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 (dθ), 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).