AUGUST 2005 ARCHER AND JACOBSON 2387

The Santa Cruz Eddy. Part II: Mechanisms of Formation

CRISTINA L. ARCHER AND MARK Z. JACOBSON Stanford University, Stanford, California

(Manuscript received 25 March 2004, in final form 1 February 2005)

ABSTRACT

The formation mechanism of the Santa Cruz eddy (SCE) is investigated using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5). Simu- lations of 25–26 August 2000 showed that two eddy instances formed on that night, a finding supported by observations. The two eddies had similar behavior: they both formed in the sheltered Santa Cruz, Califor- nia, area and then moved southeastward, to finally dissipate after 7–11 h. However, the first eddy had greater vorticity, wind speed, horizontal and vertical extents, and lifetime than the second eddy. Numerical simulations showed that the SCEs are formed by the interaction of the main northwesterly flow with the topographic barrier represented by the Santa Cruz Mountains to the north of Monterey Bay. Additional numerical experiments were undertaken with no diurnal heating cycle, no (molecular or eddy) viscosity, and no horizontal thermal gradients at ground level. In all cases, vertical vorticity was still created by the tilting of horizontal vorticity generated by the solenoidal term in the vorticity equation. This baroclinic process appeared to be the fundamental formation mechanism for both SCEs, but more favorable conditions in the late afternoon (including a south-to-north pressure gradient, flow turning due to the sea breeze, and an expansion fan) coincided to intensify the first eddy.

1. Introduction 2. SCE simulations In Archer and Jacobson (2005), a cyclonic vortex that The SCE event of 25–26 August 2000, described in forms in the summer over Monterey Bay (California), Archer and Jacobson (2005), was chosen as the test the Santa Cruz eddy (SCE), was investigated from the case for the simulations. The model used in this study is observational point of view. A limited mesonet of 10 the fifth-generation Pennsylvania State University– surface stations was able to provide information about National Center for Atmospheric Research Mesoscale several aspects of the eddy (such as timing and corre- Model (MM5), described in Dudhia (1993). Initial and lation with pressure patterns) but was inadequate for boundary conditions were provided by the Eta model, finding the mechanism(s) of SCE formation. In this pa- with ϳ40 km horizontal resolution; one-way nesting per, each possible formation mechanism claimed for was imposed between the parent domain (“domain 1,” other known vortices is isolated and investigated via a with horizontal resolution of 5 km, 150 ϫ 120 grid numerical approach. First, results obtained for a test points, 29 vertical levels, and 15-s time step), which case will be presented in detail, with special emphasis covers the entire California area, and a nested grid on vorticity patterns. Then, a series of numerical tests (“domain 2,” with horizontal resolution of 1 km, 150 ϫ will be introduced to evaluate the relative importance 120 grid points, 29 vertical levels, and 3-s time step), of individual factors, such as topography or viscosity, on centered on the Monterey Bay area (Fig. 1). The fol- eddy formation. lowing parameterizations were selected: Eta Mellor– Yamada scheme for turbulence (Mellor and Yamada 1982; Janjic´ 1990, 1994); no cumulus parameterization; simple-ice explicit scheme for resolved precipitation Corresponding author address: Cristina L. Archer, Department of Civil and Environmental Engineering, Stanford University, (Hsie et al. 1984); cloud-radiation scheme (Stephens Stanford, CA 94305. 1978); Ohio State University (OSU)/Eta land surface E-mail: [email protected] model (Pan and Mahrt 1987; Chen et al. 1996, 1997); no

© 2005 American Meteorological Society

MWR2979 2388 MONTHLY WEATHER REVIEW VOLUME 133

FIG. 1. Topography details of the Monterey Bay area (m, shaded) and station locations. The area shown coincides with the high-resolution domain (domain 2). four-dimensional data assimilation. All runs started at ness length varied from 0.01 cm over water to 50 cm 1200 UTC on 24 August 2000, a day before the day of over evergreen needle forest), friction against the sides interest, to allow the model to adjust to the initial con- of the Santa Cruz Mountains (SCM), and flow conver- ditions. The runs were carried out over 48–60 h. gence due to the blocking effect of mountains. A de- In the next sections, the evolution of two SCE occur- tailed analysis of the vorticity formation will be intro- rences (indicated as first or evening eddy, and second duced in section 3d. or nocturnal eddy, respectively) simulated by MM5 will The sea breeze was also responsible for the southerly be presented at four times (unless otherwise stated): flow to the east of Santa Cruz. Vorticity was created during the afternoon sea breeze (prior to the eddy for- there as a result of two mechanisms: the turning of the mation), during the mature stage of the first SCE, dur- flow from northwesterly at the entrance of the bay to ing its dissipating phase, and during the mature stage of southerly a few kilometers to the east, and advection of the second SCE. vorticity created along the coast to the northwest of Santa Cruz, as described above. Observed winds agree a. Winds and vorticity well with MM5 wind patterns in Fig. 2a, with the only In the rest of this study, the Pacific daylight time exception being Watsonville (WVI), where the simu- (PDT) will be used, corresponding to Ϫ7 h from the lated flow was too westerly (see Fig. 1 for station loca- coordinated universal time (UTC) in the summer. Dur- tions). ing the afternoon (1300 PDT), simulated 10-m wind Before and during the early stages of eddy formation, streamlines (Fig. 2a) suggest that the flow over an area of high wind speed (greater than 6 m sϪ1) Monterey Bay was westerly (due to the sea breeze), formed offshore and to the west of Santa Cruz (Figs. whereas off the coast the main synoptic flow was north- 3a,b). According to Burk et al. (1999) and Burk and westerly, parallel to the coast. Positive vorticity was Haack (2000), an area of supercritical flow can form formed along the coast, both to the north and to the either at or past a convex bend in topography, such as south of the bay, due to horizontal shear caused by fast the Monterey Bay. Supercritical conditions in atmo- winds over water and slower winds over land (as rough- spheric flow occur when the wind speed exceeds the AUGUST 2005 ARCHER AND JACOBSON 2389

