JULY1977 R.E. THOMSON, j. F. R. GOWER AND N. W. BOWKER 873Vortex Streets 'in the Wake of the Aleutian Islands RICHARD E. THOraSO~ A~D JAMES F. R. GOWERInstitute of Ocean Sciences, Environment Canada, Victoria, British Columbia VSW 1Y4 NOULAN W. BOWKER MacDonald Dettwiler fi~ Associates Ltd., Richmond, British Columbia V6X 2Z9 (Manuscript received 15 February 1977)ABSTRACT The characteristics of a series of cloud-delineated wake patterns downwind of isolated mountain barrierson the Alaskan Peninsula and eastern Aleutian Islands have been studied using a geometrically correctedNOAA satellite picture in conjunction with available meteorological information. Four of these wakesare shown to be atmospheric analogs of K~rm~n-type vortex streets observed in laboratory experiments.A critical Reynolds number of 924-5 has been estimated for the flow. The drag coefficients associatedwith the vortex streets varied from 1.1 for an irregular, asymmetrical wake to 2.3 for a regular, symmetricalwake; the turbulent eddy viscosity ranged from 1.2-1.8 X 103 m2 s-~ for the four vortex streets. The two vortexstreets having the lowest Reynolds number flows (R = 97, 112) appear to have developed through a "doublevortex street" laminar instability while the vortex street having the largest Reynolds number flow (R = 183)apparently developed through a "single vortex street" instability. Formation of the remaining vortex street(R= 120) appeared to result from a downstream growth of a mountain-induced instability in the wind field.1. Introduction Satellite imagery frequently reveals the presence ofmesoscale cloud patterns in the lee of large oceanicislands which bear a striking resemblance to vortexstreets that develop in the wakes of two-dimensionalbluff bodies in laboratory experiments. By assumingthat such patterns were in fact the atmospheric analogof laboratory vortex streets, Chopra and Hubert (1965)were able to ascribe values to such quantities as therate of vortex shedding, eddy lifetime, eddy viscosityand obstacle drag for an observed wake downwind ofMadeira Island in the Canary Island Group. Also onthis basis, Wilkins (1968) was able to obtain an estimate for the kinetic energy dissipated by vortex trailsfor three islands in the Atlantic and Pacific Oceans. Inparticular, he found that the total eddy-dissipatedenergy was fifty times that due to the steady background turbulence over an equal period of time. Similarly, Lyons and Fujita (1968), in considering therelationship between the topography of the westernAleutian Islands and observed wakes (clear areas inthe stratus clouds), determined that one of the largerislands (Kiska) was generating a vortex street. Finally,Tsuchiya (1969) analyzed a pair of ESSA satelliteimages taken 4 h apart over the lee area of ChejuIsland, Korea, and found that the cloud wake patterncould be interpreted as a vortex street propagatingdownstream at about 76% of the undisturbed windspeed. As with previous investigations of large-scalevortex patterns, he also found that values of thevarious nondimensional parameters that characterizethe flow were consistent with those obtained in laboratory investigations. Hubert and Krueger (1962) first pointed out thatthe visualization of atmospheric vortex trails by satellites is made possible by a fairly special combinationof geographic and atmospheric conditions. These include 1) an extensive oceanic area covered by stratusor stratocumulus clouds lying beneath a strong inversion, 2) relatively strong and directionally persistentlow-level winds, and 3) mountainous islands that penetrate many hundreds of meters above the inversion.Unfortunately the atmospheric conditions are typicallyshort-lived compared to the period of about 1 day between most satellite passes and are usually not ofsufficient spatial extent to delineate the full wake.Past studies of mesoscale vortex streets have thereforebeen limited to only portions of what were undoubtedlymuch more extensive patterns in the velocity and pressure fields. Moreover, none of these studies has dealtwith a series of vortex streets generated simultaneouslyby adjacent islands under nearly identical atmosphericconditions. The purpose of this paper is twofold: 1) it brings tothe fore what we believe to be some of the best examplesto date of observed vortex streets in the atmosphere(Fig. 1); and 2) it presents an analysis of these vortextrails for comparison with laboratory