Skip to main content
SpringerLink
Log in
Book cover

Boundary-Layer Meteorology 25th Anniversary Volume, 1970–1995 pp 351–382Cite as

Coherent Eddies and Turbulence in Vegetation Canopies: The Mixing-Layer Analogy

  • Chapter

Abstract

This paper argues that the active turbulence and coherent motions near the top of a vegetation canopy are patterned on a plane mixing layer, because of instabilities associated with the characteristic strong inflection in the mean velocity profile. Mixing-layer turbulence, formed around the inflectional mean velocity profile which develops between two coflowing streams of different velocities, differs in several ways from turbulence in a surface layer. Through these differences, the mixing-layer analogy provides an explanation for many of the observed distinctive features of canopy turbulence. These include: (a) ratios between components of the Reynolds stress tensor; (b) the ratio K H /K M of the eddy diffusivities for heat and momentum; (c) the relative roles of ejections and sweeps; (d) the behaviour of the turbulent energy balance, particularly the major role of turbulent transport; and (e) the behaviour of the turbulent length scales of the active coherent motions (the dominant eddies responsible for vertical transfer near the top of the canopy). It is predicted that these length scales are controlled by the shear length scale L s = U(h)/U′(h) (where h is canopy height, U(z) is mean velocity as a function of height z, and U′ = dU/dz). In particular, the streamwise spacing of the dominant canopy eddies Λ x = mL s , with m = 8.1. These predictions are tested against many sets of field and wind-tunnel data. We propose a picture of canopy turbulence in which eddies associated with inflectional instabilities are modulated by larger-scale, inactive turbulence, which is quasi-horizontal on the scale of the canopy.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Amiro, B. D.: 1990a, ‘Comparison of Turbulence Statistics Within Three Boreal Forest Canopies,’ Boundary-Layer Meteorol. 51, 99–121.

    Article  Google Scholar 

  • Amiro, B. D.: 1990b, ‘Drag Coefficients and Turbulence Spectra Within Three Boreal Forest Canopies’, Boundary-Layer Meteorol. 52, 227–246.

    Article  Google Scholar 

  • Antonia, R. A.: 1981, ‘Conditional Sampling in Turbulence Measurement’, Ann. Rev. Fluid Mech. 13, 131–156.

    Article  Google Scholar 

  • Antonia, R. A., Chambers, A. J., Friehe, C. A., and Van Atta, C. W.: 1979, ‘Temperature Ramps in the Atmospheric Surface Layer’, J. Atmos. Sci. 36, 99–108.

    Article  Google Scholar 

  • Baldocchi, D. D. and Meyers, T. P.: 1988a, ‘Turbulence Structure in a Deciduous Forest’, Boundary-Layer Meteorol. 43, 345–364.

    Article  Google Scholar 

  • Baldocchi, D. D. and Meyers, T. P.: 1988b, ‘A Spectral and Lag-correlation Analysis of Turbulence in a Deciduous Forest Canopy’, Boundary-Layer Meteorol. 45, 31–58.

    Article  Google Scholar 

  • Bell, J. H. and Mehta, R. D.: 1990, ‘Development of a Two-stream Mixing Layer from Tripped and Untripped Boundary Layers’, AIAA J. 28, 2034–2038.

    Article  Google Scholar 

  • Bergstrom, H. and Högström, U.: 1989, ‘Turbulent Exchange Above a Pine Forest II. Organized Structures’, Boundary-Layer Meteorol. 49, 231–263.

    Article  Google Scholar 

  • Betchov, R. and Criminale, W. O.: 1967, Stability of Parallel Flows, Academic Press, New York, 330 pp.

    Google Scholar 

  • Bisset, D. K., Antonia, R. A., and Raupach, M. R.: 1991, ‘Topology and Transport Properties of Large-scale Organized Motion in a Slightly Heated Rough Wall Boundary Layer’, Phys. Fluids A 3, 2220–2228.

    Article  Google Scholar 

  • Blackwelder, R. F. and Kaplan, R. E.: 1976, ‘On the Wall Structure of the Turbulent Boundary Layer’, J. Fluid Mech. 76, 89–112.

