Eulerian and Lagrangian Comparison of Primary and Secondary Wind Jets in the Tokar Gap Region. by

The Lagrangian and Eulerian structure and dynamics of a strong wind event in the Tokar Gap region are described using a WRF model hindcast for 2008. Winds in the Tokar Gap reach 25 m s and remain coherent as a jet far out over the Red Sea, whereas equally strong wind jets occurring in neighboring gaps are attenuated abruptly by a jumplike hydraulic transition that occur just offshore of the Sudan coast. The transition is made possible by the supercritical nature of the jets, which are fed by air that spills down from passes at relatively high elevation. By contrast, the spilling flow in the ravine-like Tokar Gap does not become substantially supercritical and therefore does not undergo a jump, and also carries more total horizontal momentum. The Tokar Wind Jet carries some air parcels across the Red Sea and into Saudi Arabia, whereas air parcel trajectories in the neighboring jets ascend as they cross through the jumps, then veer sharply to the southeast and do not cross the Red Sea. The mountain parameter Nh/U is estimated to lie in the rage 1.0-4.0 for the general region, a result roughly consistent with a primary gap jet having a long extension, and supercritical jets spilling down from higher elevation passes. The strong event is marked by the formation of a cyclonic cell near the upstream entrance to the Tokar Gap, a feature absent from the more moderate events that occur throughout the summer. The cell contains descending air parcels that are fed into the primary and secondary jets. An analysis of the Bernoulli function along air parcel trajectories reveals an approximate balance between the loss of potential energy and gain of internal energy and pressure, with surprisingly little contribution from kinetic energy, along the path of the descending flow. All jets attain the critical wind Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 September 2020 doi:10.20944/preprints202009.0738.v1

al. 2010 show that ocean dipoles spun up by gap winds in the Philippine Archipelago can strip nutrient-laden waters from the coast and transport the nutrients far offshore.
The driving of air from high pressure to low pressure across the Red Sea Hills is evident in a regional simulation (Fig.3) (Fig. 1). The gap then descends through its narrowest width of about 100 km before reaching the Tokar Delta, a rich alluvial plain formed by flooding of the Baraka River and extending 50 km to the Red Sea and 80 km in either direction along the coastline. Both the Arabian and African coasts are sources of silt for dust storms (Kalenderski and Stenchikov 2016). Hickey and Goudie (2007) have identified the Sudanese coast immediately around the Tokar Gap delta as one of two major sources regions for silt for Northern Hemispheric dust storms (Fig. 2). By contrast, Gaps 2 and 3 terminate closer to the coast and do not have broad deltas.
A feature that distinguishes the TWJ and neighboring gap jets from many other coastal gap winds is their strong diurnal variability. Jiang et al. (2009) found that the jets are present on a nearly daily basis from mid-June thru mid-September in a 2008 hindcast.
There is a strong daily cycle, with winds typically peaking around 04-06 UTC (7−9 AM local time) and maintaining a high directional consistency. The Red Sea also experiences a strong land/sea breeze (Pedgley 1974), but the phasing can be slightly different from that of the TWJ. Davis et al. (2015) cite the diurnal variation of the intertropical discontinuity, the leading edge of the southern monsoon air mass that feeds the TWJ, as a possible influence. The elevated moisture content of the jets constitutes another distinguishing feature. During the week-long simulation analyzed by Davis et al. (2015) the elevated humidity levels in the TWJ and neighboring jets led to significant pulses of moisture into the southern Red Sea region.
Our primary purpose is to compare and contrast the downstream reach of the TWJ and secondary jets, and to identify key dynamical processes that account for the differences.
Included in the analysis will be maps of air parcel pathways at different levels for the three jets as a way to provide comparison in terms of upstream origins and downstream destinations. This Lagrangian analysis also allows for quantification of the energy transformations that occur along pathways. To set the stage for these analyses we present information regarding the overall Eulerian structure, time dependence, and hydraulic transitions characteristic of a wind event that occurred on 11-12 July 2008 and that is the central focus of our paper. The analysis is done using the same regional model output that was analyzed by Davis et al. (2005). A key element that will emerge is that the vertical thickness of the jets in the neighboring gaps is less than that of TWJ, whereas the peak winds are at least as large, causing them to be hydraulically supercritical and therefore subject to hydraulic jump formation. These features are described in Section 3 along with other relevant properties. Differences in Eulerian properties also lead to differences in Lagrangian characteristics, in terms of the rate of stirring of air parcels, in the energy conversions that take place along parcel trajectories, and in the geographic origins and destinations of parcels, all discussed in Section 4. Section 5 briefly explores some related issues, including comparison with other strong wind events in the region and conditions for lofting dust into the atmosphere.

