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Turbulence in waving wheat

I. Mean Statistics and Honami

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Abstract

Measurements of mean and fluctuating velocities, surface pressure and stalk waving have been made in a uniform wheat canopy. Features of the vertical profiles of mean turbulence quantities are discussed in the context of the resonant waving of wheat stalks. The discrete and prominent peaks in the velocity spectra measured in and above the canopy are then analyzed in the light of the organized travelling wave-type structure or ‘honami’, observed in such crops on windy days. Prominent peaks in the spectra are identified with the arrival of gusts, the stalk-waving frequency, and the frequency of oscillations in canopy height. Two possible mechanisms are proposed to account for the observed height dependence of the peak frequencies, directly associated with stalk waving.

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Abbreviations

x :

streamwise co-ordinate, positive downwind

y :

cross-stream co-ordinate

z :

vertical co-ordinate, positive upwards

ũ:

instantaneous streamwise velocity

\(\tilde v\) :

instantaneous cross-stream velocity

\(\tilde w\) :

instantaneous vertical velocity

figure 1
\(\tilde p\) :

instantaneous pressure

figure 2
ĥ:

characteristic height of hill in theory of Jackson and Hunt (1974)

\(\hat L\) :

characteristic length of hill in theory of Jackson and Hunt (1974)

C d (z):

dimensionless drag coefficient of foliage

A(z):

area of foliage per unit volume of space

u * :

friction velocity =\(( - \overline {uw} )^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \)

i u :

streamwise turbulence intensity =\((\overline {u^2 } )^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} /U\)

i w :

vertical turbulence intensity =\((\overline {w^2 } )^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} /U\)

ϕ uu :

power spectral density of streamwise velocity fluctuations

ϕitww :

power spectral density of vertical velocity fluctuations

ϕ uw :

cross-spectral density of streamwise and vertical velocity fluctuations

ξ:

instantaneous displacement of wheat stalk from its mean position in the x direction

ξ0 :

amplitude of periodic displacement

λ:

wavelength of honami waves

f :

frequency of honami waves

Θ:

phase velocity of honami waves = λf

f g :

frequency of arrival of gusts at the surface

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Authors and Affiliations

  1. Division of Environmental Mechanics, CSIRO, Canberra, Australia

    J. J. Finnigan

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Finnigan, J.J. Turbulence in waving wheat. Boundary-Layer Meteorol 16, 181–211 (1979). https://doi.org/10.1007/BF02350511

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