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Flow–plant interactions at leaf, stem and shoot scales: drag, turbulence, and biomechanics

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Abstract

Flow–plant interactions are experimentally investigated at leaf, stem, and shoot scales in an open-channel flume at a range of Reynolds numbers. The experiments included measurements of instantaneous drag forces acting on leaves, stems, and shoots of the common freshwater plant species Glyceria fluitans, complemented with velocity measurements, high-resolution video recordings, and biomechanical tests of leaf and stem properties. The analyses of bulk statistics, power spectral densities, transfer functions, and cross-correlations of measured velocities and drag forces revealed that flow characteristics, drag force, and plant biomechanical and morphological properties are strongly interconnected and scale-dependent. The plant element–flow interactions can be subdivided into two classes: (I) passive interactions when the drag variability is due to the time variability of the wetted and frontal areas and squared approach velocity (due to the large-scale turbulence); and (II) active interactions representing a range of element-specific instabilities that depend on the element flexural rigidity and morphology. Implications of experimental findings for plant biophysics and ecology are briefly discussed.

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Abbreviations

ADV:

Acoustic Doppler velocimeter

A :

Reference area

A f :

Frontal projection area of plant

A i :

Characteristic plant diameter × lateral projection plant height

A w :

Total wetted area

α :

Vogel number

B :

Mean leaf width or mean stem diameter

C d :

Drag coefficient

\(C_{d - FPL}\) :

Drag coefficient of laminar flat plate flow

\(C_{d - FPT}\) :

Drag coefficient of turbulent flat plate flow

\(C_{xy}\) :

Covariance function

CV :

Coefficient of variation

d :

Characteristic plant diameter

\(\Delta z\) :

Leaf ridge height

\(\delta\) :

Viscous sublayer height

\(\delta^{ + }\) :

Normalised height of the viscous sublayer

DMD:

Drag measurement device

E:

‘Tension’ Young’s modulus

Eb :

‘Bending’ Young’s modulus

EI:

Flexural rigidity

f :

Frequency

f s :

Sampling frequency

F :

Mean drag force

\(F_{m}\) :

Total mean drag force (i.e., tip + leaf)

\(\hat{F}_{m}\) :

Instantaneous total drag force (i.e., tip + leaf)

\(F_{t}\) :

Mean drag force acting on the rod tip

\(\hat{F}_{t}\) :

Instantaneous drag force acting at the rod tip

h :

Water depth

h i :

Height of the lateral projection of plant

I :

Second moment area

K d :

Kurtosis coefficient

L :

Leaf, stem or shoot length

L f :

Length of plant lateral projection

LFTF:

Leaf force transfer function

LBL:

Leaf boundary layer

LVTF:

Leaf velocity transfer function

\(MR_{{\hat{F}_{m} u_{d} }}\) :

Average of maximum cross-correlation coefficients between drag force and downstream velocity

\(MR_{{u_{a} \hat{F}_{m} }}\) :

Average of maximum cross-correlation coefficients between approach velocity and drag force

\(MR_{{u_{a} u_{d} }}\) :

Average of maximum cross-correlation coefficients between approach velocity and downstream velocity

n :

Number of samples

PSD:

Power spectral density

Q :

Discharge

\(R_{xy}\) :

Cross-correlation function

\(R_{{\hat{F}_{m} U_{d} }}\) :

Cross-correlation function between drag force and downstream velocity

\(R_{{u_{a} \hat{F}_{m} }}\) :

Cross-correlation function between approach velocity and drag force

\(R_{{u_{a} u_{d} }}\) :

Cross-correlation function between approach and downstream velocities

Re:

Reynolds number

Re h :

Depth-based Reynolds number

Re L :

Plant length-based Reynolds number

\(\text{Re}_{Lc}\) :

Critical Reynolds number for transition from laminar boundary layer to the turbulent boundary layer

\(\rho\) :

Fluid density

\(\sigma_{d}\) :

Standard deviation of drag force

\(\sigma_{{u_{a} }}^{{}}\) :

Standard deviation of approach velocity

\(\sigma_{{u_{d} }}\) :

Standard deviation of the downstream velocity

\(\sigma_{m}^{2}\) :

Total variance of drag force

\(\sigma_{t}^{2}\) :

Variance related to the rod tip

\(\sigma_{{u_{a} }}^{2}\) :

Variance of approach velocity

S b :

Flume bed slope

S d :

Skewness coefficient

\(S_{{\hat{F}_{m} }}\) :

Power spectral density of drag force

\(S_{{u_{a} }}\) :

Power spectral density of approach velocity

\(S_{{u_{d} }}\) :

Power spectral density of downstream velocity

SFTF:

Shoot force transfer function

SVTF:

Shoot velocity transfer function

STFTF:

Stem force transfer function

STVTF:

Stem velocity transfer function

t :

Time

\(\tau\) :

Time lag

\(\tau_{0}\) :

Mean shear stress at a leaf surface

u :

Instantaneous longitudinal velocity

u′ :

Fluctuating component of longitudinal velocity

\(u_{*}\) :

Friction velocity

U :

Time-averaged longitudinal velocity

U a :

Time-averaged velocity in front of a shoot or its parts

U f :

Undisturbed velocity integrated over A f

U i :

Undisturbed velocity integrated over h i

U m :

Cross-sectional average velocity

\(\upsilon\) :

Fluid kinematic viscosity

\(z^{ + }\) :

Leaf ridge Reynolds number

\(\overline{{z^{ + } }}\) :

Average \(z^{ + }\)

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Acknowledgments

The work was supported by the Leverhulme Trust, Grant F/00152/Z ‘Biophysics of flow–plant interactions in aquatic systems’. The final stage of this work has been supported by ETH-Zürich, Leibniz Institute of Freshwater Ecology and Inland Fisheries-Berlin, University of Aberdeen, and NERC’s Center for Ecology and Hydrology. The Centre for Ecology and Hydrology (CEH, Edinburgh) supplied the strain gauge equipment used in this work. The authors are grateful to Valentin Eydoux and Santiago Halle for their help with the experimental work.

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Authors and Affiliations

  1. Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich, Wolfgang-Pauli-Str. 27, 8093, Zurich, Switzerland

    Ismail Albayrak

  2. School of Engineering, Fraser Noble Building, University of Aberdeen, Aberdeen, AB24 3UE, UK

    Vladimir Nikora

  3. Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Müggelseedamm 301, 12587, Berlin, Germany

    Oliver Miler

  4. Centre for Ecology and Hydrology Edinburgh, Bush Estate, Penicuik, Midlothian, EH26 0QB, UK

    Matthew T. O’Hare

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  1. Ismail Albayrak
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  2. Vladimir Nikora
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  4. Matthew T. O’Hare
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Correspondence to Ismail Albayrak.

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Albayrak, I., Nikora, V., Miler, O. et al. Flow–plant interactions at leaf, stem and shoot scales: drag, turbulence, and biomechanics. Aquat Sci 76, 269–294 (2014). https://doi.org/10.1007/s00027-013-0335-2

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