Model Overview
Our results are based on 14-month run of the Weather Research and Forecasting (WRF) model, version 3.0.1.1, with a 10-km horizontal resolution Red Sea subdomain nested within a 30-km resolution domain covering most of the Middle East, for which the 1° NCEP Global Final Analysis was used as initial and boundary conditions. The model employs 35 vertical levels, uses terrain-following eta coordinates, has daily reinitializations, and produces output at 1 hour intervals. Further details can be found in Skamarock et al. (2008) and Lo et al. (2008). The model run was originally produced by A view of the temporal evolution of the wind field over the 24-hour period of 12 July 2008 is provided by Hovmöller plots showing the horizontal velocity as a function of elevation and time (Fig. 4). The three plots are made at successive locations proceeding downstream: near the upstream entrance of the Tokar Gap (Fig. 4a), in the narrowest part of the Tokar Gap (4b), and out over the Red Sea (4c). All locations are indicated by stars in Fig. 1 and each was selected to lie in the high velocity core of the flow. The velocity contours indicate the magnitude of horizontal velocity directed along the axis (or 'thalweg') BCDE that begins in the north entrance channel of the Gap.
The evolution below 2000 m shows a strong diurnal character, with high velocities during the night and early morning and nearly stagnant conditions during the late afternoon. The down-canyon winds extend up 15002000 m above ground level and are generally weakest near the channel entrance, strongest at the narrowest section (Fig. 4b), and still strong at the Red Sea section (Fig. 4c). The downslope winds relax at around 12 UTC but remain positive in the gap itself. At the Red Sea location the surface winds are eventually overcome by the opposing sea breeze and reverse direction at about 14 UTC. It is notable that the velocities in Fig. 4c, which are predicted at a location nearly midway across the Red Sea, are nearly as large as those in the narrows (Fig. 4b). A striking feature of all plots is the reverse flow that develops aloft, roughly between 1500 m and 3500 m, and is strongest when the jet is active. Gohm et al. (2008, Figs. 5c and 5f) notice a similar wind reversal during the strong phase of a bora.

b. longitudinal structure
Insights into the along-axis thermal and velocity structure of the Tokar Gap flow can be gained from the Fig. 5a,b plots of potential temperature and along-axis velocity along the piecewise constant paths ADE and BCDE. The plots show data at 05 UTC, corresponding to peak winds in the downstream reaches of the gap. The overall longitudinal picture is one of spilling and acceleration through the compound gap, with the highest velocities of approximately 20 m/s occurring downstream of the junction (D), where the gap narrows and then opens up over the delta. There is also some evidence of a decrease in static stability above the outflow: for example, the vertical displacement between the 315 K and 318 K potential temperature surfaces increases from 1000 m to 2000 m in the downstream direction. Another notable feature in the thermal structure is a slight increase in ground level potential temperature where the winds descend over land, followed by a decrease where the winds blow out over the cooler Red Sea.
Comparison with the winds in Gap 2, plotted at 05 UTC in Fig. 6, reveals larger peak winds (25m/s) along the downslope, and in the region extending from the pass near 80 km to the Red Sea shoreline near 165 km. However, the strong winds terminate about 10 km offshore. Whether one takes the 312 K or 315 K potential temperature contour as an upper boundary for the descending flow, the vertical thickness (700-1000 m at the 125 km mark) is somewhat smaller than the thickness of the downslope wind layer in the Tokar Gap. The 312 K surface rises abruptly downstream of the core of strongest downslope winds, whereas the same surface continues to descend (Fig. 5) where the Tokar Gap winds run out over the Red Sea.

