Flows over 3D and 2D Hills

A wind tunnel study was conducted to examine the flowfield and the ground-level scalar concentrations from a variety of scalar source positions (locations and heights) both upstream and downstream of two model hills, an axisymmetric hill (maximum slope 24o) and a two-dimensional ridge (maximum slope 16o), immersed in a simulated neutral atmospheric boundary layer.

Wind Tunnel

The experiments performed in this study were conducted in the meteorological wind tunnel of the U.S. Environmental Protection Agency's Fluid Modelling Facility. It is a low-speed, open-return wind tunnel with a test section 2.1 m high, 3.7 m wide and 18.3 m long. Detailed features and operational characteristics of the wind tunnel are described by Snyder (1979).


The axisymmetric hill was an idealised version of Cinder Cone Butte (Lavery et al., 1982), an isolated, nearly axisymmetric hill located in south-western Idaho. The model was 155 mm in height, 1550 mm in diameter, and had the shape of a fourth order polynomial:

\[ f(r) = \frac{h+c}{1+(r/L)^4} - c \]

where \(r\) is the radial distance from the hill centre; \(h = 155\) mm, \(L = 388\) mm and \(c = 10\) mm, for \(r \le 775\) mm. For \(r > 775\) mm the surface is flat, ie. \(f(r)=0\).

The top of the model hill was a relatively flat plateau about 400 mm in diameter, while the sides sloped gradually to the surface with no discontinuities. The maximum slope was 24o.

The two dimensional ridge was identical in shape and construction to “Hill 5” as described by Khurshudyan et al (1981), except that it was covered with gravel of a smaller size. The height of the model was 118 mm, its chord was 1180 mm, and its maximum slope was l6o. The shape is described by the following parametric equations for \(- a < \xi < a\):

\[ x = (1/2) \xi \left( 1 + \frac{a^2}{\xi^2 + m^2(a^2 - \xi^2)} \right) \] \[ y = (1/2) m \sqrt{a^2 - \xi^2} \left( 1 - \frac{a^2}{\xi^2 +m^2 (a^2 - \xi^2)} \right) \]

where \(m = 1.22\), \(a = 590\) mm and \(\xi\) is an arbitrary parameter.

Cross sectional views of both the hill and ridge are shown in figure 1.

Flow configuration Fig. 1: Isotachs over the centreline of the axisymmetric hill (top) and 2D ridge (bottom). Note that vertical distance is scaled by a factor of 3 compared to horizontal, to enhance clarity.

Velocity Measurements

Measurements of mean velocity, longitudinal and vertical components of turbulence intensity and Reynolds stress were made using hot-wire anemometers with x-array sensors. The sensors were calibrated in the free-stream flow using a Pitot tube and capacitance manometer as a reference.

Corrections were applied to account for the effects of ambient temperature drift (Bearman, 1971) and finite length sensor yaw response (Lawson and Britter l983). All measurements were carried out at a free-stream wind speed of 4 m/s.

Concentration Measurements

A hydrocarbon tracer technique was used to measure ground-level concentrations downwind of the source. The HC tracer used was ethane (C2H6), which has a molecular weight very near that of air, so that the plume was neutrally buoyant. The tracer was released through a hollow, perforated plastic ball 10 mm in diameter. This type of source allows for injection of a suitable quantity of tracer gas while at the same time minimise the effluent momentum in any preferred direction; it simulates a point source and avoids any plume rise. Samples were withdrawn through sampling ports mounted on the surface of the model and on the tunnel floor. Port-to-port spacing was 150 mm which determined the spatial resolution with which the maximum ground-level concentration was determined. The samples were routed to flame ionisation detectors (FlDs) which produced output voltages linearly related to concentration.

The concentration of tracer material was measured as a function of distance downstream of the source for several different source locations and heights.

The data available includes:

  • Mean velocity and Reynolds stress profiles in the undisturbed boundary layer (flat plate case), and at several streamwise locations in the axisymmetric hill and 2D ridge cases.
  • Surface tracer concentrations downstream of the tracer source for a range of source locations and heights (for the flat plate, axisymmetric hilll and 2D ridge cases).
  • Measurements of tracer concentration at various heights above the surface for selected tracer source locations (for the flat plate and axisymmetric hill cases).

Sample plots of selected quantities are available.

The data can be downloaded as compressed archives from the links below, or as individual files.