Ϫ FIG. 2. Simulated streamlines of 10-m winds, observed wind barbs (1 barb ϭ 1ktϭ 0.94 m s 1) at station locations, and simulated vertical vorticity (10Ϫ3 sϪ1, gray shaded) on domain 2 during 25–26 Aug 2000 at key times of the SCE evolution: (a) sea breeze (1300 PDT); (b) mature stage of the first SCE occurrence (2100 PDT); (c) dissipating stage (0300 PDT); and (d) mature stage of the second SCE occurrence (0800 PDT). Terrain elevation is contoured with dotted lines every 200 m. phase speed of internal gravity waves. If the area of valid only under the shallow-water approximation and supercritical flow forms past the convex bend and it is not when either stability or wind speed vary within a accompanied by divergence and by lowering of the layer, as in the SCE case. boundary layer, then it is called an “expansion fan.” If With these limitations in mind, approximate Fr val- the flow does not reach supercritical conditions, the ues were calculated from the MM5 simulated flow fol- high (but not supercritical) speed area forms upstream lowing Haack et al. (2001). The value used for ␪ in Eq. from the bend (Burk et al. 1999). If U is the upstream (1) is the average potential temperature within the wind speed, gЈ the reduced gravity g ϫ (⌬␪/␪)(⌬␪ is the layer below the marine inversion, whose top is located difference in potential temperature ␪ across the inver- at the height h where the potential temperature in- sion), and h the height of the marine boundary layer crease with height becomes less steep; U is the average (MBL), the Froude number wind speed in the layer, and ⌬␪ is the difference be- tween potential temperature at the inversion top and U U the average potential temperature below the inversion. Fr ϭ ϭ ͑1͒ ͌gЈh ͱ ⌬␪ For the flow upstream of Monterey Bay, Fr was ap- g ␪ h proximately 0.66 (subcritical), whereas in the center of the accelerated flow Fr was ϳ1.12 (supercritical) during can be used to determine the flow criticality. Froude the day. These values were calculated at the subcritical number values greater (smaller) than one indicate su- point marked in Fig. 3a and at the supercritical point percritical (subcritical) flow. However, this is strictly marked in Fig. 3c. The daytime average values were 2390 MONTHLY WEATHER REVIEW VOLUME 133

Ϫ Ϫ FIG. 3. Simulated wind speed (m s 1, solid line every 2 m s 1) on domain 2 during 25–26 Aug 2000 at key times of the SCE evolution: (a) sea breeze (1300 PDT); (b) mature stage of the first SCE occurrence (2100 PDT); (c) dissipating stage (0300 PDT); and (d) mature stage of the second SCE occurrence (0800 PDT). Terrain elevation is contoured with dotted lines every 200 m. The location of the north–south cross section discussed later is shown in (a). Cross marks indicate a subcritical point in (a) and a supercritical one in (c).

(with the subcritical value in parentheses) ␪ ϭ 286 (285) The mature stage of the simulated eddy was reached at ⌲; ⌬␪ ϭ 13 (14) K; U ϭ 7.7 (5.5) m sϪ1; h ϭ 99 (170) m; about 2100 PDT (Fig. 2b), where closed streamlines Fr ϭ 1.12 (0.62). The 60-h averages were ␪ ϭ 286 (285) and high vorticity define the presence of the SCE. ⌲; ⌬␪ ϭ 12 (13) K; U ϭ 6.7 (5.6) m sϪ1; h ϭ 147 (207) Model results are in good agreement with observations m; Fr ϭ 0.96 (0.66). Given the location of the high wind at all stations. speed area (i.e., past and not upstream of the bay), the The SCE detached from the SCM and moved south- approximate Fr greater than one, and the lowering of eastward in the next hours. In the rest of the paper, the the MBL (not shown), the simulated high wind speed fact that the eddy detaches from the mountains will be area can be considered an expansion fan. Expansion fans indicated as “vortex shedding.” Technically, vortex have been associated with scalloped areas of clearing shedding refers to the detachment of couples of coun- from the fog in the lee of concave bendings along the terrotating vortices in the (unstable) wake of an ob- California coast, including at the Monterey Bay entrance, stacle. Even though no anticyclonic eddy forms on the by Haack et al. (2001) and Koracˇin and Dorman (2001). lee of the SCM, this notation will be used for the SCE Observations showed that the first SCE formed at because it is nonstationary, it detaches from the SCM, about 1700 PDT, whereas model results showed the and it has multiple occurrences. Vortex shedding will first appearance of a closed circulation only 2 h later, at be discussed further in section 4. Vorticity decreased in 1900 PDT (not shown). Like the observed one, it was the eddy center as soon as it detached from the land initially limited to the northeastern portion of the bay. (not shown). By 0600 PDT, about 2 h after reaching AUGUST 2005 ARCHER AND JACOBSON 2391 land, the first SCE had completely dissipated. Vorticity Note that the maximum of the simulated pressure gra- was still forming along the northern coastline, where it dient was reached about 2 h after that of the observed will continue to form throughout the entire simulation. one, just as the simulated eddy started 2 h after the The expansion fan had disappeared at this hour, as only observed one. However, the simulated second eddy two small areas of wind speed greater than 6 m sϪ1 were formed without any pressure gradient. The absence of left offshore at 0300 PDT (Fig. 3c). the second maximum of the simulated pressure gradi- At 0300 PDT, observations showed the presence of a ent confirms that the south-to-north pressure gradient second SCE offshore from Santa Cruz (not shown), but was not necessary for SCE formation. Note that obser- the simulated eddy was again delayed by about2hand vational findings in Archer and Jacobson (2005) reached its mature stage at about 0800 PDT (Fig. 2d). showed that such a pressure gradient was not sufficient This second SCE occurrence was characterized by gen- either. erally slower wind speeds and lower vorticity than the earlier one. It detached at 0900 and dissipated by 1000 c. Vertical structure PDT, when its core vorticity fell below 0.5 ϫ 10Ϫ3 sϪ1. The MM5 performance was verified by comparing its results for Fort Ord (Fig. 6) with the observed profiler b. Temperature and pressure data shown in Fig. 5 of Archer and Jacobson (2005). During the day, the Santa Cruz area was character- Simulated (virtual) temperature showed the typical ized by not only the highest temperatures, but also the profile of a marine location, with cooler temperatures lowest relative humidities in the entire Monterey Bay close to the ground and warmer air above. The simu- (Archer 2004). Vice versa, Monterey was cloudy and lated (and observed) inversion was not elevated but had a temperature of ϳ14°C, ϳ6°C cooler than Santa ground based; its top (where maximum temperatures Cruz. Moisture from the south bay was advected north- were found) was located at about 500 m, as observed. ward during the eddy, in a “wrapping” fashion. The first However, the inversion strength was underestimated, eddy had a warm core, as air with warmer temperature as the observed maximum temperature was ϳ27°C, was trapped in the center of the circulation, whereas the whereas the simulated maximum was only ϳ23°C. Near second eddy had a cooler core, as it was formed with the surface, low temperatures were observed in the af- cooler air advected into the bay from the northern ternoon and in the early morning hours, whereas MM5 coast. Aside from that, the temperature and moisture results showed only a nighttime minimum. The deep- fields over Monterey Bay became uniform at night; ening of the MBL on 26 August was well simulated by hence the SCE had a “homogenizing” effect on the bay. MM5. Winds below 300 m were generally well repro- The simulated sea level pressure pattern was consis- duced by the model, although they showed a stronger tent with the presence of lower pressure in the Santa westerly component than observed. Above the inver- Cruz area and relatively high pressure in the southern sion, observed winds were light and chaotic up to 1000 bay, as suggested by the observational analysis in Arch- m, but simulated winds showed a more westerly com- er and Jacobson (2005). Simulated sea level pressure is ponent. No clear indication of an SCE presence could shown in Fig. 4. Note the ridge of higher pressure along be detected from the simulated or observed winds at the eastern part of the bay prior to the eddy formation. Fort Ord. During the mature stage of the first SCE, a local “low” In summary, simulated temperatures were too warm formed near the center of the eddy, as indicated by the near the surface and too cold in the inversion, and simu- almost closed contour of the 1015-hPa isobar offshore lated winds had a stronger westerly component than from Santa Cruz (Fig. 4b). At this time, a light south- observed winds. However, MM5 successfully repro- to-north pressure gradient was still present over the duced general trends of the MBL evolution, inversion bay. However, during the dissipating stage (Fig. 4c), the location, and wind patterns in the lowest levels, which south-to-north pressure gradient was destroyed too, are the most important parameters for the SCE. leaving uniform pressure of about 1015 hPa over the To describe the vertical structure of the two SCE whole Monterey Bay. The second SCE formed, there- occurrences of 25 August 2000, a cross section was se- fore, without any south-to-north pressure gradient. lected, indicated in Fig. 3a. It was oriented north–south Trends of simulated sea level pressure at two key and was intended to show the influence of the Santa locations are shown in Fig. 5, together with the south- Cruz Mountains on the eddy. In the afternoon (Fig. 7a), to-north pressure gradient between MRY (Monterey) light and subsiding winds occurred from 300 to 1000 m, and LML (Santa Cruz). The strength of the pressure except at the mountain tops, where higher tempera- gradient of the first eddy was well reproduced by MM5. tures caused upslope flow. The marine layer below 300 m 2392 MONTHLY WEATHER REVIEW VOLUME 133

