# A numerical simulation of boundary-layer flows near shelterbelts

## Authors

- Revised:

DOI: 10.1007/BF00721047

- Cite this article as:
- Wang, H. & Takle, E.S. Boundary-Layer Meteorol (1995) 75: 141. doi:10.1007/BF00721047

- 48 Citations
- 310 Views

## 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

*C*_{d}Drag coefficient for unit plant area density

*c*_{i}Experimental constants of turbulent closure scheme (Mellor and Yamada, 1982)

*E*Turbulent kinetic energy (TKE)

*F*_{i}Drag force in the

*i*direction exerted on air flow by obstacle elements*f*_{k}Coriolis parameter

*g*_{i}Acceleration vector due to gravity

*H*Height of shelterbelt

*i, j, k, q*Subscript variables, indicating

*x, y*and*z*directions, respectively, and grid numbers in these three directions*K*_{0}Turbulent exchange coefficient for neutral, obstacle-free ABL

*K*_{m}Turbulent exchange coefficient for momentum transport

*K*_{E}Turbulent exchange coefficient for TKE transport

*k*_{r}Resistance coefficient of shelterbelts

*l*Mixing length of turbulence

- MKE
Mean kinetic energy

*n*Timestep of model integration

**n**,*n*_{i}Vector and its component in the

*i*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 in

*x*and*z*directions, respectively*u′, w′*Fluctuating windspeed components in

*x*and*z*directions*u*_{i}Windspeed in the

*i*direction*u*_{*}Friction velocity

*u*_{*0}Friction velocity for obstacle-free ABL

*u*_{t},*v*_{t}*u*and*v*at model top*u*^{aux}, and*w*^{aux}Intermediate prediction velocities of

*u*and*w*without the dynamic pressure perturbation*u*^{n+1}and*w*^{n+1}Prediction velocities of

*u*and*w*at the*n*+1 timestep of model integration*V*Volume of the spatial averaging process

*x*Horizontal coordinate axis perpendicular to shelterbelt

*x*_{i}*i*=1, 2, 3-three direction coordinate,*x, y, z**z*Vertical coordinate axis upward

*z*_{0}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 for

*u, v, w, E*and*E*1