopy flow. J. Appl. Meteorol. 16, 11971205.
46. Wüest, A. & Lorke, A. 2003 Small-scale hydrodynamics in lakes. Annu. Rev. Fluid Mech. 35, 373412.
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A k–ε turbulence model based on the scales of vertical shear and stem wakes valid for emergent and submerged vegetated flows

  • A. T. King (a1), R. O. Tinoco (a1) and E. A. Cowen (a1)

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