Abstract
How the spatial perturbations of the first and second moments of the velocity and pressure fields differ for flow over a train of gentle hills covered by either sparse or dense vegetation is explored using large-eddy simulation (LES). Two simulations are investigated where the canopy is composed of uniformly arrayed rods each with a height that is comparable to the hill height. In the first simulation, the rod density is chosen so that much of the momentum is absorbed within the canopy volume yet the canopy is not dense enough to induce separation on the lee side of the hill. In the second simulation, the rod density is large enough to induce recirculation inside the canopy on the lee side of the hill. For this separating flow case, zones of intense shear stress originating near the canopy-atmosphere interface persist all the way up to the middle layer, ‘contaminating’ much of the middle and outer layers with shear stress gradients. The implications of these persistent shear-stress gradients on rapid distortion theory and phase relationships between higher order velocity statistics and hill-induced mean velocity perturbations (Δu) are discussed. Within the inner layer, these intense shear zones improve predictions of the spatial perturbation by K-theory, especially for the phase relationships between the shear stress (~ ∂Δu/∂z) and the velocity variances, where z is the height. For the upper canopy layers, wake production increases with increasing leaf area density resulting in a vertical velocity variance more in phase with Δu than with ∂Δu/∂z. However, background turbulence and inactive eddies may have dampened this effect for the longitudinal velocity variance. The increase in leaf area density does not significantly affect the phase relationship between mean surface pressure and topography for the two simulations, though the LES results here confirm earlier findings that the minimum mean pressure shifts downstream from the hill crest. The increase in leaf area density and associated flow separation simply stretches this difference further downstream. This shift increases the pressure drag, the dominant term in the overall drag on the hill surface, by some 15%. With regards to the normalized pressure variance, increasing leaf area density increases \({\sigma_p/u_{*}^{2}}\) near the canopy top, where u * is the longitudinally averaged friction velocity at the canopy top and σ p is the standard deviation of the pressure fluctuations. This increase is shown to be consistent with a primitive scaling argument on the leading term describing the mean-flow turbulent interaction. This scaling argument also predicts the spatial variations in σ p above the canopy reasonably well for both simulations, but not inside the canopy.
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References
Athanassiadou M, Castro I (2001) Neutral flow over a series of rough hills: a laboratory experiment. Boundary-Layer Meteorol 101(1): 1–30
Aubinet M, Heinesch B, Yarneaux M (2003) Horizontal and vertical CO2 advection in a sloping forest. Boundary-Layer Meteorol 108: 397–417
Aubinet M, Berbigier P, Bernhofer C, Cescatti A, Feigenwinter C, Granier A, Grunwald H, Havrankova K, Heinesch B, Longdoz B, Marcolla B, Montagnani L, Sedlak P (2005) Comparing CO2 storage fluxes and advection at night at different CARBOEUROFLUX sites. Boundary-Layer Meteorol 116: 63–94
Ayotte K (1997) Optimization of upstream profiles in modelled flow over complex terrain. Boundary-Layer Meteorol 83(2): 285–309
Ayotte K, Hughes D (2004) Observations of boundary layer wind tunnel flow over isolated ridges of varying steepness and roughness. Boundary-Layer Meteorol 112: 525–556
Belcher S, Hunt J (1998) Turbulent flow over hills and waves. Ann Rev Fluid Mech 30: 507–538
Belcher S, Wood N (1996) Form and wave drag due to stably stratified turbulent flow over low ridges. Q J Roy Meteorol Soc 122(532, Part B): 863–902
Beljaars A, Brown A, Wood N (2004) A new parametrization of turbulent orographic form drag. Q J Roy Meteorol Soc 130(599, Part B): 1327–1347. doi:10.1256/qj.03.073
Besio S, Mazzino A, Ratto C (2001) Local law-of-the-wall in complex topography: a confirmation from wind tunnel experiments. Phys Lett A 282(4–5): 325–330
Bitsuamlak G, Stathopoulos T, Bedard C (2004) Numerical evaluation of wind flow over complex terrain: review. J Aerosp Eng 17(4): 135–145. doi:10.1061/(ASCE)0893-1321(2004)17:4(135)
Bitsuamlak G, Stathopoulos T, Bedard C (2006) Effects of upstream two-dimensional hills on design wind loads: a computational approach. Wind Struct 9(1): 37–58