    Article  Google Scholar 

  • Bradshaw, R: 1967, ‘Inactive Motion and Pressure Fluctuations in Turbulent Boundary Layers’, J. Fluid Mech. 30, 241–258.

    Article  Google Scholar 

  • Browand, E. K. and Troutt, T. R.: 1980, ‘A Note on Spanwise Structure in the Two-dimensional Mixing Layer’, J. Fluid Mech. 97, 771–781.

    Article  Google Scholar 

  • Brown, G. L. and Roshko, A.: 1974, ‘On Density Effects and Large Structure in Turbulent Mixing Layers’, J. Fluid Mech. 64, 775–816.

    Article  Google Scholar 

  • Brunet, Y. and Collineau, S.: 1994, ‘Wavelet Analysis of Diurnal and Nocturnal Turbulence Above a Maize Crop’, in E. Foufoula-Georgiou and R. Kumar (eds.), Wavelets in Geophysics, Academic Press, New York, pp. 129–150.

    Google Scholar 

  • Brunet, Y., Finnigan, J. J., and Raupach, M. R.: 1994, ‘A Wind Tunnel Study of Air Flow in Waving Wheat: Single-point Velocity Statistics’, Boundary-Layer Meteorol. 70, 95–132.

    Article  Google Scholar 

  • Cellier, P.: 1986, ‘On the Validity of Flux-gradient Relationships Above Very Rough Surfaces’, Boundary-Layer Meteorol. 36, 417–419.

    Article  Google Scholar 

  • Cellier, R. and Brunet, Y.: 1992, ‘Flux-gradient Relationships Above Tall Forest Canopies’, Agric. For. Meteorol. 58, 93–117.

    Article  Google Scholar 

  • Chen, C. P. and Blackwelder, R. F.: 1978, ‘Large-scale Motion in a Turbulent Boundary Layer: A Study Using Temperature Contamination’, J. Fluid Mech. 89, 1–31.

    Article  Google Scholar 

  • Chen, F. and Schwerdtfeger, R: 1989, ‘Flux-gradient Relationships for Momentum and Heat Over a Rough Natural Surface’, Quart. J. Roy. Meteorol. Soc. 115, 335–352.

    Article  Google Scholar 

  • Collineau, S. and Brunet, Y.: 1993a, ‘Detection of Turbulent Coherent Motions in a Forest Canopy, Part I: Wavelet Analysis’, Boundary-Layer Meteorol. 65, 357–379.

    Google Scholar 

  • Collineau, S. and Brunet, Y.: 1993b, ‘Detection of Turbulent Coherent Motions in a Forest Canopy, Part II: Timescales and Conditional Averages’, Boundary-Layer Meteorol. 66, 49–73.

    Article  Google Scholar 

  • Comte, P., Lesieur, M., and Lamballais, E.: 1992, ‘Large-and Small-scale Stirring of Vorticity and a Passive Scalar in a 3-D Temporal Mixing Layer’, Phys. Fluids A 4, 2761–2778.

    Article  Google Scholar 

  • Coppin, P. A., Raupach, M. R., and Legg, B. J.: 1986, ‘Experiments on Scalar Dispersion Within a Model Plant Canopy, Part II. An Elevated Plane Source’,Boundary-Layer Meteorol. 35, 167–191.

    Google Scholar 

  • Denmead, O. T. and Bradley, E. F.: 1985, ‘Flux-gradient Relationships in a Forest Canopy’, In: B. A. Hutchison and B. B. Hicks (eds.), The Forest-Atmosphere Interaction, D. Reidel Publishing Co. Dordrecht, The Netherlands, pp. 421–442.

    Chapter  Google Scholar 

  • Denmead, O. T. and Bradley, E. F.: 1987, ‘On scalar transport in plant canopies’, Irrig. Sci. 8, 131–149.

    Article  Google Scholar 

  • Dimotakis, P. E. and Brown, G. L.: 1976, ‘The Mixing Layer at High Reynolds Number: Large-structure Dynamics and Entrainment’, J. Fluid Mech. 78, 535–560.