FIG. 4. Simulated sea level pressure (mb, solid line every 0.25 mb) on domain 2 during 25–26 Aug 2000 at key times of the SCE evolution: (a) sea breeze (1300 PDT); (b) mature stage of the first SCE occurrence (2100 PDT); (c) dissipating stage (0300 PDT); and (d) mature stage of the second SCE occurrence (0800 PDT). Terrain elevation is contoured with dotted lines every 200 m. was stable, as potential temperature was increasing north, and it is thus generally warmer and drier than the with height everywhere over water. Relative humidity rest of the bay. Note also the upslope flow along the (RH; instead of potential temperature) was thus used mountainside in Fig. 7a. The rising of warm air from the to identify the MBL as the layer with values of RH lower levels therefore caused the MBL to break down greater than 50% (not shown). It was found that the in the Santa Cruz area. The cross section shows that the 296-K potential temperature contour could be used to high vertical vorticity shown previously in Fig. 2a orig- determine approximately the top of the marine layer inated at the surface, therefore suggesting that surface (or the bottom of the inversion) during the day. At effects may be important for the eddy formation. night, the 292-K contour was a better choice. At the eddy onset, approximately 1900 PDT, the tilt- Figure 7 shows that the marine layer was tilted up- ing of the marine layer was accentuated (Fig. 7b) and so ward over Monterey, due to the combination of two was the thermal contrast between Santa Cruz and factors. First, the north-northwesterly flow entering Monterey. Vorticity extended up to about 500 m and its Monterey Bay was blocked by the Monterey peninsula maximum was still at the surface. Vertical motion, as- and forced to decelerate. Vertical motion was inhibited sociated with wind convergence into the eddy center, by the stable conditions and therefore cold, dense air extended up to 800 m, in opposition to the general converged over Monterey, causing the marine layer to subsiding motion noted earlier. Cooler air advected rise. Second, the Santa Cruz area is protected from the from the south had reached Santa Cruz, therefore caus- cold north-northwesterly flow by the mountains to its ing temperature to decrease. AUGUST 2005 ARCHER AND JACOBSON 2393

FIG. 5. Trends of simulated sea level pressure (hPa) at LML and MRY for 24 h starting at 1200 PDT on 25 Aug 2000. Observed and simulated south-to-north pressure gradients be- tween the two stations are also plotted.

The homogenizing effect of the SCE can be noticed a els. In its fully developed stage, the eddy center had a few hours later, at 2100 PDT (Fig. 7c), when the tem- temperature slightly warmer (ϳ2°C) than its surround- perature difference between south and north bay had ings. almost disappeared. The SCE vorticity was continu- By 0300 PDT (not shown), the SCE had completely ously depleted as the eddy moved southward and the dissipated at all levels, although a pocket of its vorticity positive vertical velocity was limited to the lowest lev- remained aloft at about 300 m. Temperature and mois-

FIG. 6. Simulated wind barbs and virtual temperature (°C) at Fort Ord for 24 h starting at 1200 PDT on 25 Aug 2000, from ground level to 1-km elevation. 2394 MONTHLY WEATHER REVIEW VOLUME 133

FIG. 7. North–south cross section of MM5 results for domain 2 during 25–26 Aug 2000 at key times of the SCE evolution: (a) sea breeze (1300 PDT); (b) onset of the first SCE occurrence (1900 PDT); (c) mature stage of the first eddy (2100 PDT); and (d) mature stage of the second SCE (0800 PDT). Terrain is shown with gray blocks. Vectors of wind components parallel to the section (i.e., ␷ in m sϪ1 and w in cm sϪ1) are shown together with vertical vorticity (10Ϫ3 sϪ1, gray shaded) and potential temperature (K, solid line every 2 K).