results but in the874 MONTHLY WEATHER REVIEW VoLumE105 Fro. la. Portion of a NOAA 4 satellite VHRR (visible) image taken at 2006.2GMT 5 April 1976 over the northeast Pacific Ocean. The Alaskan Peninsulaand eastern Aleutian Islands appear in the upper left hand corner. This figure hasbeen corrected to remove both the strong geometrical distortion that normallyaffects areas near the side edges of VHRR imagery and the lesser effect due to theearth's rotation common to all satellite scanner imagery. (A flaw appears nearthe tgp of the picture.)light of certain modern developments, and allows anintercomparison of widely different wake patternsunder almost identical atmospheric conditions.180- 1.70-W 160- 150-' ' ' ' I ' ' ' 'Bering: ' '1711~ _' '~~~d _:_, '- - - i,~- -~ ~;.. - - .... 5 5- xgxo....7~-' --' ,, , , 50-N 1 North I Pacific Ocean.... , ........ , ........ ~ .... 45- Fro. lb. Dashed box shows area covered by Fig. la.2. General properties of vortex streets The formation of vortex streets associated with theperiodic shedding of vorticity into the wake of a bluffbody was first described by Strouhal in 1878. However,it was not until yon Kirmln's theoretical formulationin 1911 that the subject received active study in thelaboratory. The term "Kirmln vortex street" has subsequently been adopted for these patterns althoughvon Kirmln's work originally dealt with the idealizedand readily parameterized arrangement of point vortices generated by initially two-dimensional potentialflow incident on a parallel cylinder. In general, nonlinear interactions prevent vorticity from forming intoisolated eddies and the structure of the vortex[ streetsis made appreciably more complex than yon Kirmln'ssimple theory would suggest.a. The ratio h/a Kirmin vortex streets consist of two rows of closedvortices having a span-wise separation h roughly equalto the diameter d of the cylinder; the vortices arestaggered such that a vortex in one row lies oppositeJui.-1977 R.E. THOMSON, J. F. R. GOWER AND N. W. BOWKER 875WINDuo ~' ;:i:~_ .1'~ ~ h _t__Fro: 2. Schematization of a K~,rmfi, n vortex street in the wake of a cylindrical object of diameter d in a two*dimensional flow.the center of the downstream spacing a between adjacent vortices in the other row (Fig. 2). According toyon K/~rm/m's theoretical formulation, h/a=0.2805 forneutrally stable dimensions. In actual laboratory situations, however, this ratio is dependent upon the shapeof the obstacle, the characteristics of the flow and thedistance along the wake, and is observed to lie in therange 0.28<h/a<0.52 (1)(Chopra and Hubert, 1965). Moreover, the vortexstreet broadens downstream due to viscous diffusionand to the sweeping of vorticity from one side of thewake to the other (Abernathy and Kronauer, 1962;Mair and Maull, 1971). There may also be an accompanying but much slower increase in the wavelength(e.g. Papailiou and Lykoudis, 1974). Although the range (1) has been determined fromlaboratory experiments, it also appears to be applicableto vortex streets that form in the atmosphere and ocean(cf. Barkley, 1972). None of the latter studies, however,have dealt with the downstream widening of the wakepatterns nor with possible alteration of the wavelength.[-Hendry and Wunsch (1973) further caution againstthe interpretation of oceanic measurements in terms ofKgrmgn vortex streets.~b. The Reynolds and Strouhal numbers Provided the Reynolds number R= Uod/v (formedby the diameter d, the kinematic molecular viscosity vand the free stream speed U0) falls within the approximate range 40~<R~<200, (2)the vortex street behind a parallel cylinder is laminarand stable. Below a critical Reynolds number of about40, on the other hand, no vortex street is formed, andfor values in the range from about 200 to 105 the velocity fluctuations within the wake become irregular,although a predominant frequency can be determined.For 105,,~<R,~<3.5 X 10~ there is a complete loss of periodicity, but for larger Reynolds numbers some periodicity returns to the near wake (Papailiou and Lykoudis,1974). Vortex streets in the wake of cylindrical cones havebeen investigated by Gaster (1969). Using two coneswith taper ratios 36:1 and 18:1, he found that theformation of these patterns was a strongly threedimensional phenomenon in which the frequency ofvortex shedding was controlled by the local diameterand was slightly lower than that for a parallel cylinderof the same