c. Three Dimensional Structure
For gap wind applications, the branching, ravine-like topography of the Tokar Gap is less typical than the topographies of Gaps 2 and 3. For this reason, we examine the threedimensional structure of the Tokar Gap winds further using a series of cross-sections  (Fig. 6b), which is located at the junction of the approach channels, the separate jets merge to form a single core. The section extends to the north and south (left and right) across the bounding ridges. A high-speed core of flow can be seen along the sloping terrain to the south, across the ridge located near 200 km, revealing the presence of strong winds in this neighboring gap. Section cc (Fig. 7c), which cuts across the narrowest part of the gap, shows even higher velocities concentrated in a single core that fills the primary gap but continues into the neighboring gap to the south. Section dd cuts across the delta, ee lies near the shoreline, and ff and gg lie mostly offshore (Figs. 7dg).
The narrow (150 km wide), high velocity (25 m s -1 ) core continues through ff, diminishing somewhat by gg. At section ee there are shallower, secondary regions of high velocity to the left and right (north and south) of the primary core. In the region lying between 0 and 100 km in Fig. 7e the high winds are due to air spilling down the slope of the ridge that lies immediately to the north of the Tokar Gap. The weaker core to the south (between 300 and 350 km) consists of flow from Gap 2, which lies to the south of the Tokar Gap.
The surface expression of all three jets (Tokar, Gap 2 and Gap 3) during maximum intensity (05 UTC) are apparent in maps of 10 m winds (Fig. 8a) and surface potential temperature (Fig. 8b). Secondary jets and the neighboring downslope winds experience an increase of surface potential temperature as they spill down over land, then undergo a decrease in potential temperature as they leave the coast and move offshore. By contrast, the TWJ experiences only very little offshore cooling. The disproportionally large reach of the TWJ compared to secondary jets during this event is apparent in Fig. 8a but it is not explained by differences in the surface winds, since the maximum speeds in the (narrower) secondary jets are as large as those in the TWJ.

d. Mountain Parameter
There have been a number of modeling studies of gap winds in idealized settings, including Overland (1984), Saito (1993), Zangl (2002, and Gabersek andDurran (2004 and2006). Gabersek and Durran (2004), consider a long ridge of height h and an upstream wind with uniform velocity U and buoyancy frequency N, approaching from the direction perpendicular to the ridge. A notch is cut through the ridge and thus an approaching air parcel can go around or over the ridge, or through the gap. The lowest elevation in the gap is the same as that of the surrounding flat terrain, so there is no sill.
One of the key parameters for flow over ridges with or without gaps is Nh/U. For values less than about 0.5, the flow tends to be inertial and the lower level air parcels ride directly up and over the topography in the manner of a hydraulically supercritical flow. over much of this range, but decrease to zero near ground ( Fig. 9). We average these values from ground level to 750hPa in order to estimate the scales U and N. The resulting estimate of Nh/U, computed over the duration of the strong wind event (roughly 10 UTC on 11 July to 15 UTC on 12 July) varies from between 1.0 and 4.0. For the model considered by Gabersek and Durran (2004), such values would suggest the existence of a strong gap jet with a long downstream extension as well as spilling flows across higher elevation ridges. However, the ridge in the Gabersek and Durran (2004) model lies at constant elevation, whereas the Red Sea Hills ridges are irregular and punctuated by peaks and cols, so there is little guidance as to where exactly spilling and lee wave breaking would occur. Also, there is no evidence of the weakly recirculating or stagnant 'wake' eddies that are seen in Gabersek and Durran (2004), possibly because the multiple jets in our case are too closely spaced to allow such features between them. The presence of the prevailing northwesterly winds along the axis of the Red Sea may also discourage closed circulation patterns.

e. Downstream turning
Hickey and Goudie (2007) refer to the anticyclonic bending of dust plumes emanating from the Tokar Gap. As a result, the dust is transported southeast, along the axis of the Red Sea, sometimes covering the entire southern portion. This picture is consistent with the behavior of the 10 m winds (Fig. 8a,b), which show the TWJ extending across the Red Sea towards the Saudi coast and then veering towards the southeast. The veering is even more pronounced for the secondary jets, although they do not extend as far offshore.
The inertial radius U/f based on a typical velocity U=15 m s -1 at 20°N is about 300 km, which is only moderately larger than the 200 km radius of curvature required for a southwesterly wind to veer anticyclonically 90° and flow towards the southeast before reaching the Saudi coast. So the idea, mentioned by Hickey and Goudie (2007) and others, that the turning is simply due to the Coriolis acceleration acting on the jets, has some support. However, bending may also be induced by collision of the TWJ with the prevailing, geostrophic northwesterly winds that flow along the axis of the Red Sea. We also note that the Rossby number U/fL for a L=150 km wide jet with the above velocity scale is about 2, so the inertial character of the jets is significant.