ture fields were uniform everywhere over Monterey eddy had a homogenizing effect over the bay, by ad- Bay. The second SCE eddy started forming slightly to vecting cool and moist air from the south into the the west of this cross section at this hour. warmer and drier Santa Cruz. The second/nocturnal The mature stage of the second SCE (Fig. 7d) was eddy instead formed in horizontally uniform tempera- characterized by smaller vertical extent (generally be- ture and moisture conditions. Moreover, the evening low 400 m), lower values of vorticity, and shorter life- eddy had a warm core while the nocturnal eddy had a time (6 h as opposed to 9) than the first eddy. It also cooler center. However, they both formed in the Santa had a cool center and dissipated over water rather than Cruz area and had a vertical profile of vorticity that over land, suggesting that the eddy dissipation is not nec- decreased with height. Moreover, they both dissipated essarily caused by increased surface friction over land. their vertical vorticity while moving southward after they detached from the SCM. This suggests that the mechanism of formation may d. Summary of findings from the test case be the same for both eddies, but more favorable con- It appeared from the surface and vertical analyses ditions in the late afternoon (e.g., south-to-north pres- that the first/evening and the second/nocturnal eddies sure gradient, stronger turning of the flow during the had different characteristics and formed in different day, and upslope flow along the southern side of the ambient conditions. The first/evening eddy had higher Santa Cruz Mountains) make the evening/first eddy vorticity, stronger vertical velocity, greater vertical ex- stronger and longer lasting. Since vorticity maxima are tent and lasted longer than the second one. The first found in the same area (i.e., by Santa Cruz) where both AUGUST 2005 ARCHER AND JACOBSON 2395 eddies initiate, finding the origin of the SCEs coincides batic heating were suppressed, the midchannel eddy with finding the origin of such vorticity. would be weaker and the Gaviota eddy would not form at all. Diurnal effects were also invoked for the Auck- land eddy by McKendry and Revell (1992). To verify 3. Mechanisms of formation the effect of diurnal cycle and heat exchange at the In this section, possible sources of the vertical vortic- ground on the SCE, run “NOSUN” was carried out ity associated with the SCE formation are investigated with the following settings: through a sensitivity approach, in which one or more • constant ground temperature (set equal to its initial parameters (or physical components) are varied at a value, representative of nocturnal conditions); time. • no surface heat (and moisture) fluxes; The following possible factors and mechanisms of • no solar cycle (by setting the solar constant to a very formation are discussed: small number). • Diabatic effects: the solar cycle is ultimately respon- In this run no substantial land heating occurred (Fig. 8), sible for the south-to-north pressure gradient, the and therefore the pressure gradient force between flow turning at the entrance of Monterey Bay, and ocean and land was greatly reduced (not shown). Con- the upslope flow along the south-facing sides of the sequently, no significant sea breeze formed in the af- Santa Cruz Mountains. By running MM5 with no so- ternoon and the main flow off the coast remained un- lar cycle and no heat exchanges at the bottom level, changed, that is, northwesterly. At 1500 PDT, an SCE such effects would be eliminated. No significant dif- was already fully developed (Fig. 9). This eddy was ferences between first and second eddy should thus almost stationary throughout the night and it never dis- be found. sipated. Vorticity was still formed along the western • ⌻␱pography: the mountains to the north and to the sides of the Santa Cruz Mountains, but did not reach south of Monterey Bay act as obstacles on the main values as high as it did in the test case (maxima were northwesterly flow. Ϫ Ϫ Ϫ Ϫ about 0.8 ϫ 10 3 s 1 as opposed to 1.3 ϫ 10 3 s 1 for • Viscosity: the fact that vorticity maxima are found RUN1). No upslope flow developed along the southern near the surface and that vorticity streaks emanate sides of the Santa Cruz Mountains (not shown). from the western side of the Santa Cruz Mountains In conclusion, the solar cycle was not a cause of the suggest that the SCE could be formed by boundary SCE events studied, since, after removing the solar layer separation, caused ultimately by internal and/or cycle, the eddy still formed with approximately the surface friction. Inviscid conditions would then pre- same size and vorticity as the nocturnal SCE from the vent the SCE formation. test case. The effect of the diurnal cycle was twofold. • 〉aroclinic mechanism: vertical vorticity can form in First, it destroyed the nocturnal eddy in the late morn- an inviscid and adiabatic flow past an obstacle, due to ing, as surface heating was responsible for the sea the tilting of horizontal vorticity generated by the breeze, which swept away the circulation associated solenoidal term. with the SCE. Second, the diurnal cycle enhanced the Since these sensitivity runs have a rather large effect, evening eddy by increasing its vorticity due to the results will be shown for a portion of domain 1 covering greater turning of the flow when the land is allowed to both San Francisco Bay and Monterey Bay. The base warm up and to the formation of a favorable south-to- scenario, described in the previous section, will be re- north pressure gradient. ferred to as “RUN1.” The focus will be on vorticity formation. Vortex shedding and hydraulic jump dy- b. Topography namics will be analyzed in section 4. Two mountain chains are found in the Monterey Bay area: SCM, located to the northwest of the bay, and the a. Diabatic effects Santa Lucia Mountains (SLM), located to the south of According to Davis et al. (2000), diurnal heating is the bay (Fig. 1). To evaluate their effects on the SCE, fundamental for the formation of the Catalina eddy. In the two chains were removed from both domains in their simulations with MM5, they showed that a stron- separate runs, without SCM (run named “NOSCM”) ger eddy would form if the ground was kept at its mid- and without SLM (“NOSLM”). Land-use and soil pa- day temperature. Vice versa, no eddy could form if the rameters were not modified; a plateau of 10 m elevation ground temperature was kept equal to its nocturnal replaced the original orography. value. Similarly, Wilczak et al. (1991) found that if dia- Without SCM, the SCE did not form at any time. At 2396 MONTHLY WEATHER REVIEW VOLUME 133

FIG. 8. Simulated temperature field (°C, solid line) and terrain elevation (m, dotted line) on domain 1 at 1500 PDT on 25 Aug 2000 from (a) RUN1 and (b) NOSUN.

