An illustration of the effect of expansion fans on the height of the PBL and, subsequently, on the wind speed, is depicted in Fig. 12, where the regions of maximum wind speed (closer to the surrounding topography) in the diurnal 500 m-AGL mean wind field coincide with the locations of low diurnal mean heights of the PBL along the OLLJ corridor. In the Orinoco River basin, as the large-scale wind flows through the valley, the main stream is deflected by bending terrain, producing point wakes at three specific locations: the Guiana Highlands (Cerro La Emilia), Eastern Cordillera (Cerro Umpara), and Macarena mountain range (refer to cyan areas in Fig. 5). The regions of enhanced wind speed associated with their corresponding expansion fans, produce the C2–C4 cores depicted in Fig. 4. A summary of the main features of the point wakes and their associated phenomena is indicated in Table 2.
According to supercritical-channel-flow hydraulic theory, Fr and the angular change in the flow direction due to the bending boundary (), predict the final flow wind speed and PBL height depending on:
\begin{equation} \sin\beta=\frac{c}{U}=\frac{\sqrt{g^{{}^{\prime}}h}}{U}=\frac{1}{\text{Fr}}\nonumber \\ \end{equation}\begin{equation} \frac{dU_{n}}{\text{dθ}}=\frac{-U_{n}}{\cos\beta}\nonumber \\ \end{equation}\begin{equation} \frac{dU_{n}}{\text{dh}}=-\frac{g^{\prime}}{U_{n}}\nonumber \\ \end{equation}\begin{equation} \frac{U^{2}}{2}+g^{{}^{\prime}}h=B\nonumber \\ \end{equation}
Where \(\beta\) is the angle of the expansion fan with respect to upstream flow, \(c\) is the gravity wave phase speed, \(U\) is the flow speed, \(g^{{}^{\prime}}\) is the reduced gravity, \(h\) is the PBL height,\(U_{n}\) is the component of the velocity normal to the wave that stems from the point where the boundary bends, and \(B\) is the Bernoulli function. The final depth of the PBL obeys the steady-state momentum equation [Eq. (6)], while the total velocity (if the flow is frictionless) follows Eq. (7).