ACC Data Files (Relate to Flat Plate and Axisymmetric Hill Cases)

Locations of surface measurement ports accprt-001.dat
Boundary Layer Measurements (Flat Plate Case)
Streamwise distance Vertical profiles on \(y=0\) Lateral profile on \(z=80\) mm Lateral profile on \(z=160\) mm
UW probe data UV probe data
\(x=10\) m accvp-004.dat accvp-009.dat accvp-006.dat accvp-005.dat
\(x=12\) m accvp-008.dat
\(x=14\) m accvp-007.dat accvp-010.dat
ACCCMM-Series Concentration Measurements
Surface Concentration (Axisymmetric Hill Case)
Stack Location Stack Height
80 mm 160 mm
\(X=6h\) acccmm-158.dat
\(X=7h\) acccmm-139.dat acccmm-136.dat
Vertical Concentration Profiles on \(y=0\) (without hill)
Distance from source Stack Height
80 mm 160 mm
\(x=625\) mm acccmm-003.dat
\(x=1250\) mm acccmm-001.dat
\(x=2500\) mm acccmm-004.dat
\(x=825\) mm acccmm-007.dat
\(x=1650\) mm acccmm-005.dat
\(x=3300\) mm acccmm-006.dat
ACCCM-Series Concentration Measurements
Streamwise profiles on \(y=0\) at various heights \(z\) (Flat Plate Case)
Stack height Location above surface
\(z=0\) mm \(z=40\) mm \(z=80\) mm \(z=120\) mm
0 mm acccm-021.dat acccm-022.dat acccm-023.dat acccm-024.dat
40 mm acccm-005.dat acccm-006.dat acccm-007.dat acccm-008.dat
80 mm acccm-001.dat acccm-002.dat acccm-003.dat acccm-004.dat
120 mm acccm-009.dat acccm-010.dat acccm-011.dat acccm-012.dat
160 mm acccm-013.dat acccm-014.dat acccm-015.dat acccm-016.dat
200 mm acccm-017.dat acccm-018.dat acccm-019.dat acccm-020.dat
Lateral profiles at various \(x\) locations (Flat Plate Case) for Stack height 80 mm
\(x\) location Location above surface
\(z=0\) mm \(z=40\) mm \(z=80\) mm \(z=120\) mm
\(x=625\) mm acccm-041.dat acccm-042.dat acccm-043.dat acccm-044.dat
\(x=1250\) mm acccm-045.dat acccm-046.dat acccm-047.dat acccm-048.dat
\(x=2500\) mm acccm-057.dat acccm-058.dat acccm-059.dat acccm-060.dat
Lateral profiles at various \(x\) locations (without hill) for Stack height 160 mm
\(x\) location Location above surface
\(z=0\) mm \(z=40\) mm \(z=80\) mm \(z=120\) mm
\(x=1650\) mm acccm-065.dat acccm-066.dat acccm-067.dat acccm-068.dat
\(x=3300\) mm acccm-069.dat acccm-070.dat acccm-071.dat acccm-072.dat
Lateral profiles at various \(x\) locations (with hill) for Stack height 80 mm
\(x\) location Location above surface
\(z=0\) mm \(z=10\) mm \(z=20\) mm \(z=30\) mm
Above Port 42 acccm-380.dat acccm-381.dat acccm-382.dat acccm-383.dat
Above centre acccm-384.dat acccm-385.dat acccm-386.dat acccm-387.dat
Above Port 15 acccm-388.dat acccm-389.dat acccm-390.dat acccm-391.dat
Lateral profiles at \(x=825\) mm (with hill) for Stack height 160 mm
\(x\) location Location above surface
\(z=0\) mm \(z=40\) mm
\(x=825\) mm acccm-081.dat acccm-082.dat

GEP Data Files (Relate to Flat Plate, Axisymmetric Hill and 2D Ridge Cases)

GEPRP-Series Pitot Tube Measurements on \(y=0\) (Axisymmetric Hill Case)
Streamwise location File
\(x=2h\) geprp-001.dat
\(x=3h\) geprp-002.dat
\(x=4h\) geprp-003.dat
\(x=4.2h\) geprp-005.dat
\(x=4.56h\) geprp-004.dat
GEPMV-Series Boundary Layer Measurements on \(y=0\) (Flat Plate, Axisymmetric Hill and 2D Ridge Cases)
Flat Plate Case (2 measurements per location)
Location File 1 File 2
\(x=6\) m gepmv-001.dat gepmv-004.dat
\(x=10\) m gepmv-002.dat gepmv-005.dat
\(x=15\) m gepmv-003.dat gepmv-006.dat
Axisymmetric Hill and 2D Ridge Cases
Location Axisymmetric Hill 2D Ridge
\(x=-15h\) gepmv-015.dat gepmv-026.dat
\(x=-10h\) gepmv-014.dat gepmv-025.dat
\(x=-7h\) gepmv-013.dat gepmv-027.dat
\(x=-5h\) gepmv-012.dat gepmv-028.dat
\(x=-4h\) gepmv-011.dat gepmv-029.dat
\(x=-3h\) gepmv-010.dat gepmv-030.dat
\(x=-2h\) gepmv-009.dat gepmv-031.dat
\(x=-1h\) gepmv-008.dat gepmv-032.dat
\(x=0\) gepmv-007.dat gepmv-024.dat
\(x=1h\) gepmv-016.dat gepmv-033.dat
\(x=2h\) gepmv-017.dat gepmv-034.dat
\(x=3h\) gepmv-018.dat gepmv-035.dat
\(x=4h\) gepmv-019.dat gepmv-036.dat
\(x=5h\) gepmv-020.dat gepmv-037.dat
\(x=7h\) gepmv-021.dat gepmv-038.dat
\(x=10h\) gepmv-022.dat gepmv-039.dat
\(x=15h\) gepmv-023.dat gepmv-040.dat
GEPMCX-Series Surface Concentration Measurements on \(y=0\) (Flat Plate, Axisymmetric Hill and 2D Ridge Cases)
Flat Plate Case
Stack Location Stack Height
30 mm 40 mm 80 mm 120 mm 180 mm 200 mm
\(x=6.5\) m gepmcx-001.dat
gepmcx-003.dat gepmcx-004.dat gepmcx-005.dat gepmcx-006.dat gepmcx-007.dat
\(x=11.3\) m gepmcx-008.dat gepmcx-009.dat
Axisymmetric Hill Case
Stack Location Stack Height
20 mm 40 mm 80 mm 120 mm 160 mm 200 mm 250 mm
\(x=0\) mm gepmcx-039.dat gepmcx-040.dat
\(x=314\) mm gepmcx-034.dat gepmcx-035.dat gepmcx-036.dat gepmcx-037.dat gepmcx-038.dat gepmcx-034.dat
\(x=468\) mm gepmcx-047.dat gepmcx-048.dat gepmcx-049.dat gepmcx-050.dat gepmcx-051.dat
\(x=616\) mm gepmcx-055.dat gepmcx-028.dat
gepmcx-030.dat gepmcx-031.dat gepmcx-032.dat gepmcx-033.dat gepmcx-052.dat
\(x=794\) mm gepmcx-054.dat gepmcx-041.dat gepmcx-042.dat gepmcx-043.dat gepmcx-044.dat gepmcx-045.dat gepmcx-053.dat
\(x=936\) mm gepmcx-056.dat gepmcx-017.dat gepmcx-018.dat gepmcx-019.dat
gepmcx-020.dat gepmcx-021.dat gepmcx-022.dat
\(x=1279\) mm gepmcx-023.dat gepmcx-024.dat gepmcx-025.dat gepmcx-026.dat gepmcx-027.dat
\(x=1560\) mm gepmcx-010.dat gepmcx-011.dat
\(x=1620\) mm gepmcx-012.dat gepmcx-013.dat gepmcx-014.dat gepmcx-015.dat gepmcx-016.dat
\(x=2031\) mm gepmcx-057.dat gepmcx-058.dat
2D Ridge Case
Stack Location Stack Height
30 mm 60 mm 90 mm 120 mm 150 mm 180 mm 200 mm
\(x=4\) mm gepmcx-060.dat gepmcx-061.dat
\(x=h\) gepmcx-062.dat gepmcx-063.dat gepmcx-064.dat gepmcx-065.dat
\(x=2h\) gepmcx-066.dat gepmcx-067.dat gepmcx-068.dat
\(x=5h\) gepmcx-069.dat gepmcx-071.dat gepmcx-072.dat gepmcx-073.dat gepmcx-074.dat gepmcx-075.dat gepmcx-076.dat
\(x=1285\) mm gepmcx-078.dat
  1. Bearman, P.W. (1971). Corrections for the effects of ambient temperature drift on hot-wire measurements in incompressible flow. DIS.4 Information, Vol. 11, pp. 25-30.
  2. Khurshudyan, L.H., Snyder, W.H., Nekrasov, I.V. (1981). Flow and dispersion of pollutants over two-dimensional hills: summary report on joint Soviet-American study. Rpt. No. EPA-600/4-81-067, Envir. Prot. Agcy., Res. Tri. Pk., NC.
  3. Lavery, T.F., Bass, A., Strimaitis, D.G., Venkatram, A., Greene, B.R., Drivas, P.J., Egan, B.A. (1982). EPA complex terrain modeling program: first milestone report-1981. Rpt. No. EPA-600/3-82-036, Envir. Prot. Agcy., Res. Tri. Pk., NC.
  4. Lawson, R.E. Jr., Britter, R.E. (1983). A note on the measurement of transverse velocity fluctuations with heated cylindrical sensors at small mean velocities. J. Phys. E: Sci. Insts., Vol. 16, pp. 563-567.
  5. Lawson, R.E., Snyder, W.H., Thompson, R.S. (1989). Estimation of maximum surface concentrations from sources near complex terrain in neutral flow. Atmospheric Environment, Vol. 23, pp. 321-331.
  6. Snyder, W.H. (1979). The EPA meteorological wind tunnel: its design, construction and operating characteristics. Rpt. No. EPA-600/4-79-051, Envir. Prot. Agcy., Res. Tri. Pk., NC.
  7. Thompson, R.S., Lawson, R.E. (1990). Terrain amplification factors for sources near complex terrain. Data report, project ACCD, GEPCPX, U.S. EPA.
  8. Thompson, R.S., Shipman, M.S., Rottman, J.W. (1991). Moderately stable flow over a 3D hill -- A comparison of linear theory with laboratory measurements. Tellus, 43A, pp. 49-63.

Indexed data:

case042 (dbcase, semi_confined_flow)
titleFlows over 3D and 2D Hills
authorThompson, Lawson
flow_tag2d, 3d, scalar, separated, surface_mounted_body