2100 PDT, a large eddy was present over Monterey Bay turn the flow into a more westerly direction, as ex- as simulated by RUN1 and as confirmed by observa- pected for a system with high pressure to the west and tions (Fig. 10a). However, simulated streamlines ob- low pressure to the east. Vertical vorticity still formed tained with NOSCM at the same hour show no closed along the western flanks of the plateau, but less than in circulation, but rather a cyclonic turn of the flow in the RUN1 (0.6 ϫ 10Ϫ3 as opposed to 1.1 ϫ 10Ϫ3 sϪ1). A Santa Cruz area, induced mainly by the blocking effect closed cyclonic circulation formed by the city of San of the SLM to the south (Fig. 10b). Clearly, the SCM Francisco for a few hours at about 0500 PDT (not represent an obstacle to the main northwesterly flow, shown), a San Francisco Eddy indeed! without which the SCE cannot form. The removal of the Santa Lucia Mountains in run Without SCM, the entire peninsula from San Fran- NOSLM did not prevent the formation of the SCE, but cisco to Santa Cruz was swept by a strong northwesterly it changed some of its characteristics. The first eddy flow in the afternoon (not shown). Surface friction still formed farther to the east of Santa Cruz in NOSLM acted to reduce the wind speed over land and to slightly than in RUN1 (Fig. 11). Since the SLM blocking effect

Ϫ Ϫ FIG. 9. Streamlines of simulated winds at the lowest sigma level and simulated vertical vorticity (10 3 s 1, gray shaded) on domain 1 at 1500 PDT on 25 Aug 2000 from (a) RUN1 and (b) NOSUN. Terrain elevation is contoured with dotted lines every 200 m. AUGUST 2005 ARCHER AND JACOBSON 2397

Ϫ Ϫ FIG. 10. Streamlines of simulated winds at the lowest sigma level and simulated vertical vorticity (10 3 s 1, gray shaded) on domain 1 at 2100 PDT on 25 Aug 2000 from (a) RUN1 and (b) NOSCM. Terrain elevation is contoured with dotted lines every 200 m. was missing, the main northwesterly flow entering too was confined to the northeastern corner of Monterey Bay did not turn to a southwesterly direction Monterey Bay and had the same elongated and twisted as much as it did in RUN1. As a consequence, the eddy axis as the first one. No detachment occurred for the was confined to the eastern part of the bay and had a second SCE instance either. This suggests that the elimi- more elongated shape, with the symmetry axis parallel nation of the SLM effectively suppressed vortex shedding. to the mean flow. Furthermore, less vorticity was cre- In summary, topography dramatically affected the ated, since less turning of the flow occurred. In general, SCE. The SCM are necessary for the eddy formation: wind speeds were higher everywhere without SLM (not without them, no obstacle interacts with the main shown). In particular, the expansion fan was so much northwesterly flow and not enough vorticity forms. The larger in NOSLM that it occupied most of the bay. The SLM are not necessary for the SCE formation, but they first SCE never detached and quickly dissipated by affect its shape and duration. Without them, the eddy is 2200 PDT. A second eddy formed at about 0200 PDT confined to the northwestern part of Monterey Bay, it and lasted until 0900 PDT (not shown). Since the ex- has a more elongated shape, and no vortex shedding pansion fan lasted longer in NOSLM, the second SCE occurs.

Ϫ Ϫ FIG. 11. Streamlines of simulated winds at the lowest sigma level and simulated vertical vorticity (10 3 s 1, gray shaded) on domain 1 at 2000 PDT on 25 Aug 2000 from (a) RUN1 and (b) NOSLM. Terrain elevation is contoured with dotted lines every 200 m. 2398 MONTHLY WEATHER REVIEW VOLUME 133

-c. Viscosity ten as ␷ٌ2␻ and thus molecular viscosity can only dif fuse vorticity. For compressible flows, with the irrota- In general, the mean kinetic energy directly dissi- tional and barotropic assumptions [i.e., all terms on pated by molecular viscosity is negligible compared right hand side of Eq. (2) are zero except for the last with that dissipated by turbulent (or eddy) viscosity. one], vorticity can still be generated by the curl of eddy For this reason, molecular viscosity is ignored in MM5, friction, that is, by horizontal and/or vertical wind speed but eddy viscosity is not. The MM5 system is still vis- gradients. Haynes and McIntyre (1987) and Schär and cous because the dissipative effect of viscosity is in- Smith (1993a) introduced a “dissipative flux” to express cluded in the eddy friction term. A truly inviscid system the same concept. Grubišic´ et al. (1995) found that vor- is one in which both molecular and eddy viscosities and ticity production by the dissipative flux was negligible surface friction between air and the ground are zero. away from regions with horizontal variations of either Surface friction can be removed by setting, for example, fluid depth or surface roughness. Epifanio and Durran a free-slip boundary condition, as opposed to a viscous (2002b) found little contribution of eddy viscosity to the no-slip condition. Surface friction is not a separate wake vorticity generation. physical process but a manifestation of the flow viscos- The importance of viscosity on the SCE was investi- ity at the fluid/solid interface. gated in run NOPBL, where no turbulence parameter- The literature related to flow past an obstacle is vast ization was used (thus no eddy viscosity) and where a and is only briefly described here. The fact that more free-slip condition was forced at the surface (thus no than one SCE formed and moved southward brings to surface friction). Consequently, no momentum, heat, or mind the von Kármán vortex streets in two-dimen- moisture fluxes were allowed in the domains, neither at sional, homogeneous, viscous flow past a cylinder the surface nor aloft. Ground temperature was kept (Kundu 1990). For such flow, a wake with a pair of constant too. To maintain numerical stability, a hori- stationary, counterrotating vortices forms when the zontal diffusion term is present in MM5 (Grell et al. Reynolds number [Re ϭ (VD/␷), where V is the up- 1994). Since the horizontal diffusion operator is applied stream velocity, ␷ the kinematic viscosity, and D the on sigma surfaces, it could potentially generate vertical cylinder diameter] is greater than four; the wake breaks diffusion and dissipation and thus violate the inviscid into an oscillating Kármán vortex street if Re Ͼ 40 constraint. On one hand, this effect was found to be (Kundu 1990, p. 321). Laboratory studies too have at- negligible in an earlier version of MM5 (Kuo et al. tributed the formation of lee vortices downstream of 1988). Numerical diffusion was added also in Schär and three-dimensional obstacles to the separation of the vis- Smith (1993a) to smooth fields, but it did not affect the cous boundary layer from the lower surface (Brighton inviscid nature of their results (away from jumps). On 1978; Hunt and Snyder 1980; Castro et al. 1983; Snyder the other hand, Vosper (2000) found a large effect of et al. 1985). The extension of the boundary layer sepa- numerical viscosity in another numerical model with ration theory from homogeneous to stratified flows was the sigma-pressure coordinate. Some numerical viscos- first proposed by Chopra and Hubert (1965). Even ity was found in MM5 in this study also, as discussed in though subsequent studies (discussed in the next sec- section 4. However, for the purpose of this discussion, tion) have proven that boundary layer separation is not the settings imposed on MM5 made the system as close necessary for eddy formation in stratified flows, the to inviscid as technically possible. effect of viscosity on the SCE is still studied here from Great differences between the results obtained with the point of view of the vorticity equation: NOPBL and the test case can be noticed already in the divergence afternoon. Since the ground was not allowed to warm d␻ 1 ١p up during the day, and since no surface fluxes could ϫ ͪ ١ͩ u͒ Ϫ · ١͒u Ϫ ␻͑١ · ϭ ͑␻ dt ␳ exchange heat between air and soil, the temperature tiltingրstretching solenoidal difference between ocean and land was much lower in molec. viscosity NOPBL (not shown). Consequently, the pressure gra- -ϫ FЈ, ͑2͒ dient between ocean and land was reduced and there ١ ϫ ͑␷ٌ2u͒ ϩ ١ ϩ eddy viscosity fore the main flow over Monterey Bay was weaker and less westerly in NOPBL than in the test case (Figs. where u ϭ ui ϩ ␷j ϩ wk is the three-dimensional wind 12a,b). Since the flow was weaker, winds were affected vector, ␳ is density, p is pressure, ␻ is absolute vorticity, more by local features, such as valleys or slopes, in ␯ is molecular viscosity, and FЈ is eddy friction. Note NOPBL. An SCE had already formed at noon; since it that, only for incompressible flows with uniform and formed within weaker synoptic forcing, the eddy was constant ␷, the molecular viscosity term can be rewrit- larger in the horizontal than under normal conditions. AUGUST 2005 ARCHER AND JACOBSON 2399