    Article  Google Scholar 

  • Drazin, P. G. and Reid, W. H.: 1981, Hydrodynamic Stability, Cambridge University Press, Cambridge, 527 pp.

    Google Scholar 

  • Fiedler, H. E.: 1974, ‘Transport of Heat across a Plane Turbulent Mixing Layer’, Adv. Geophys. 18, 93–109.

    Article  Google Scholar 

  • Finnigan, J. J.: 1979a, ‘Turbulence in Waving Wheat. I. Mean Statistics and Honami’, Boundary-Layer Meteorol. 16, 181–211.

    Article  Google Scholar 

  • Finnigan, J. J.: 1979b, ‘Turbulence in Waving Wheat. II. Structure of Momentum Transfer’, Boundary-Layer Meteorol. 16, 213–236.

    Article  Google Scholar 

  • Finnigan, J. J. and Brunet, Y.: 1995, ‘Turbulent Airflow in Forests on Flat and Hilly Terrain’, Proc. IUFRO Conf. on Wind and Wind-related Damage to Forests, Edinburgh, 1993. In Wind and Trees (Eds M. P. Coutts and J. Grace), Cambridge University Press, Cambridge, pp. 3–40.

    Google Scholar 

  • Finnigan, J. J., and Raupach, M. R.: 1987, ‘Transfer Processes in Plant Canopies in Relation to Stomatal Characteristics’, In: E. Zeiger, G. D. Farquhar, and I. R. Cowan (eds.), Stomatal Function, Stanford University Press, Stanford, CA, pp. 385–429.

    Google Scholar 

  • Fitzjarrald, D. R. and Moore, K. E.: 1990, ‘Mechanisms of Nocturnal Exchange Between the Rain Forest and the Atmosphere’, J. Geophys. Res. 95, 16839–16850.

    Article  Google Scholar 

  • Fitzjarrald, D. R., Moore, K. E., Cabral, O. M. R., Scolar, J., Manzi, A. O., and De Abreu Sà, L. D.: 1990, ‘Daytime Turbulent Exchange Between the Amazon Forest and the Atmosphere’, J. Geophys. Res. 95, 16825–16838.

    Article  Google Scholar 

  • Gao, W., Shaw, R. H., and Paw U, K. T.: 1989, ‘Observation of Organized Structure in Turbulent Flow Within and Above a Forest Canopy’, Boundary-Layer Meteorol. 47, 349–377.

    Article  Google Scholar 

  • Gardiner, B. A.: 1994, ‘Wind and Wind Forces in a Plantation Spruce Forest’, Boundary-Layer Meteorol. 67, 161–186.

    Article  Google Scholar 

  • Garratt, J. R.: 1978, ‘Flux Profile Relations Above Tall Vegetation’, Quart. J. Roy. Meteorol. Soc. 104, 199–212.

    Article  Google Scholar 

  • Garratt, J. R.: 1992, The Atmospheric Boundary Layer, Cambridge University Press, Cambridge, 316 pp.

    Google Scholar 

  • Grant, H. L.: 1958, ‘The Large Eddies of Turbulent Motion’, J. Fluid Mech. 4, 149–190.

    Article  Google Scholar 

  • Ho, C., and Huerre, P.: 1984, ‘Perturbed Free Shear Layers’, Ann. Rev. Fluid Mech. 16, 365–424.

    Article  Google Scholar 

  • Hunt, J. C. R. and Carruthers, D. J.: 1990, ‘Rapid Distortion Theory and the ‘Problems’ of Turbulence’, J. Fluid Mech. 212, 497–532.

    Article  Google Scholar 

  • Inoue, E.: 1955, ‘Studies of the Phenomena of Waving Plants (“Honami”) Caused by Wind. Part I. Mechanism and Characteristics of Waving Plants Phenomena’, J. Agric. Met. Japan 11, 18–22.

