3.3 Point wakes and
expansion fans
Previous studies have shown that supercritical-channel-flow hydraulic
theory can be used to explain particular accelerating flow regions
associated with bending topography in coastal environments (Juliano et
al., 2017; Patricola & Chang, 2017; Samelson, 1992; Söderberg &
Tjernström, 2001; Winant et al., 1988). Since the OLLJ is a channeled
flow bounded by topography and capped by the inversion at the top of the
planetary boundary layer (PBL), the same hydraulic theory arguments are
used herein to explain the preferred location of some of the OLLJ cores.
In a channel flow—represented by a two-layer shallow water model in
which the lower layer is the PBL and the upper layer is the free
troposphere—the ratio of the flow velocity to the speed of long
gravity waves on the interface (i.e., the Froude Number, Fr)
will determine the behavior of the flow when the vertical boundaries
expand or contract. When Fr is supercritical (i.e.,Fr > 1), because the speed of the flow is faster
than the speed of any gravity wave generated, the effect of a change in
the geometry of the channel cannot be communicated upstream, and all the
information travels downstream in the mean flow. Thus, if the lateral
boundary of the channel (e.g., shoreline topography, mountains) turns
away from the mainstream, a hydraulic expansion fan is induced downwind,
whereas if it turns closer to the flow, it produces a hydraulic
compression jump.
Points (terrain prominences) along bounding topography mark the
locations where the flow separates from the terrain—producing
low-speed point wakes—or if under supercritical conditions remains
attached to it, where expansion fans are generated. The characteristics
of an expansion fan downwind of a point wake are lateral spreading of
the flow, decrease in thickness of the PBL, and accelerating flow as a
result of the conservation of the Bernoulli function (Patricola &
Chang, 2017; Samelson, 1992; Söderberg & Tjernström, 2001; Winant et
al., 1988; Young & Winstead, 2005). On the other hand, a low-speed
point wake can be recognized as an extended region of low wind trailing
downwind from the point (Young & Winstead, 2005).