Ϫ Ϫ FIG. 12. Streamlines of simulated winds at the lowest sigma level and simulated vertical vorticity (10 3 s 1, gray shaded) on domain 2 at 1200 and 1800 PDT on 25 Aug 2000 from (left) RUN1 and (right) NOPBL. Terrain elevation is contoured with dotted lines every 200 m.

No expansion fan formed offshore from Santa Cruz and would have otherwise dissipated the eddy during the therefore vorticity was generally lower in run NOPBL day. Vortex shedding was almost suppressed, as only (Figs. 12c,d). The first SCE detached at 0100 and dis- one eddy (the first one) detached from the SCM. This sipated by 0300 PDT, but a second eddy formed an may appear surprising, as a decrease in friction should hour later. This SCE was more elongated and narrow enhance vortex shedding rather than suppress it than the corresponding one in the test case (not shown); (Grubišic´ et al. 1995; Vosper 2000). However, the re- it continued until 0900 PDT but it never detached. A versed flow in the wake is weaker in the inviscid case third eddy started at about 1000 PDT on 26 August (not and consequently wake instability and vortex shedding shown). All eddies had a smaller vertical size than in are less likely to develop. Overall, it can be concluded the test case. that frictional generation of vorticity in the SCE case is In conclusion, the mixing of momentum and heat greater than frictional dissipation. produced by turbulent friction does not appear to be a fundamental mechanism for the SCE formation, but it d. Baroclinic mechanism affects several details of its evolution. With no friction, Modeling studies have first shown that, in three- an SCE still formed on the south side of the SCM. dimensional stratified flow, vortices would intensify However, it was characterized by weaker winds and when surface friction was either reduced (Wilczak and vorticity, a more elongated shape, and smaller vertical Glendening 1988) or removed (Smolarkiewicz et al. development than in the test case. Furthermore, mul- 1988; Kuo et al. 1988). As such, the analogy between tiple instances of the SCE formed throughout the 2-day vortex street in homogeneous flow and vortex shedding period, regardless of the time of the day, due to the in stratified flow was compromised. It was only a year absence of heat or momentum fluxes at all levels, which later that Smolarkiewicz and Rotunno (1989a) pro- 2400 MONTHLY WEATHER REVIEW VOLUME 133

