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).