Britter R, Hunt J, Richards K (1981) Air-flow over a two-dimensional hill—studies of velocity speed-up, roughness effects and turbulence. Q J Roy Meteorol Soc 107(451): 91–110
Brown A, Hobson J, Wood N (2001) Large-eddy simulation of neutral turbulent flow over rough sinusoidal ridges. Boundary-Layer Meteorol 98(3): 411–441
Cava D, Katul GG (2008) Spectral short-circuiting and wake production within the canopy trunk space of an alpine hardwood forest. Boundary-Layer Meteorol 126(3): 415–431. doi:10.1007/s10546-007-9246-x
Deardorff J (1980) Stratocumulus-capped mixed layers derived from a 3-dimensional model. Boundary-Layer Meteorol 18(4): 495–527
Dupont S, Brunet Y, Finnigan J (2008) Large-eddy simulation of turbulent flow over a forested hill: Validation and coherent structure identification. Q J Roy Meteorol Soc 134: 1911–1929. doi:10.1002/qj.328
Dwyer M, Patton E, Shaw R (1997) Turbulent kinetic energy budgets from a large-eddy simulation of airflow above and within a forest canopy. Boundary-Layer Meteorol 84(1): 23–43
Feigenwinter C, Bernhofer C, Vogt R (2004) The influence of advection on short term CO2 budget in and above a forest canopy. Boundary-Layer Meteorol 113: 201–224
Finnigan J (2000) Turbulence in plant canopies. Ann Rev Fluid Mech 32: 519–571
Finnigan J, Belcher S (2004) Flow over a hill covered with a plant canopy. Q J Roy Meteorol Soc 130(596, Part A): 1–29. doi:10.1256/qj.02.177
Finnigan J, Shaw R (2008) Double-averaging methodology and its application to turbulent flows in above vegetation canopies. Acta Geophys 56(3): 534–561. doi:10.2478/s11600-008-0034-x
Gong W, Ibbetson A (1989) A wind-tunnel study of turbulent-flow over model hills. Boundary-Layer Meteorol 49(1–2): 113–148
Gong W, Taylor P, Dornbrack A (1996) Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves. J Fluid Mech 312: 1–37
Grace J, Malhi Y (2002) Global change—carbon dioxide goes with the flow. Nature 416: 594–595
Henn D, Sykes R (1999) Large-eddy simulation of flow over wavy surfaces. J Fluid Mech 383: 75–112
Hunt J, Carruthers D (1990) Rapid distortion theory and the problems of turbulence. J Fluid Mech 212: 497–532
Hunt J, Leibovich S, Richards KJ (1988) Turbulent shear flows over low hills. Q J Roy Meteorol Soc 114(484): 1435–1470
Jackson P, Hunt J (1975) Turbulent wind flow over a low hill. Q J Roy Meteorol Soc 101(430): 929–955
Katul G, Albertson J, Hsieh C, Conklin P, Sigmon J, Parlange M, Knoerr K (1996) The ‘inactive’ eddy motion and the large-scale turbulent pressure fluctuations in the dynamic sublayer. J Atmos Sci 53(17): 2512–2524
Katul G, Porporato A, Nathan R, Siqueira M, Soons M, Poggi D, Horn H, Levin S (2005) Mechanistic analytical models for long-distance seed dispersal by wind. Am Nat 166(3): 368–381
Katul G, Finnigan J, Poggi D, Leuning R, Belcher S (2006) The influence of hilly terrain on canopy-atmosphere carbon dioxide exchange. Boundary-Layer Meteorol 118(1): 189–216. doi:10.1007/s10546-005-6436-2
Kim H, Lee C, Lim H, Kyong N (1997) An experimental and numerical study on the flow over two-dimensional hills. J Wind Eng Ind Aerodyn 66(1): 17–33
Launiainen S, Vesala T, Molder M, Mammarella I, Smolander S, Rannik U, Kolari P, Hari P, Lindroth A, Katul G (2007) Vertical variability and effect of stability on turbulence characteristics down to the floor of a pine forest. Tellus 59B(2): 919–936
Massman W (1997) An analytical one-dimensional model of momentum transfer by vegetation of arbitrary structure. Boundary-Layer Meteorol 83(3): 407–421
Nathan R, Katul G (2005) Foliage shedding in deciduous forests lifts up long-distance seed dispersal by wind. Proc Natl Acad Sci 102(23): 8251–8256. doi:10.1073/pnas.0503048102
Nathan R, Katul G, Horn H, Thomas S, Oren R, Avissar R, Pacala S, Levin S (2002) Mechanisms of long-distance dispersal of seeds by wind. Nature 418: 409–413
Patton EG, Sullivan PP, Ayotte KW (2006) Turbulent flow over isolated ridges: influence of vegetation. In: 17th symposium on boundary layers and turbulence, San Diego, CA, J6.12. http://ams.confex.com/ams/pdfpapers/110925.pdf
Poggi D, Katul GG (2006) Two-dimensional scalar spectra in the deeper layers of a dense and uniform model canopy. Boundary-Layer Meteorol 121(2): 267–281. doi:10.1007/s10546-006-9075-3
Poggi D, Katul G (2007a) The ejection-sweep cycle over bare and forested gentle hills: a laboratory experiment. Boundary-Layer Meteorol 122(3): 493–515. doi:10.1007/s10546-006-9117-x
Poggi D, Katul GG (2007b) An experimental investigation of the mean momentum budget inside dense canopies on narrow gentle hilly terrain. Agric For Meteorol 144(1–2): 1–13. doi:10.1016/j.agrformet.2007.01.009