    Article  Google Scholar 

  • Kaimal, J. C. and Finnigan, J. J.: 1994, Atmospheric Boundary Layer Flows, Oxford University Press, New York, Oxford, 289 pp.

    Google Scholar 

  • Kaimal, J. C., Wyngaard, J. C., Izumi, Y., and Coté, O. R.: 1972, ‘Spectral Characteristics of Surface-layer Turbulence’, Quart. J. Roy. Meteorol. Soc. 98, 563–589.

    Article  Google Scholar 

  • Leclerc, M. Y., Beissner, K. C., Shaw, R. H., Den Hartog, G., and Neumann, H. H.: 1990, ‘The Influence of Atmospheric Stability on the Budgets of the Reynolds Stress and Turbulent Kinetic Energy Within and Above a Deciduous Forest’, J. Appl. Meteorol. 29, 916–933.

    Article  Google Scholar 

  • Lu, C. H. and Fitzjarrald, D. R.: 1994, ‘Seasonal and Diurnal Variations of Coherent Structures Over a Deciduous Forest’, Boundary-Layer Meteorol. 69, 43–69.

    Article  Google Scholar 

  • Lu, S. S. and Willmarth, W. W.: 1973, ‘Measurements of the Structure of the Reynolds Stress in a Turbulent Boundary Layer’, J. Fluid Mech. 60, 481–571.

    Article  Google Scholar 

  • Maitani, T. and Seo, T.: 1985, ‘Estimates of Velocity-pressure and Velocity-pressure-gradient Interactions in the Surface Layer Over Plant Canopies’, Boundary-Layer Meteorol. 33, 51–60.

    Article  Google Scholar 

  • Maxey, M. R.: 1982, ‘Distortion of Turbulence in Flows with Parallel Streamlines’, J. Fluid Mech. 124, 261–282.

    Article  Google Scholar 

  • Meyers, T. P. and Baldocchi, D. D.: 1991, ‘The Budgets of Turbulent Kinetic Energy and Reynolds Stress Within and Above a Deciduous Forest’, Agric. For. Meteorol. 53, 207–222.

    Article  Google Scholar 

  • Michalke, A.: 1964, ‘On the Inviscid Instability of the Hyperbolic-tangent Velocity Profile’, J. Fluid Mech. 19, 543–556.

    Article  Google Scholar 

  • Michalke, A.: 1965, ‘On Spatially Growing Disturbances in an Inviscid Shear Layer’, J. Fluid Mech. 23, 521–544.

    Article  Google Scholar 

  • Monin, A. S. and Yaglom, A. M.: 1971, Statistical Fluid Mechanics: Mechanics of Turbulence, M.I.T. Press, Cambridge, 769 pp.

    Google Scholar 

  • Moore, D. W., and Saffman, P. G.: 1975, ‘The Density of Organized Vortices in a Turbulent Mixing Layer’, J. Fluid Mech. 69, 465–473.

    Article  Google Scholar 

  • Nakagawa, H. and Nezu, I.: 1977, ‘Prediction of the Contributions to the Reynolds Stress from Bursting Events in Open-channel Flows’, J. Fluid Mech. 80, 99–128.

    Article  Google Scholar 

  • Paw U, K. T., Brunet, Y., Collineau, S., Shaw, R. H., Maitani, T., Qiu, J., and Hipps, L.: 1992, ‘On Coherent Structures in Turbulence Above and Within Agricultural Plant Canopies’, Agric. For. Meteorol. 61, 55–68.

    Article  Google Scholar 

  • Perry, A. E., Henbest, S., and Chong, M. S.: 1986, ‘A Theoretical and Experimental Study of Wall Turbulence’, J. Fluid Mech. 165, 163–199.

    Article  Google Scholar 

  • Pierrehumbert, R. T. and Widnall, S. E.: 1982, ‘The Two-and Three-dimensional Instabilities of a Spatially Periodic Shear Layer’, J. Fluid Mech. 112, 467–474.

    Google Scholar 

  • Priestley, C. H. B.: 1959, Turbulent Transfer in the Lower Atmosphere, University of Chicago Press, Chicago, 130 pp.

