Boundary-Layer Meteorology

, Volume 75, Issue 1–2, pp 141–173 | Cite as

A numerical simulation of boundary-layer flows near shelterbelts

  • Hao Wang
  • Eugene S. Takle
Article

Abstract

We have developed a shelterbelt boundary-layer numerical model to study the patterns and dynamic processes relating to flow interaction with shelterbelts. The model simulates characteristics of all three zones of airflow passing over and through shelterbelts: the windward windspeed-reduction zone, the overspeeding zone above the shelterbelt, and the leeward windspeed-reduction zone. Locations of the maximum windspeed reduction and recirculation zone, as well as the leeward windspeed-recovery rate are well simulated by the model. Where comparisons with field measurements and wind-tunnel experiments were possible, the model demonstrated good performance for flows over and through shelters ranging from almost completely open to almost solid.

The dynamic pressure resulting from the convergence and divergence of the flow field alters the perturbation pressure field. The disturbed pressure controls not only the formation of the separated flow but also the location of maximum windspeed reduction, streamline curvature, speed-up over the shelterbelt, and leeward windspeed recovery rate. The interaction of pressure with the flow produces complex flow patterns, the characteristics of which are determined, to a great extent, by shelterbelt structure.

Notation

<>

Spatial averaged value

(−)

Temporal averaged value

(′)

Departure of variable from its averaged value

A

Leaf surface-area density

ABL

Atmospheric boundary layer

C

Drag coefficient for obstacle exerted on air

Cd

Drag coefficient for unit plant area density

ci

Experimental constants of turbulent closure scheme (Mellor and Yamada, 1982)

E

Turbulent kinetic energy (TKE)

Fi

Drag force in thei direction exerted on air flow by obstacle elements

fk

Coriolis parameter

gi

Acceleration vector due to gravity

H

Height of shelterbelt

i, j, k, q

Subscript variables, indicatingx, y andz directions, respectively, and grid numbers in these three directions

K0

Turbulent exchange coefficient for neutral, obstacle-free ABL

Km

Turbulent exchange coefficient for momentum transport

KE

Turbulent exchange coefficient for TKE transport

kr

Resistance coefficient of shelterbelts

l

Mixing length of turbulence

MKE

Mean kinetic energy

n

Timestep of model integration

n,ni

Vector and its component in thei direction of the interface of the averaging volume

p

Atmospheric pressure perturbation

S

Interface surface of the averaging volume

t

Time

U

Total mean windspeed

u, w

Mean windspeed components inx andz directions, respectively

u′, w′

Fluctuating windspeed components inx andz directions

ui

Windspeed in thei direction

u*

Friction velocity

u*0

Friction velocity for obstacle-free ABL

ut,vt

u andv at model top

uaux, andwaux

Intermediate prediction velocities ofu andw without the dynamic pressure perturbation

un+1 andwn+1

Prediction velocities ofu andw at then+1 timestep of model integration

V

Volume of the spatial averaging process

x

Horizontal coordinate axis perpendicular to shelterbelt

xi

i=1, 2, 3-three direction coordinate,x, y, z

z

Vertical coordinate axis upward

z0

Ground surface roughness length

β

Weight coefficient for numerical differencing scheme

γ

Coefficient of air thermal expansion

Dissipation rate of turbulence

ijk

Einstein summation symbol

ρ0

Air density

ϑ

Potential-temperature departure from its basic state

ν

Coefficient of air molecular viscosity

t

Time step of model integration

κ

von Karman constant

ϕ

Macry symbol, standing foru, v, w, E andE1

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Hao Wang
    • 1
  • Eugene S. Takle
    • 1
  1. 1.Department of Geological and Atmospheric Sciences, and Department of AgronomyIowa State UniversityAmesUSA

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