f. abrupt transitions
In order to interpret some of the behavior cited above, it is helpful to make an analogy with the hydraulics of a single, homogeneous layer flowing beneath an inactive upper layer. The shallow-water analogy has been used in connection with other spilling mountain winds (e.g. Gohm et al. 2008). Baines (1995) describes a number of conditions that would allow shallow-water/hydraulic interpretation to be valid. These include the presence of wave overturning aloft, which can produce a reflecting upper boundary, and the presence of a reflecting critical level. The features are certainly not ubiquitous in our model runs, but there is evidence of their presence at certain times and locations. For example, the wind reversals observed above the jet indicates that the along-axis flow changes sign at a level slightly above that of the spilling layer/jet . This level would also correspond to a critical level for stationary disturbances. In addition, the TWJ and secondary jets, though stratified, exhibit strong vertical coherence, as would a single, homogeneous layer.
As a bounding upper surface or interface of this hypothetical layer, we pick an isentropic surface (here 312 K) that roughly marks the top of the range of high, down-slope velocities. Inspection of Fig. 5 suggests that the 312 K surface is a reasonable choice, particularly over the high-velocity portions of the downstream flow. The resulting lower layer thickness (Fig. 10a) suggests a pattern of spilling and thinning as air travels through the Tokar and secondary gaps and out over the Red Sea. A significant difference is that the secondary flows (including the downslope flows in Gaps 2 and 3, and along the neighboring terrain), which contain air spilling from higher elevations, become quite shallow (dark blue) over the sloping terrain, but experience a rebound in layer thickness (light blue) as they move out over water. In contrast, the Tokar Gap outflow thins continuously as it spills out over the Red Sea, though it never becomes as shallow as the secondary jets. Note that the spilling air is not confined to the main and secondary jets, but occurs broadly over the downslopes, as suggested in Fig. 8a,b.
The local hydraulic state of the active layer of a 1.5-layer system is measured by the local Froude number where g is the reduced gravity g(q 2 -q 1 ) / q 1 based on the average potential temperatures q 1 and q 2 below the interface and in the region of homogeneous potential temperature above the interface. Also,  (Fig. 6), the overlying 315K contour descends down the lee slope but suddenly rises at the base of the slope (near 150 km). For a single layer flow, the relative change in layer thickness across a jump is given by where Fo is the value of

g. downstream extent
The presence of hydraulic transitions in the secondary jets, and the absence of such in the Tokar Wind Jet, suggests that the latter might have much longer downstream extent than the former, as observed. For one thing, the TWJ would not suffer the energy dissipation that occurs in a hydraulic jump, and that is proportional to the cube of the upstream/downstream difference in layer thickness. Another quantity that favors the TWJ in terms of downstream reach is the offshore momentum flux. For a 1.5-layer system, the momentum flux (or total 'flow force') per unit breadth is given by where u is the offshore component of the vertically averaged velocity over the layer.
With estimated values of the layer thickness d and velocity along the centerlines of the TWJ and Gap 2 jet, we find M in the range (6−10)10 5 m 2 s -1 for the former, and (2−3)10 5 m 2 s -1 for the later. So despite the fact that the offshore velocities in the secondary jets can be larger than those in the TWJ, the latter carries two to three times larger total momentum flux than the secondary jets.