    Google Scholar 

  • Qiu, J., Paw U, K. T., and Shaw, R. H.: 1995, ‘Pseudo-wavelet Analysis of Turbulence Patterns in Three Vegetation Layers’, Boundary-Layer Meteorol. 72, 177–204.

    Article  Google Scholar 

  • Raupach, M. R.: 1979, ‘Anomalies in Flux-gradient Relationships Over Forest’, Boundary-Layer Meteorol. 16, 467–486.

    Article  Google Scholar 

  • Raupach, M. R.: 1981, ‘Conditional Statistics of Reynolds Stress in Rough-wall and Smooth-wall Turbulent Boundary Layers’, J. Fluid Mech. 108, 363–382.

    Article  Google Scholar 

  • Raupach, M. R.: 1988, ‘Canopy Transport Processes’, in W. L. Steffen and O. T. Denmead (eds.), Flow and Transport in the Natural Environment: Advances and Applications, Springer, Berlin, pp. 95–127.

    Chapter  Google Scholar 

  • Raupach, M. R.: 1989, ‘A Practical Lagrangian Method for Relating Scalar Concentrations to Source Distributions in Vegetation Canopies’, Quart. J. Roy. Meteorol. Soc. 115, 609–632.

    Article  Google Scholar 

  • Raupach, M. R., Antonia, R. A., and Rajagopalan, S.: 1991, ‘Rough-wall Turbulent Boundary Layers’, Appl. Mechs. Revs. 44, 1–25.

    Article  Google Scholar 

  • Raupach, M. R., Coppin, P. A., and Legg, B. J.: 1986, ‘Experiments on Scalar Dispersion Within a Plant Canopy, Part I: The Turbulence Structure’, Boundary-Layer Meteorol. 35, 21–52.

    Article  Google Scholar 

  • Raupach, M. R., Finnigan, J. J., and Brunet, Y.: 1989, ‘Coherent Eddies in Vegetation Canopies’, Proc. Fourth Australasian Conf. on Heat and Mass Transfer, Christchurch, New Zealand, 9–12 May 1989.

    Google Scholar 

  • Raupach, M. R. and Thom, A. S.: 1981, ‘Turbulence in and Above Plant Canopies’, Ann. Rev. Fluid Mech. 13, 97–129.

    Article  Google Scholar 

  • Rogers, M. M. and Moser, R. D.: 1994, ‘Direct Simulation of a Self-similar Turbulent Mixing Layer’, Phys. Fluids A 6, 903–922.

    Article  Google Scholar 

  • Savill, A. M.: 1987, ‘Recent Developments in Rapid-distortion Theory’, Ann. Rev. Fluid Mech. 19, 531–575.

    Article  Google Scholar 

  • Seginer, I., Mulhearn, P. J., Bradley, E. F., and Finnigan, J. J.: 1976, ‘Turbulent Flow in a Model Plant Canopy’, Boundary-Layer Meteorol. 10, 423–453.

    Article  Google Scholar 

  • Shaw, R. H., Brunet, Y., Finnigan, J. J., and Raupach, M. R.: 1995, ‘A Wind Tunnel Study of Air Flow in Waving Wheat: Two-point Velocity Statistics’, Boundary-Layer Meteorol. 76, 349–376.

    Article  Google Scholar 

  • Shaw, R. H., Den Hartog, G., and Neumann, H. H.: 1988, ‘Influence of Foliar Density and Thermal Stability on Profiles of Reynolds Stress and Turbulent Intensity in a Deciduous Forest’, Boundary-Layer Meteorol. 45, 391–409.

    Article  Google Scholar 

  • Shaw, R. H., Paw U, K. T., and Gao, W.: 1989, ‘Detection of Temperature Ramps and Flow Structures at a Deciduous Forest Site’, Agric. For. Meteorol. 47, 123–138.

    Article  Google Scholar 

  • Shaw, R. H., Silversides, R. H., and Thurtell, G. W.: 1974, ‘Some Observations of Turbulence and Turbulent Transport Within and Above Plant Canopies’, Boundary-Layer Meteorol. 5, 429–449.

