On Displacement Height, from Classical to Practical Formulation: Stress, Turbulent Transport and Vorticity Considerations

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Displacement height (d) is an important parameter in the simple modelling of wind speed and vertical fluxes above vegetative canopies, such as forests. Here we show that, aside from implicit definition through a (displaced) logarithmic profile, accepted formulations for d do not consistently predict flow properties above a forest. Turbulent transport can affect the displacement height, and is an integral part of what is called the roughness sublayer. We develop a more general approach for estimation of d, through production of turbulent kinetic energy and turbulent transport, and show how previous stress-based formulations for displacement height can be seen as simplified cases of a more general definition including turbulent transport. Further, we also give a simplified and practical form for d that is in agreement with the general approach, exploiting the concept of vortex thickness scale from mixing-layer theory.We assess the new and previous displacement height formulations by using flow statistics derived from the atmospheric boundary-layer Reynolds-averaged Navier–Stokes model SCADIS as well as from wind-tunnel observations, for different vegetation types and flow regimes in neutral conditions. The new formulations tend to produce smaller d than stress-based forms, falling closer to the classic logarithmically-defined displacement height. The new, more generally defined, displacement height appears to be more compatible with profiles of components of the turbulent kinetic energy budget, accounting for the combined effects of turbulent transport and shear production. The Coriolis force also plays a role, introducing wind-speed dependence into the behaviour of the roughness sublayer; this affects the turbulent transport, shear production, stress, and wind speed, as well as the displacement height, depending on the character of the forest. We further show how our practical (‘mixing-layer’) form for d matches the new turbulence-based relation, as well as correspondence to previous (stress-based) formulations.
Original languageEnglish
JournalBoundary-Layer Meteorology
Pages (from-to)361–381
Number of pages21
ISSN0006-8314
DOIs
Publication statusPublished - 2016

Keywords

  • Canopy flow
  • Displacement height
  • Mixing-layer theory
  • Turbulent kinetic energy
  • Turbulent transport

Cite this

@article{0c66227349714f759983a3cb508fc30b,
title = "On Displacement Height, from Classical to Practical Formulation: Stress, Turbulent Transport and Vorticity Considerations",
abstract = "Displacement height (d) is an important parameter in the simple modelling of wind speed and vertical fluxes above vegetative canopies, such as forests. Here we show that, aside from implicit definition through a (displaced) logarithmic profile, accepted formulations for d do not consistently predict flow properties above a forest. Turbulent transport can affect the displacement height, and is an integral part of what is called the roughness sublayer. We develop a more general approach for estimation of d, through production of turbulent kinetic energy and turbulent transport, and show how previous stress-based formulations for displacement height can be seen as simplified cases of a more general definition including turbulent transport. Further, we also give a simplified and practical form for d that is in agreement with the general approach, exploiting the concept of vortex thickness scale from mixing-layer theory.We assess the new and previous displacement height formulations by using flow statistics derived from the atmospheric boundary-layer Reynolds-averaged Navier–Stokes model SCADIS as well as from wind-tunnel observations, for different vegetation types and flow regimes in neutral conditions. The new formulations tend to produce smaller d than stress-based forms, falling closer to the classic logarithmically-defined displacement height. The new, more generally defined, displacement height appears to be more compatible with profiles of components of the turbulent kinetic energy budget, accounting for the combined effects of turbulent transport and shear production. The Coriolis force also plays a role, introducing wind-speed dependence into the behaviour of the roughness sublayer; this affects the turbulent transport, shear production, stress, and wind speed, as well as the displacement height, depending on the character of the forest. We further show how our practical (‘mixing-layer’) form for d matches the new turbulence-based relation, as well as correspondence to previous (stress-based) formulations.",
keywords = "Canopy flow, Displacement height, Mixing-layer theory, Turbulent kinetic energy, Turbulent transport",
author = "Andrey Sogachev and Kelly, {Mark C.}",
year = "2016",
doi = "10.1007/s10546-015-0093-x",
language = "English",
pages = "361–381",
journal = "Boundary-Layer Meteorology",
issn = "0006-8314",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - On Displacement Height, from Classical to Practical Formulation: Stress, Turbulent Transport and Vorticity Considerations

AU - Sogachev, Andrey

AU - Kelly, Mark C.

PY - 2016

Y1 - 2016

N2 - Displacement height (d) is an important parameter in the simple modelling of wind speed and vertical fluxes above vegetative canopies, such as forests. Here we show that, aside from implicit definition through a (displaced) logarithmic profile, accepted formulations for d do not consistently predict flow properties above a forest. Turbulent transport can affect the displacement height, and is an integral part of what is called the roughness sublayer. We develop a more general approach for estimation of d, through production of turbulent kinetic energy and turbulent transport, and show how previous stress-based formulations for displacement height can be seen as simplified cases of a more general definition including turbulent transport. Further, we also give a simplified and practical form for d that is in agreement with the general approach, exploiting the concept of vortex thickness scale from mixing-layer theory.We assess the new and previous displacement height formulations by using flow statistics derived from the atmospheric boundary-layer Reynolds-averaged Navier–Stokes model SCADIS as well as from wind-tunnel observations, for different vegetation types and flow regimes in neutral conditions. The new formulations tend to produce smaller d than stress-based forms, falling closer to the classic logarithmically-defined displacement height. The new, more generally defined, displacement height appears to be more compatible with profiles of components of the turbulent kinetic energy budget, accounting for the combined effects of turbulent transport and shear production. The Coriolis force also plays a role, introducing wind-speed dependence into the behaviour of the roughness sublayer; this affects the turbulent transport, shear production, stress, and wind speed, as well as the displacement height, depending on the character of the forest. We further show how our practical (‘mixing-layer’) form for d matches the new turbulence-based relation, as well as correspondence to previous (stress-based) formulations.

AB - Displacement height (d) is an important parameter in the simple modelling of wind speed and vertical fluxes above vegetative canopies, such as forests. Here we show that, aside from implicit definition through a (displaced) logarithmic profile, accepted formulations for d do not consistently predict flow properties above a forest. Turbulent transport can affect the displacement height, and is an integral part of what is called the roughness sublayer. We develop a more general approach for estimation of d, through production of turbulent kinetic energy and turbulent transport, and show how previous stress-based formulations for displacement height can be seen as simplified cases of a more general definition including turbulent transport. Further, we also give a simplified and practical form for d that is in agreement with the general approach, exploiting the concept of vortex thickness scale from mixing-layer theory.We assess the new and previous displacement height formulations by using flow statistics derived from the atmospheric boundary-layer Reynolds-averaged Navier–Stokes model SCADIS as well as from wind-tunnel observations, for different vegetation types and flow regimes in neutral conditions. The new formulations tend to produce smaller d than stress-based forms, falling closer to the classic logarithmically-defined displacement height. The new, more generally defined, displacement height appears to be more compatible with profiles of components of the turbulent kinetic energy budget, accounting for the combined effects of turbulent transport and shear production. The Coriolis force also plays a role, introducing wind-speed dependence into the behaviour of the roughness sublayer; this affects the turbulent transport, shear production, stress, and wind speed, as well as the displacement height, depending on the character of the forest. We further show how our practical (‘mixing-layer’) form for d matches the new turbulence-based relation, as well as correspondence to previous (stress-based) formulations.

KW - Canopy flow

KW - Displacement height

KW - Mixing-layer theory

KW - Turbulent kinetic energy

KW - Turbulent transport

U2 - 10.1007/s10546-015-0093-x

DO - 10.1007/s10546-015-0093-x

M3 - Journal article

SP - 361

EP - 381

JO - Boundary-Layer Meteorology

JF - Boundary-Layer Meteorology

SN - 0006-8314

ER -