Doubleaveraging methodology and its application to turbulent flow in and above vegetation canopies
 John J. Finnigan,
 Roger H. Shaw
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Double averaged equations for atmospheric boundary layer flows are introduced as natural extensions of single averaged Reynolds equations. We show that in circumstances where double averaged equations are needed, the two fundamental properties of Reynolds averaging are violated. First, we consider doubleaveraging in free air turbulence, where the aim is to separate coherent motions from background turbulence. We illustrate the different properties of the main operators that have been used and the physical meaning of the terms that result. Second, in canopy flows, the multiply connected nature of the canopy airspace leads to a different set of departures from the standard Reynolds equations. We establish the physical meaning of the extra terms that arise. Finally we briefly discuss the problems, both practical and theoretical, that arise when we use double averaged equations to interpret real data.
 Antonia, R.A. (1981), Conditional sampling in turbulence measurement, Ann. Rev. Fluid Mech. 13, 131–156. CrossRef
 Aubry, N., P. Holmes, J.L. Lumley, and E. Stone (1988), The dynamics of coherent structures in the wall region of a turbulent boundary layer, J. Fluid Mech. 192, 115–173. CrossRef
 Belcher, S.E., J.J. Finnigan, and I.N. Harman (2008), Flows through forest canopies in complex terrain, Ecological Applications (in press).
 Bohm, M., J.J. Finnigan, and M.R. Raupach (2000), Dispersive fluxes and canopy flows: just how important are they? Proc. 24th Conference on Agricultural and Forest Meteorology, Amer. Meteor. Soc., Davis, 14–18 August 2000.
 Bracewell, R. (1965), The Fourier Transform and its Application, McGraw Hill, New York.
 Brown, K.W., and W. Covey (1966), The energybudget evaluation of the micrometeorological transfer processes within a cornfield, Agric. Meteorol. 3, 73–96. CrossRef
 Brunet, Y., J.J. Finnigan, and M.R. Raupach (1994), A wind tunnel study of air flow in waving wheat: singlepoint velocity statistics, Bound.Layer Meteor. 70, 95–132. CrossRef
 Coceal, O., A. Dobre, T.G. Thomas, and S.E. Belcher (2007), Structure of turbulent flow over regular arrays of cubical roughness, J. Fluid Mech. 589, 375–409. CrossRef
 Corrsin, S. (1974), Limitations of gradient transport models in random walks and turbulence, Adv. Geophys. 18A, 25–60.
 Davis, R.E. (1969), On the high Reynolds number flow over a wavy boundary, J. Fluid Mech. 36, 337–346. CrossRef
 Einaudi, F., and J.J. Finnigan (1981), The interaction between an internal gravity wave and the planetary boundary layer. Part I: The linear analysis, Quart. J. Roy. Meteor. Soc. 107, 793–806. CrossRef
 Einaudi, F., A.J. Bedard Jr., and J.J. Finnigan (1989), A climatology of gravity waves and other coherent disturbances at the Boulder Atmospheric Observatory during March–April 1984, J. Atmos. Sci. 46, 303–329. CrossRef
 Finnigan, J.J. (1985), Turbulent transport in flexible plant canopies. In: B.A. Hutchison and B.B Hicks (eds.), The ForestAtmosphere Interaction, Reidel Publishing Co., Dordrecht, 443–480.
 Finnigan, J.J. (1988), Kinetic energy transfer between internal gravity waves and turbulence, J. Atmos. Sci. 45, 486–505. CrossRef
 Finnigan, J.J. (1998), A note on waveturbulence interaction and the possibility of scaling the very stable boundary layer, Bound.Layer Meteor. 90, 529–539. CrossRef
 Finnigan, J.J., and F. Einaudi (1981), The interaction between an internal gravity wave and the planetary boundary layer. Part II: Effect of the wave on the turbulence structure, Quart. J. Roy. Meteor. Soc. 107, 807–832. CrossRef
 Finnigan, J.J., and R.H. Shaw (2000), A wind tunnel study of airflow in waving wheat: an Empirical Orthogonal Function analysis of the largeeddy motion, Bound.Layer Meteor. 96, 211–255. CrossRef
 Finnigan, J.J., F. Einaudi, and D. Fua (1984), The interaction between an internal gravity wave and turbulence in the stablystratified nocturnal boundary layer, J. Atmos. Sci. 41, 2409–2436. CrossRef
 Fitzmaurice, L., R.H. Shaw, K.T. Paw U, and E.G. Patton (2004), Threedimensional scalar microfront systems in a largeeddy simulation of vegetation canopy flow, Bound.Layer Meteor. 112, 107–127. CrossRef
 Gao, W., R.H. Shaw, and K.T. Paw U (1989), Observation of organized structure in turbulent flow within and above a forest canopy, Bound.Layer Meteor. 47, 349–377. CrossRef
 Holmes, P., J.L. Lumley, and G. Berkooz (1996), Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Cambridge.
 Howes, F.A., and S. Whitaker (1985), The spatial averaging theorem revisited, Chem. Eng. Sci. 40, 1387–1392. CrossRef
 Hunt, J.C.R., and D.J. Carruthers (1990), Rapid distortion theory and the ‘problems’ of turbulence, J. Fluid Mech. 212, 497–532. CrossRef
 Kendall, J.M. (1970), The turbulent boundary layer over a wall with progressive surface waves, J. Fluid Mech. 41, 259–281. CrossRef