    Article  Google Scholar 

  • Shaw, R. H., Tavangar, J., and Ward, D. R: 1983, ‘Structure of the Reynolds Stress in a Canopy Layer’, J. Climate Appl. Meteorol. 22, 1922–1931.

    Article  Google Scholar 

  • Shuttleworth, W. J.: 1989, ‘Micrometeorology of Temperate and Tropical Forest’, Phil. Trans. Roy. Soc. Lond. B 324, 299–334.

    Article  Google Scholar 

  • Taylor, R. J.: 1958, ‘Thermal Structures in the Lowest Layers of the Atmosphere’, Aust. J. Phys. 11, 168–176.

    Article  Google Scholar 

  • Townsend, A. A.: 1970, ‘Entrainment and the Structure of Turbulent Flow’, J. Fluid Mech. 41, 13–46.

    Article  Google Scholar 

  • Townsend, A. A.: 1976, The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge, 429 pp.

    Google Scholar 

  • Wallace, J. M., Eckelmann, H., and Brodkey, R. S.: 1972, ‘The Wall Region in Turbulent Flow’, J. Fluid Mech. 54, 39–48.

    Article  Google Scholar 

  • Wilczak, J. M.: 1984, ‘Large-scale Eddies in the Unstably Stratified Atmospheric Surface Layer. Part I: Velocity and Temperature Structure’, J. Atmos. Sci. 41, 3537–3550.

    Article  Google Scholar 

  • Wilson, J.D., Ward, D. R, Thurtell, G. W., and Kidd, G. E.: 1982, ‘Statistics of Atmospheric Turbulence Within and Above a Corn Canopy’, Boundary-Layer Meteorol. 24, 495–519.

    Article  Google Scholar 

  • Wilson, N. R., and Shaw, R. H.: 1977, ‘A Higher-order Closure Model For Canopy Flow’, J. Appl. Meteorol. 16, 1198–1205.

    Article  Google Scholar 

  • Winant, C. D. and Browand, F. K.: 1974, ‘Vortex Pairing: the Mechanism of Turbulent Mixing Layer Growth at Moderate Reynolds Numbers’, J. Fluid Mech. 63, 237–255.

    Article  Google Scholar 

  • Wygnanski, I. and Fiedler, H. E.: 1970, ‘The Two-dimensional Mixing Region’, J. Fluid Mech. 41, 327–361.

    Article  Google Scholar 

  • Wyngaard, J. C.: 1988, ‘Convective Processes in the Lower Atmosphere’, In: W. L. Steffen and O. T. Denmead (eds.), Flow and Transport in the Natural Environment: Advances and Applications, Springer, Berlin, pp. 240–260.

    Chapter  Google Scholar 

  • Zhang, C., Shaw, R. H., and Paw U, K. T.: 1992, ‘Spatial Characteristics of Turbulent Coherent Structures Within and Above an Orchard Canopy’, In: S. E. Schwartz and W. G. N. Slinn (eds.), Precipitation Scavenging and Atmosphere-Surface Exchange, Hemisphere Publishing Co. Washington, pp. 741–751.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CSIRO Centre for Environmental Mechanics, GPO Box 821, Canberra, ACT, 2601, Australia

    M. R. Raupach, J. J. Finnigan & Y. Brunet

Authors
  1. M. R. Raupach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. J. Finnigan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Brunet
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Division of Atmospheric Research, CSIRO, Melbourne, Australia

    J. R. Garratt

  2. Department of Earth and Atmospheric Science, York University, Toronto, Canada

    P. A. Taylor

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Raupach, M.R., Finnigan, J.J., Brunet, Y. (1996). Coherent Eddies and Turbulence in Vegetation Canopies: The Mixing-Layer Analogy. In: Garratt, J.R., Taylor, P.A. (eds) Boundary-Layer Meteorology 25th Anniversary Volume, 1970–1995. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0944-6_15

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0944-6_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4740-3

  • Online ISBN: 978-94-017-0944-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation