# Experimental Study of Downburst Wind Flow over a Typical Three-Dimensional Hill
## 2 Experimental Setup  
As shown in Figure 2a, the laboratory tests were conducted by using a physical downburst simulator in Zhejiang University. The impinging jet consists of four parts: a fan, a diffuser, a settling chamber, and a contraction unit [21]. In the tests, the jet diameter \(D_{\text{jet}}\) was 0.6 m; the jet height \(h\), from the ground to the nozzle, was set to be two times the jet diameter; \(r\) denotes the radial horizontal distance from the stagnation point. The temperature of the downdraft was the same as the indoor ambient temperature, ranging from 6 to 14 \({}^{\circ}\)C. A Cartesian coordinate system for the hill was employed and is illustrated in Figure 2b, with the origin set at the center of the hill bottom face, and where \(x\) and \(y\) are the orthogonal horizontal coordinates. Without loss of generality, the \(x\)-axis of the hill coincided with the radial direction of the jet flow. A cosine-squared cross-section was adopted to represent an idealized axisymmetric hill [22], in the form of  
\[z(x,y)=\left\{ \begin{array}{ll}H\cos^{2}(\pi\sqrt{x^{2}+y^{2}}/2L),&\sqrt{x^ {2}+y^{2}}<L\\ 0,&\sqrt{x^{2}+y^{2}}\geq L\end{array} \right. \tag{1}\]  
where \(L\) is the radius of the bottom face of the hill and \(z\) is the altitude of the point on the hill surface. Accordingly, Equation (1) yields \(L=2L_{\text{u}}\). Moreover, a local coordinate, \(Z\), is used to denote the relative height from the surface of the hill. A total of 12 hill models, with parameters tabulated in Table 2, were employed in the laboratory tests to investigate the effects of the height, size, and location of the hill on the wind field above the hill. The hill models can be classified into two categories, namely the hill models with \(L=0.5D_{\text{jet}}\) and those with \(L=1.0D_{\text{jet}}\). The hill models were made from rigid extruded polystyrene foam \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Reference**} & \multirow{2}{*}{\(D_{\text{jet}}\)} & \multirow{2}{*}{\(h\)/\(D_{\text{jet}}\)} & \multirow{2}{*}{**Terrain \({}^{**}\)**} & \multirow{2}{*}{\(\phi\)} & \multirow{2}{*}{\(H\)/\(D_{\text{jet}}\)} & \multirow{2}{*}{\(r_{\text{u}}\)/\(D_{\text{jet}}\)} & \multicolumn{2}{c}{**Maximum of \(M_{\text{class}}\)**} & \multirow{2}{*}{**Method**} \\ \cline{3-3} \cline{5-8}  & & & & & & & & & **Value** & **Location** \\ \hline [PERSON] et al. [6] & 900 m & 2.98 & E (2D) & 0.25 & 0.044 & 1.29 & / & Crest & CFD \\ [PERSON] et al. [8] & 0.31 m & 2.00 & E (2D) & 0.5 & 0.129 & 1.5, 2.0 & 0.96–1.22 \({}^{*}\) & Crest & CFD \\ [PERSON] et al. [9] & 0.104 m & 2.00 & E, TH, BH (2D) & 0.25, 0.024/0.048 & 10.1, 1.5 & 10.0–1.26 & Crest & CFD \\ [PERSON] et al. [10] & 1000 m, 3000 m & 0.67, 2.00 & BH, BE (2D) & 0.2–1.0 & 0.07–1.00 & 0.7–1.75 & 1.0–1.71 & Crest & CFD \\ [PERSON] et al. [5] & 0.75 m & 3.50 & E, TH (2D) & 0.2 & 0.048 & 1.74 & 1.19, 1.21 & Crest & CFD \\ [PERSON] et al. [12] & 0.60 m & 2.00 & E(3D) & 0.25–0.5 & 0.125/0.20 & 1.5 & 0.9–1.0 \({}^{*}\) & Crest & CFD \\ [PERSON] et al. [7] & 1225 m & 0.72 & E (3D) & 0.26 & 0.082 & 10.1, 1.4 & 10.8–1.33 \({}^{*}\) & Crest & Test \\ [PERSON] et al. [8] & 0.31 m & 2.00 & E (3D) & 0.5 & 0.129 & 15.2, 0.98–1.11 & Crest & Test \\ [PERSON] et al. [9] & 0.104 m & 2.00 & E, TH, BH (3D) & 0.2, 0.5 & 0.048 & 1.0 & 1.10–1.24 & Crest & Test \\ [PERSON] et al. [11] & 0.40 m & 3.00 & CH (3D) & 0.58 & 0.5 & 1.8, 2.8 & 0.80 \({}^{*}\),1.02 \({}^{*}\) & Hill foot & Test \\ [PERSON] et al. [12] & 0.60 m & 2.00 & E (3D) & 0.25–0.5 & 0.125–0.250 & 1.5 & 0.9–1.1 \({}^{*}\) & Crest & Test \\ \hline \hline \end{tabular}  
* \(M_{\text{class}}\) is computed via the data read directly from the relevant figures. \({}^{**}\) “E”, “BE”, “BH”, “CH”, and “CH” indicate that the terrains investigated were escarment, bell-shaped escarment, bell-shaped hill, triangular hill, and cosine-shaped hill respectively.  
\end{table} 
Table 1: Selected topographic multipliers in the literature. board.