Lagrangian Structure
To obtain a more comprehensive view of the Lagrangian structure of the winds in and around the Tokar Gap, we initiate groups of trajectories in the high-speed outflow regions and integrate backward and forward in time. For example, Fig. 11 shows backward-time and d indicate that this cell is slowly moving upstream, seen more clearly in a video (see WRFVEL_0711 in Supplemental Information). As for the downstream (black) segments, it is apparent that the majority of air parcels cross the Red Sea and come close to the Saudi coast, some penetrating inshore and up and over the Saudi coastal mountain range (Frame a). This penetration is notable given the excess moisture content of such parcels, as described by Davis et al. (2015).
A better view of the vertical Lagrangian structure of the TWJ appears in Fig. 12, where the viewer now faces southeast. Each frame shows four groups of color coded trajectories initiated at levels of 100m, 500m, 1000m and 1500m, and the release times are as in Fig.   11. It can be seen that the funneling winds are fed by a horizontally broad collection of trajectories that cover the upstream plane. Trajectories released at higher levels, colored yellow, tend to originate from the north portion of the upstream plateau (the portion closer to the viewer). Interestingly, trajectories released at lower elevations (magenta) predominantly originate from the southern portion of the plateau and make up the bulk of the air parcels that descend from the isolated cell mentioned in the previous paragraph. A small number of the trajectories originate at higher elevation above the Red Sea and move westwards before descending and reversing direction as they flow down into the gap. The forward (green and blue) trajectories all cross the Red Sea, and most of the ones released at lower elevation (predominantly blue) cross the Saudi coast and penetrate inland.
The wind jets that form in Gap 2 and Gap 3, exhibit some Lagrangian characteristics that are distinct from those of the TWJ. The winds in Gap 2 spill over a relatively high and narrow sill at 1360 m elevation (Fig. 6). Trajectories initiated within the outflow region at 100 m (not shown) show no connection to the upstream cyclonic cell, while those initiated at (or above) 500 m (Fig. 13a-d) exhibit a strong connection. In addition, none of the trajectories cross the Red Sea but instead turn southwards and flow parallel to the coast, some eventually crossing back into Africa (frames a-c). A magnified and rotated view (Fig. 13e) of Frame c more clearly shows that after air parcels leave the coast, they experience a rapid ascent as they pass through the suspected hydraulic jump, then turn rapidly towards the southeast. Trajectories in Gap 3 (not shown), which is broader than Gap 2 and has a higher-elevation (1430 m) sill, exhibits similar features.
The upstream region of descending air parcels bears resemblance to a feature identified where e is the specific internal energy. For a dry gas, the latter is equal to the product of the specific heat cv [assumed to have constant value 171 J/(kg K)] and the in situ temperature T. In a steady, adiabatic and isentropic flow, B is conserved along fluid trajectories. While these conditions do not generally hold in our applications, the winds during the strong phase of the 12 July 2008 event are approximately steady and, as we will show, the value of B undergoes only slight variation for an air parcel descending through the Tokar Gap or neighboring gaps during this phase of the event. In addition, the variation of B during this phase can be shown to be primarily due to diabatic heating.
We have chosen 5 trajectories (Fig. 15f)  can be attributed to diabatic heating, as evidenced by an increase in potential temperature (Fig. 15g). In fact, changes in B over the entire period track potential temperate changes closely, suggesting that it is diabatic heating/cooling, and not timedependence, that is primarily responsible for changes in B.
The plot of potential energy gz (Fig. 15d) shows that the Tokar Gap trajectories (in pink) experience a gradual and nearly monotonic descent as they pass through the gap and out over water during the first 6 hours of the stong wind event, whereas the Gap-2 trajectories (in red) ascend and then descend rapidly as they move up and over a ridge at much higher elevation. The Gap-2 trajectories also experience an abrupt rebound (at about t=8) shortly after they have moved out over water (see black extensions of red curves). This rebound coincides with the suspected hydraulic jump. Panel e shows that the kinetic energy of the air parcels in the Tokar Gap outflow remains high for 3 or 4 hours after the parcels have left the coast, whereas the Gap-2 trajectories experience a sudden decrease in kinetic energy at the positions of the jumps. Although the changes in kinetic and potential energy meet expectations for a hydraulic jump, the value of B itself does not experience any notable change. As shown in Frame g, the jump occurs during the period when the air parcels are experiencing the strongest periods of diabatic warming, and this may compensate for the dissipation of kinetic energy within the jump (a process that is poorly resolved by the model). We also note that Ogden and Helfrich (2016) have documented examples of stratified jumps that exhibit little or no energy dissipation. A model with higher horizontal and vertical resolution may ultimately be needed to clarify this picture.
Overall, the most significant constituents of B are the pressure term p/ , the potential energy gz and the internal energy cvT (Fig. 15, panels b-d). As the air parcels descend over the topography, cvT and p/ both increase at the expense of gz. Interestingly, although the kinetic energy increases it does not contribute significantly to the balance. This is in sharp contrast to deep overflows in the ocean (Pratt and Whitehead 2008), which are nearly incompressible and experience only minor changes in internal energy, and where the kinetic energy increase plays a more substantial role in the overall budget.
Although the flow in Gaps 2 and 3 likely experience hydraulic jumps, the overall horizontal spread of air parcels is weaker than for the TWJ. To quantify particle spreading, we computed the single-particle dispersion tensor where , = 1,2,3 correspond to the Cartesian coordinates x,y,z, overbars denote the ensemble mean, and = ( ) − (0) is the displacement of an n-th parcel from its initial position. The dispersion matrix can then be put in a diagonal form, with the 3 eigenvalues, , , , on the diagonal. A comparison (Fig. 16) based on these three coefficients between trajectories released at the exits of the Tokar Gap (left panels) and Gap 2 (right panels) yields some striking differences. At each location, a group of 25 air parcels is released every hour from 00 UTC until 09 UTC at z=500 m elevation at the exit and where velocity exceeds 15 m/s. The horizontal components of dispersion, and for trajectories released in Gap 2 grow at a slower rate than those for an equivalent group of parcels released at the exit of the Tokar Gap. The difference is not surprising given the large spread of trajectories originating in the Tokar Gap (top panels of Fig. 16). The vertical dispersion , on the other hand, is slightly larger for the Gap-2 parcels during the initial 6 hours since particle release and until TWJ parcels reach the opposite coast and start rising up over the mountain ranges, at which time the vertical dispersion for the TWJ parcels becomes larger. The same is true for parcels released at 100 m (not shown).
In both cases the dispersion is dominated by the horizontal spreading of the trajectories, which is more pronounced in the TWJ.