posed a new vorticity formation mechanism for invis- able for idealized runs (Chuang and Sousonis 2000), cid, stratified flow past a three-dimensional obstacle, fully adiabatic and inviscid conditions cannot be namely the baroclinic mechanism. To illustrate it, the achieved during the simulations. The best solution was vorticity vector is split here into its vertical (␨) and to use the same conditions as in NOSUN, but with ␻ horizontal ( h) components, which both satisfy the in- neither a turbulence parameterization nor surface fric- viscid vorticity equation [Eq. (2)] as follows: tion, to make the flow inviscid. Since the solenoidal d␨ 1 term could be theoretically forced by a spatial gradient ١p, ͑3͒ in (potential) temperature (Pielke and Segal 1986), the ϫ ͪ ١ͩ · u͒ Ϫ k · ١͒w Ϫ ␨͑١ · ϭ ͑␻ dt ␳ initial temperature of ground and water was set uni- d␻ 1 form to a constant value of 14°C (from this the run was ͒ ͑ ͬ ١ ϫ ͪ ϩ ͫϪ١ͩ ͒ ١͑ Ϫ ␻ ١͒ h ϭ ͑␻ · uh h · u ␳ p , 4 dt h named “UNIF”). Note, however, that temperature, where the subscript h indicates a horizontal component. pressure, and density in the initial conditions were still The tilting/stretching and divergence terms would all be the same as those in the test case, and therefore they zero in an initially irrotational system (i.e., in which ␻ were inconsistent with the horizontally homogeneous ϭ 0att ϭ 0), since vorticity appears in them as a temperature field imposed at the ground. Note also that multiplying factor. The last term, called “solenoidal” or the initial wind field was not irrotational but contained “baroclinic,” is the only one that could from vorticity. some vertical vorticity and potential vorticity, which The solenoidal term is zero in barotropic flows by were in the initial conditions. Even with these limita- definition. However, its effect in Eq. (3) is negligible tions, results from run UNIF were useful for identifying even in baroclinic flows, therefore suggesting that ver- the origin of the solenoidal term. tical vorticity cannot be directly generated inviscidly. With run UNIF, not only did the eddy still form, but This is not entirely accurate. As shown first by Smo- it also had characteristics very similar to those from run larkiewicz and Rotunno (1989a) for a simplified system NOPBL, except for a time lag of 6 h, explained by the (anelastic, adiabatic, Boussinesq, and hydrostatic), the lack of a diurnal cycle. In addition, no vortex shedding solenoidal term is not negligible in Eq. (4), and it can occurred throughout this simulation. Without any fric- ␻ therefore create horizontal vorticity. Once h becomes tion/turbulence and without any diabatic effects, the nonzero, the tilting/stretching term in Eq. (3) becomes horizontal contours of vertical vorticity (Fig. 13a) show nonzero too and thus vertical vorticity can be gener- again the typical streaks emanating from the sides of ated. Note that no assumption, besides inviscid flow, the Santa Cruz Mountains, also obtained for example was made so far. by Schär and Durran (1997), Schär and Smith (1993a), By imposing a free-slip boundary condition in their Crook et al. (1990, 1991). numerical simulations, Smolarkiewicz and Rotunno An analysis of the relative importance of all four (1989a) effectively prevented the formation of a bound- terms of the vorticity equation in the vertical was per- ary layer and yet obtained a pair of vortices for the formed at 0200 PDT, when the first eddy had formed. range 0.1 Ͻ Fr Ͻ 0.5. After their seminal study, several In general, the greatest magnitudes are given by the other studies have confirmed the validity of the baro- tilting/stretching and the advection terms (not shown). clinic mechanism (Smolarkiewicz and Rotunno 1989b; The tilting/stretching, however, is the only term with a Rotunno and Smolarkiewicz 1991; Schär and Durran significant contribution at the entrance of Monterey 1997; Rotunno et al. 1999; Vosper 2000). Kuo et al. Bay (Fig. 13b), where vorticity maxima were found. (1988) and Wilczak and Glendening (1988) found that In the horizontal, no term has a significant contribu- surface friction acted as a sink, rather than a source, of tion at the entrance of Monterey Bay except for the vorticity for the case of a mesoscale vortex that formed solenoidal term, which is greatly affected by the pres- over China and for the Denver Cyclone, respectively. ence of the SCM (Fig. 13c). In fact, at all times, the Also, Crook et al. (1990) found no significant differ- horizontal solenoidal vectors rotate clockwise around ences between runs with and without surface friction; the SCM, a pattern consistent with that of the horizon- similarly, Grubišic´ et al. (1995) showed that surface fric- tal vorticity vector in Smolarkiewicz and Rotunno tion is not the dominant vorticity formation mechanism (1989b, their Figs. 1f and 1i), Crook et al. (1990, their in shallow-water flows past an obstacle, but it interferes Fig. 13), and Schär and Durran (1997, their Fig. 11). with vortex shedding by making the wake more stable. To investigate the importance of the baroclinic 4. Other remarks mechanism and the ultimate causes of the solenoidal term, it was necessary to run a simulation as close as In this section, other factors affecting the SCE are possible to adiabatic conditions. Since MM5 is not suit- investigated. AUGUST 2005 ARCHER AND JACOBSON 2401

