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Ground level air convection produces frost damage patterns in turfgrass

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Abstract

Frost injury patterns are commonly observed on the warm-season turfgrass species bermudagrass (Cynodon species Rich.), zoysiagrass (Zoysia species Willd.), and buffalograss [Bouteloua dactyloides (Nutt.) J.T. Columbus] in cool-temperate and subtropical zones. Qualitative observations of these injury patterns are presented and discussed. A model for the formation of such patterns based on thermal instability and convection of air is presented. The characteristic length scale of the observed frost pattern injury requires a temperature profile that decreases with height from the soil to the turfgrass canopy surface followed by an increase in temperature with height above the turfgrass canopy. This is justified by extending the earth temperature theory to include a turf layer with atmosphere above it. Then the theory for a thermally unstable layer beneath a stable region by Ogura and Kondo is adapted to a turf layer to include different parameter values for pure air, as well as for turf, which is treated as a porous medium. The earlier porous medium model of Thompson and Daniels proposed to explain frost injury patterns is modified to give reasonable agreement with observed patterns.

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Abbreviations

A :

Temperature amplitude

a :

Dimensionless wave number

b :

Wave number

α :

Thermal expansion coefficient

c :

Specific heat at constant pressure

Da:

Darcy number

ΔT :

Temperature difference

δT :

Deviation from the average temperature

g :

Acceleration of gravity

γ :

Ratio of stable to unstable temperature gradients

h :

Sample height

k :

Permeability

κ :

Thermal diffusion coefficient

L :

Turf height

λ :

Pattern wavelength

μ :

Shear viscosity

ν :

Kinematic viscosity

ω :

Angular frequency

p :

Pressure

Pr:

Prandtl number

Q :

Radiative heat flux absorbed

ϕ :

Phase

Ra:

Rayleigh number

ρ :

Density

T :

Temperature

t :

Time

u :

Velocity

z :

Vertical spatial dimension

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Acknowledgments

The authors acknowledge discussions with Dr. Greg Bell, Professor Emeritus of Turfgrass Management/Science Program in the Department of Horticulture and Landscape Architecture, Oklahoma State University, Stillwater, OK, and with Karen Daniels, Department of Physics, North Carolina State University, Raleigh, NC.

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Authors and Affiliations

  1. Department of Physics, Oklahoma State University, Stillwater, OK, 74078, USA

    Bruce J. Ackerson

  2. Department of Mechanical Engineering Technology, Oklahoma State University, Stillwater, OK, 74078, USA

    Richard A. Beier

  3. Department of Horticulture and Landscape Architecture, Oklahoma State University, Stillwater, OK, 74078, USA

    Dennis L. Martin

Authors
  1. Bruce J. Ackerson
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  2. Richard A. Beier
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  3. Dennis L. Martin
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Correspondence to Bruce J. Ackerson.

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Ackerson, B.J., Beier, R.A. & Martin, D.L. Ground level air convection produces frost damage patterns in turfgrass. Int J Biometeorol 59, 1655–1665 (2015). https://doi.org/10.1007/s00484-015-0972-3

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  • DOI: https://doi.org/10.1007/s00484-015-0972-3

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