Discussion
The strong wind event discussed in this paper exhibits structural similarities with several other strong wind events during July and August (not shown) in the WRF model. Peak Even though the winds may be strong enough to lift dust, unstable stratification is required for the dust to be lofted up to 1000 m. Fig. 17 indicates that the TWJ is capped by stable stratification in the 307−312 K range, roughly from 500 to 1000 m, during its strongest phases (00−10 and 21−24 UTC). However, the region below this transition layer is relatively homogeneous in potential temperature, and statically unstable near ground level, so it is possible that dust could be lofted up to fill a column of 500 m above ground. During the weak phase of the Jet, potential temperature is well mixed up to about 1500 m, but the winds are too weak to lift the dust off the ground. Previously suspended dust within 500 m of ground could be lofted higher during afternoon weak phase by thermal convection. Cuesta et al. (2009) present a similar example over the Sahara.

Conclusions
The main thrust of this work has been to describe the anatomy and dynamics of a simulated strong wind event in the Tokar Gap and neighboring gaps, to offer an explanation for the relatively limited downstream reach of the wind jets in the neighboring gaps, and to describe a Lagrangian overview of the circulation associated with the jets. The analysis suggests that the Tokar Wind Jet (TWJ), which spills down through a ravine-like topography, never achieves supercritical speeds and therefore does not undergo a dissipative hydraulic jump as it departs the gap. By contrast, the jets in the neighboring gaps form when air spills down from relatively high passes, resulting in a layer of air that achieves comparable velocities to those of the TWJ but is shallower and therefore more supercritical. These jets do, in fact, experience features resembling hydraulic jumps after they depart the coastline, and become much thicker and weaker downstream of the jump. The model resolution is inadequate to resolve the detailed features of the presumed jumps, but the layer thickness increases, and the horizontal velocity decreases, as air parcels cross it. Downstream of the jump, air parcels turn quickly to the southeast and flow in that general direction, never crossing the Red Sea.
The downstream extension of the TWJ easily crosses the Red Sea and reaches the Saudi coast, with some air parcels penetrating across the coastal mountain range and further inland. The horizontal spread of particles, as quantified by the single-particle dispersion tensor, is larger for the Tokar Wind Jet than that for the neighboring gaps. The vertical spread is, on the other hand, slightly larger for the secondary gaps during the first 6 or so hours, plausibly due to the effects of the suspected hydraulic jumps.
The energetics of all the jets, as quantified by transitions in the various terms that constitute the Bernoulli function, suggest the primary exchange is between p/, potential energy, and internal energy, with kinetic energy changes playing a surprisingly secondary role. Diabatic heating along the coast increases the Bernoulli function and makes it difficult to isolate any dissipation of the energy associated with the jumps.
The above scenario has many elements in common with idealized models of ridges with single gaps when the mountain parameter Nh/U is comparable. This includes a gap jet with a long downstream extension, and supercritical flow that spills down from the high-          backward to 12UTC on 7/11/08 and forward in time to 24 UTC on 7/12/08. Figure 12. Similar to Fig. 11, but now the viewer faces SE and the trajectories are initiated at the four levels z=100, 500, 1000 and 1500m and where the wind speed exceeds 15m/s. Forward/backward trajectories are color-coded blue-to-green/magenta-to-yellow according to their release height (i.e., blue/magenta at 100m and green/yellow at 1500m).       Figure 11, but now the viewer faces SE and the trajectories are initiated at the four levels z=100, 500, 1000 and 1500 m and where the wind speed exceeds 15 m/s. Forward/backward trajectories are color-coded blue-togreen/magenta-to-yellow according to their increasing release height (i.e., blue/magenta at 100 m and green/yellow at 1500 m).