FIG. 13. Fields from run UNIF on isentropic surface ␪ ϭ 292 K, pierced by the Santa Cruz Mountains where shaded, at 0200 PDT on 25 Aug 2000; (a) vertical vorticity (sϪ1); (b) tilting (sϪ1); (c) horizontal solenoidal vector; and (d) potential vorticity (K m2 sϪ1 kgϪ1). Contour interval is shown on each panel; negative values are long dashed. Terrain is contoured with dotted lines every 200 m. a. Inversions is then favorable because it increases lateral mixing and consequently triggers stronger inertial oscillations. The importance of an elevated inversion was first Chopra (1973) hypothesized that the presence of an suggested by Hubert and Krueger (1962). In their inversion at half height of the mountain is necessary for study, several aspects of vortex streets observed on the the formation of a vortex street. In fact, surveys of lee of the Canary Islands were consistent with inertial sounding data confirm that most vortices form where a oscillations or inertial instabilities for stable and un- sharp inversion is located below the obstacle crest (Epi- stable wakes respectively. The presence of an inversion fanio and Rotunno 2005). The stability of the inversion 2402 MONTHLY WEATHER REVIEW VOLUME 133 causes upstream flow blocking and consequent deflec- ciated with a shock feature over Monterey Bay. How- tion around, rather than over, the obstacle. In other ever, no striking evidence of its existence was found in words, an inversion would reduce the Fr of the flow. RUN1 from either domain. Regardless, runs NOPBL Moreover, the phase diagram in Schär and Smith and UNIF showed vortex formation with no sign of (1993a, their Fig. 3) shows that a wake with reversed supercritical flow upstream of the bay. Consequently, flow always forms when the mountain height is greater vorticity formation via a hydraulic jump does not ap- than the fluid depth within the shallow-water approxi- pear fundamental in the SCE case. mation. Consistently, it was found in Archer and Ja- cobson (2005) that the SCE was more likely to form c. Potential vorticity when the marine layer was lower than 500 m, that is, Another aspect of relevance to vortex formation is when the inversion was located below the top of the potential vorticity, defined as Santa Cruz Mountains. However, sensitivity runs with- out viscosity or without diurnal cycle showed that the ␻ ͒ ͑ ١␪ baroclinic mechanism could act even without an inver- ⌸ ϭ ␳ · . 5 sion, in almost isothermal conditions (not shown). Nonetheless, the presence of the inversion is favorable From Pedlosky (1987) and following Haynes and McIn- to eddy formation because it prevents the main north/ tyre (1987), the potential vorticity equation can be writ- northwesterly flow from going over the Santa Cruz ten as Mountains, and therefore it precludes any downslope ١␪ flow from interfering with the SCE formation. Since a ⌸ ⌿␻ d Fd J, ͑6͒ · ϫ ͪ ϭϪ١ ͩ · ١ Ϫ ͪ ͩ · ١ ϭ marine inversion over central California is most com- dt ␳ ␳ ␳ mon in the summer, the summertime nature of the SCE can be partially explained. Also, the baroclinic mecha- ⌿ where includes conductive and diabatic effects, Fd is nism acts preferentially in the summer, when strong friction (due to molecular and/or eddy viscosity), and J and steady north/northwesterly flow, typical of the cen- is the dissipative vector: tral California coast, interacts with the Santa Cruz ١␪ Mountains. This same north/northwesterly flow also ⌿␻ F ϭϪ Ϫ d ϫ ͑ ͒ impinges against the Santa Lucia Mountains to the J ␳ ␳ ␳ . 7 south of Monterey Bay, contributing to the local south- to-north pressure gradient that strengthens the SCE in Potential vorticity can therefore be formed (destroyed) the afternoon. due to the convergence (divergence) of the dissipative vector, consisting of the sum of frictional and diabatic b. Hydraulic jumps effects. In adiabatic and inviscid flow, therefore, poten- Another mechanism of vorticity formation for strati- tial vorticity is conserved. For an initially irrotational fied flow past an obstacle is through discontinuities, flow, the vorticity vector must lie on isentropic surfaces such as hydraulic jumps. Schär and Smith (1993a) at all times. In UNIF, ⌸ is thus expected to be relatively showed that, within the shallow-water approximation, a small and uniform along the sides of the SCM. How- hydraulic jump and a wake with reversed flow (i.e., ever, Fig. 13d shows appreciable potential vorticity on vortex pairs) can form inviscidly when the obstacle the 292-K isentrope right where vorticity steaks pierces through the fluid depth. Dissipation, however, formed. Similarly, nonexact potential vorticity conser- occurred at the jump via jump conditions; as such, this vation was also obtained by Smolarkiewicz and Ro- system was defined as “pseudoinviscid.” Epifanio and tunno (1989a) in “regions where the ␪ surfaces lowered Durran (2002a) found similar jump features in numeri- to the point of intersecting the lower boundary of the cal simulations of free-slip, laminar, and viscous flow. model.” Skamarock et al. (2002) also found potential Via a Lagrangian vorticity decomposition with propa- vorticity anomalies on the leading edges of a simulated gator matrices, Epifanio and Durran (2002b) were able Catalina eddy, but they concluded that ⌸ did not play a to conclude that the role of hydraulic jumps is to am- significant role in vortex formation. Since no diabatic plify baroclinically generated vorticity via stretching. effects are possible without solar radiation, the only Since a region of supercritical flow was found at the explanation for potential vorticity in run UNIF is the entrance of Monterey Bay for the SCE eddy case (see inevitable numerical viscosity present in the MM5. Fig. 3), the presence of a hydraulic jump is expected Similarly, Vosper (2000, his Fig. 12) found that numeri- somewhere over the bay. Burk and Haack (2000) have cal viscosity was causing large vorticity normal to the in fact documented the formation of cloud bands asso- isentropes. AUGUST 2005 ARCHER AND JACOBSON 2403 d. Vortex shedding land, or past capes or bays over water (except for the SCE). The effect of friction on the SCE shedding ap- The final aspect to investigate is vortex shedding. In pears to be the opposite of that on shallow-water flows homogeneous flows, the transition from a stationary in that frictional generation of vorticity dominates fric- vortex pair to vortex shedding is achieved by simply tional dissipation. Further investigations are needed to increasing Re past a critical value (ϳ40). Sun and fully elucidate this aspect. Chern (1994), however, did not obtain vortex shedding in their simulations of stratified flow past an isolated mountain for 1 Ͻ Re Ͻ 1000, therefore suggesting that 5. Summary and conclusions a critical Re might not exist for vortex shedding in stratified flow. It was only by introducing some asym- The SCE formation is rather complex, since it in- metries (such as Coriolis rotation, wind perturbations, volves four different mechanisms acting together. The or asymmetric obstacle shapes) that they achieved vor- baroclinic theory, inspired by the findings of Smolar- tex shedding. Analogously, Schär and Smith (1993b) kiewicz and Rotunno (1989a), appears to be the funda- obtained vortex shedding by suppressing a symmetry mental mechanism for vertical vorticity formation. The solenoidal term, directly related to a fluid change in condition previously imposed in their method of calcu- pressure not accompanied by a density adjustment, cre- lation (Schär and Smith 1993a). By studying the evolu- ates horizontal vorticity along the Santa Cruz Moun- tion of the most unstable normal mode in a pseudoin- tains’ sides. The tilting/stretching term then acts to tilt viscid shallow-water system, they proved that vortex the horizontal vorticity into the vertical, creating the shedding was induced by a nonlinear oscillation that vertical vorticity necessary for the formation of a vortex became perfectly periodic (sinusoidal) in time, thus downstream. causing the shed vortices to align in a perfectly periodic Friction represents an additional source of vorticity, wake. They concluded that global instability of the related to the fact that viscous dissipation is present in wake was causing vortex shedding. the turbulent airflow and that velocity has to be null at An analysis of the wake instability for the SCE case the surface along the mountainsides. This wind shear, is beyond the scope of this study. However, several perpendicular to the sloped terrain, causes both hori- conclusions can be drawn from the results discussed. zontal and vertical vorticity. These two mechanisms First, the geometry of the SCM and the flow around (i.e., solenoidal and frictional) act both during the day them are nonsymmetric, thus suggesting that the simu- and night. lated vortex shedding (RUN1) is realistic. However, During the day only, two other mechanisms form such asymmetric conditions persist in all sensitivity vertical vorticity. First, the sea breeze forces a westerly runs, but vortex shedding is suppressed in most of them. flow over Monterey Bay and southerly flow to the east For example, the removal of the diurnal cycle pre- of Santa Cruz, causing an expansion fan at the entrance vented vortex shedding. This is possibly consistent with of the bay. Vorticity is therefore formed there as a Sun and Chern (1993), who found that the removal of result of both flow turning and horizontal wind shear. the diurnal cycle doubled the period of vortex shed- Finally, favorable conditions for a flow reversal (i.e., ding. Asymmetries therefore do not appear to be suf- against the main northwesterly winds) are created in ficient for SCE shedding. Second, vortex detachment the afternoon by the south-to-north pressure gradient, occurred with and without viscosity, therefore suggest- which forces flow down the gradient from the south of ing that friction is not a critical factor for shedding in Monterey Bay toward Santa Cruz. the SCE case. Furthermore, two out of three inviscid eddies were stationary. This was somewhat counterin- Acknowledgments. This work was supported by the tuitive, as Grubišic´ et al. (1995) found that surface fric- National Science Foundation (NSF) and by the Na- tion was not only reducing the size and strength of the tional Aeronautics and Space Administration (NASA). wake, but also preventing vortex shedding by making The MM5 preprocessors were run at NCAR, which also the wake more stable. Their findings are consistent with provided data for the initial conditions. 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