 Launder, B.E. (1990), Phenomenological modelling: present and future? In: J.L. Lumley (ed.) Whither Turbulence? Turbulence at the Crossroads, Springer Verlag, Berlin, 439–485. CrossRef
 Lemon, E.R., and J.L. Wright (1969), Photosynthesis under field conditions: assessing sources and sinks of carbon dioxide in a corn (Zea Mays L) crop using a momentum balance approach, Agron. J. 61, 405–411.
 Le Mone, M.A. (1973), The structure and dynamics of horizontal roll vortices in the planetary boundary layer, J. Atmos. Sci. 30, 1077–1091. CrossRef
 Leonard, A. (1974), Energy cascade in largeeddy simulations of turbulent fluid flows, Advances in Geophysics. 18A, 237–248.
 Leslie, D.C. (1973), Developments in the Theory of Turbulence, Oxford University Press, London.
 Lumley, J.L. (1967), The structure of inhomogeneous turbulent flows. In: A.M. Yaglom and V.I. Tatarsky (eds.), Atmospheric Turbulence and Radio Wave Transmission, Nauka, Moscow, 161–178.
 Lumley, J.L. (1978), Computational modeling of turbulent flows. In: Advances in Applied Mechanics. Vol. 18 (A7947538 2134) Academic Press Inc., New York, 123–176.
 Moin, P., and R.D. Moser (1989), Characteristiceddy decomposition of turbulence in a channel, J. Fluid Mech. 200, 471–509. CrossRef
 Moncrieff, J.B., R. Clement, J.J. Finnigan, and T. Meyers (2004), Averaging, detrending and filtering of eddy covariance time series. In: X. Lee, W. Massman, and B. Law (eds.), Handbook of Micrometeorology: A Guide for Surface Flux Measurements and Analysis, Kluwer Academic Publishers, Dordrecht, 7–30.
 Penman, H.L., and I.F. Long (1960), Weather in wheat: an essay in micrometeorology, Quart. J. Roy. Meteor. Soc. 86, 16–50. CrossRef
 Philips, O.N. (1966), The Dynamics of the Upper Ocean, Cambridge University Press, Cambridge.
 Raupach, M.R., and R.H. Shaw (1982), Averaging procedures for flow within vegetation canopies, Bound.Layer Meteor. 22, 79–90. CrossRef
 Raupach, M.R., P.A. Coppin, and B.J. Legg (1986), Experiments on scalar dispersion within a model plant canopy. Part I: The turbulence structure, Bound.Layer Meteor. 35, 21–52. CrossRef
 Reynolds, O. (1895), On the dynamical theory of incompressible fluids and the determination of the criterion, Phil. Trans. Roy. Soc. Lond. A 186, 123–164. CrossRef
 Reynolds, W.C., and A.K.M.F. Hussein (1972), The mechanics of an organised wave in turbulent shear flow. Part 3: Theoretical models and comparisons with experiments, J. Fluid Mech. 54, 263–288. CrossRef
 Robinson, S.K. (1991), Coherent motions in the turbulent boundary layer, Ann. Rev. Fluid Mech. 23, 601–639. CrossRef
 Shaw, R.H. (1977), Secondary wind speed maxima inside plant canopies, J. Appl. Meteorol. 16, 514–521. CrossRef
 Shaw, R.H., and U. Schumann (1992), Largeeddy simulation of turbulent flow above and within a forest, Bound.Layer Meteor. 61, 47–64. CrossRef
 Shaw, R.H., J.J. Finnigan, E.G. Patton, and L. Fitzmaurice (2006), Eddy structure near the plant canopy interface, Proc. 27 ^{ th } Conference on Agricultural and Forest Meteorology, American Meteorological Society, San Diego, California, May 22–25.
 Takeuchi, K., E. Leavitt, and S.P. Chao (1977), Effects of water waves on the structure of turbulent shear flow, J. Fluid Mech. 80, 535–559. CrossRef
 Thom, A.S. (1972), Momentum, mass and heat exchange of vegetation, Quart. J. Roy. Meteor. Soc. 98, 124–134. CrossRef
 Tomkins, C.D., and R.J. Adrian (2003), Spanwise structure and scale growth in turbulent boundary layers, J. Fluid Mech. 490, 37–74. CrossRef
 Waggoner, P.E., and W.E. Reifsnyder (1968), Simulation of the temperature, humidity and evaporation profiles in a leaf canopy, J. Appl. Meteorol. 7, 400–409. CrossRef
 Wilson, N.R., and R.H. Shaw (1977), A higher order closure model for canopy flow, J. Appl. Meteorol. 16, 1197–1205. CrossRef
 Woods, J.D. (1968), Wave induced shear instability in the summer thermocline, J. Fluid Mech. 32, 791–800. CrossRef
 Woods, J.D. (1969), On Richardson’s number as a criterion for laminarturbulentlaminar transition in the ocean and atmosphere, Radio Science 4, 1289–1298. CrossRef
 Wyngaard, J.C. (1982), Boundary layer modeling. In: F.T.M. Nieuwstadt and H. van Dop (eds.), Atmospheric Turbulence and Air Pollution Meteorology, Reidel, Dordrecht, 69–106.
 Title
 Doubleaveraging methodology and its application to turbulent flow in and above vegetation canopies
 Journal

Acta Geophysica
Volume 56, Issue 3 , pp 534561
 Cover Date
 20080901
 DOI
 10.2478/s116000080034x
 Print ISSN
 18956572
 Online ISSN
 18957455
 Publisher
 SP Versita
 Additional Links
 Topics
 Keywords

 doubleaveraging methodology
 turbulent flow
 vegetation canopies
 Industry Sectors
 Authors

 John J. Finnigan ^{(1)}
 Roger H. Shaw ^{(2)}
 Author Affiliations

 1. Centre for Complex Systems Science, CSIRO, Canberra, Australia
 2. Department of Land, Air and Water Resources, University of California, Davis, USA