Poggi D, Katul GG (2007c) Turbulent flows on forested hilly terrain: The recirculation region. Q J Roy Meteorol Soc 133(625, Part B): 1027–1039. doi:10.1002/qj.73
Poggi D, Katul G (2008) Turbulent intensities and velocity spectra for bare and forested gentle hills: Flume experiments. Boundary-Layer Meteorol 129(3): 24–46
Poggi D, Katul G, Albertson J (2004a) Momentum transfer and turbulent kinetic energy budgets within a dense model canopy. Boundary-Layer Meteorol 111(3): 589–614
Poggi D, Porporato A, Ridolfi L, Katul G, Albertson J (2004b) The effect of vegetation density on canopy sublayer turbulence. Boundary-Layer Meteorol 111(3): 565–587
Poggi D, Katul GG, Albertson JD, Ridolfi L (2007) An experimental investigation of turbulent flows over a hilly surface. Phys Fluids 19(3). doi:10.1063/1.2565528
Poggi D, Katul GG, Finnigan JJ, Belcher SE (2008) Analytical models for the mean flow inside dense canopies on gentle hilly terrain. Q J Roy Meteorol Soc 134(3): 1095–1112
Raupach M (1994) Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index. Boundary-Layer Meteorol 71(1–2): 211–216
Raupach M, Finnigan J (1997) The influence of topography on meteorological variables and surface–atmosphere interactions. J Hydrol 190(3–4): 182–213
Raupach M, Shaw R (1982) Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol 22(1): 79–90
Raupach M, Thom A (1981) Turbulence in and above plant canopies. Ann Rev Fluid Mech 13: 97–129
Raupach M, Weng W, Carruthers D, Hunt J (1992) Temperature and humidity fields and fluxes over low hills. Q J Roy Meteorol Soc 118(504, Part B): 191–225
Raupach M, Finnigan J, Brunet Y (1996) Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy. Boundary-Layer Meteorol 78(3–4): 351–382
Ross A (2008) Large eddy simulations of flow over forested ridges. Boundary-Layer Meteorol 128(1): 59–76
Ross A, Vosper S (2005) Neutral turbulent flow over forested hills. Q J Roy Meteorol Soc 131(609, Part A): 1841–1862. doi:10.1256/qj.04.129
Salvetti M, Damiani R, Beux F (2001) Drag prediction over steep sinusoidal wavy surfaces. Phys Fluids 13(9): 2728–2731
Schmid H (2002) Footprint modeling for vegetation atmosphere exchange studies: a review and perspective. Agric For Meteorol 113: 159–183
Shaw R, Patton E (2003) Canopy element influences on resolved- and subgrid-scale energy within a large-eddy simulation. Agric For Meteorol 115(1–2): 5–17
Staebler R, Fitzjarrald D (2004) Observing subcanopy CO2 advection. Agric For Meteorol 122: 139–156
Sullivan P, Edson J, Hristov T, McWilliams J (2008) Large eddy simulations and observations of atmospheric marine boundary layers above non-equilibrium surface waves. J Atmos Sci 65: 1225–1245
Tamura T, Okuno A, Sugio Y (2007) LES analysis of turbulent boundary layer over 3D steep hill covered with vegetation. J Wind Eng Ind Aerodyn 95(9–11): 1463–1475. doi:10.1016/j.jweia.2007.02.014
Taylor P (1998) Turbulent boundary-layer flow over low and moderate slope hills. J Wind Eng Ind Aerodyn 74(6): 25–47
Tennekes H, Lumley J (1972) A first course in turbulence. MIT Press, Cambridge, p 300
Vosper SB, Brown AR (2007) The effect of small-scale hills on orographic drag. Q J Roy Meteorol Soc 133(627, Part B): 1345–1352. doi:10.1002/qj.101
Wagner C, Kuhn S, von Rohr PR (2007) Scalar transport from a point source in flows over wavy walls. Exp Fluids 43(2–3): 261–271. doi:10.1007/s00348-007-0340-0
Williams C, LaDeau S, Oren R, Katul G (2006) Modeling seed dispersal distances: implications for transgenic Pinus taeda. Ecol Appl 16(1): 117–124
Wood N (2000) Wind flow over complex terrain: A historical perspective and the prospect for large-eddy modelling. Boundary-Layer Meteorol 96(1–2): 11–32
Xu D, Taylor P (1995) Boundary-layer parametrization of drag over small-scale topography. Q J Roy Meteorol Soc 121(522, Part B): 433–443
Yaglom A (1979) Similarity laws for constant-pressure and pressure gradient turbulent wall flows. Ann Rev Fluid Mech 11: 505–540
Ying R, Canuto V (1996) Turbulence modelling over two-dimensional hills using an algebraic Reynolds stress expression. Boundary-Layer Meteorol 77(1): 69–99
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Patton, E.G., Katul, G.G. Turbulent Pressure and Velocity Perturbations Induced by Gentle Hills Covered with Sparse and Dense Canopies. Boundary-Layer Meteorol 133, 189–217 (2009). https://doi.org/10.1007/s10546-009-9427-x
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DOI: https://doi.org/10.1007/s10546-009-9427-x