size. Furthermore, in the experimentalrange of Reynolds numbers 50-200 (based on localdiameters), the critical Reynolds number increased asthe taper of the cone decreased, increasing from 47 fora cylinder, to 53 for the 36:1 cone, to 65 for the flatter18:1 cone. Gaster further observed that for Reynoldsnumbers between 80 and 90 there appeared a lowfrequency modulation of the regular velocity fluctuations of the wake, and that for Reynolds numbers above170 these gave way to fluctuations with added randomness. The modulation frequency was found to dependonly on Uo2/u and to be independent of any physicaldimension of the model. An alternate explanation forthis effect in terms of multiple Kgrm&n vortex-streetmodes has been given by Weihs (1973). For geophysical scale motions, determination of theReynolds number R = Uod/K (3)requires an independent measure of the turbulent eddyviscosity K. Since observed values are found to varyover many orders of magnitude (e.g. Heffter, 1965;Gossard and Hooke, 1975), the usual procedure in thecase of mesoscale vortex streets is to obtain an indirectestimate of K via the Strouhal number S, and theparameter fi=S/R first introduced by Lin (1954).More specifically, the relation S =nd/Uo (4)is used together with (3) to yield K=fiCo2/n, (5)in which n is the vortex shedding, frequency and where10--<fi<2.5X10-a for stable vortex streets in the leeof circular cylinders. The frequency n in (5) can beexpressed in terms of the downstream propagationspeed U, of the eddies as n= U~/a= (Ue/Uo)Uo/a, (6)and calculated from values for the velocity ratio.Chopra and Hubert (1965) have estimated that U,/Uo.=0.75 for the vortex street downstream of MadeiraIsland, although a recalculation of their results wouldindicate a value closer to 0.70. (Subsequent papers onmesoscale vortex streets have also used a value of876 MONTHLY WEATHER REVIEW VOLUME1050.75.) Typical eddy viscosities determined from theabove procedure are O(103 m2 s-1) for atmosphericvortex streets and O(102 m2 s-~) for oceanic vortexstreets, while the Reynolds number (3) invariably fallswithin the range given by (2) for stable vortex streetsbehind regular cylinders. For Reynolds numbers in the range 40~<R~<200 theStrouhal number for laboratory models is found toroughly satisfy 0.12~<S~<0.19,and thereafter to reach a cofistant value of about 0.21for R>300. Roshko (1954) in particular found that inthe range (2) S=0.212--4.5/R, (7)and that the nondimensional quantity nv/Uo2 wasnearly constant. Strouhal numbers determined frommesoscale vortex street patterns generally fall within,or close to, the extended range 0.12~<S~<0.21. (8)-. Other properties Theoretically derived relationships for idealizedKgrmgn vortex streets can be used to obtain estimatesof circulation strength, relative vorticity, e-folding timeand dissipation rates for an individual vortex.Also derivable are the drag on the obstacle and thedrag coefficient. As the appropriate calculations arestraightforward and have been previously detailed(e.g. Chopra and Hubert, 1965; Barkley, 1972), onlythe final expressions will be presented here (see Table 3).3. Characteristics of the Aleutian Islands wakes Fig. 3a is a photographic enlargement of the upperleft-hand portion of Fig. 1. Dots have been used tomark the locations of the major mountain peaks, asdetermined from U. S. Geological Survey maps, andletters refer to the highest peak within each group (seealso Fig. 3b). At the time of the satellite imagery,well-defined vortex streets were being generated in thewake of four predominant groups: 1) group S, conFro. 3a. A factor of 2.3 enlargement of the wake r~gime of Fig. la. Letters and dots refer to the names and locations of the major mountain peaks appearing in Fig. 3b.1977R. E. THOMSON, J. F. R. GOWER AND N. W. BOWKER o.~,. ~- - ,~ -,~ ,1,~' ! "'~'" ,~o~c~_ ,,.. ~ ~ "~~~. -~ '%?~ ~. r ~. ~ 6~~ ~ .xs. .. North Pacific ocean877 FIG. 3b. Simplified topographic map of the Aleutian Islands-Alaskan Peninsula region.Areas whose altitude exceeds 1000 m MSL are in bold face. Altitude of a peak (m) is shownin parentheses.sisting of Shishaldin Volcano, the Isanotski Peaks andRoundtop Mountain; 2) region P, consisting ofPogromni Volcano, Faris Peak and Westdahl Peak;3) region P, formed by Pavlof Volcano, Pavlof Sisterand Little Pavlof; and 4) region V, consisting of MountVsevidof and Mount Recheshnoi. In addition, therewas a spreading laminar-like wake in the lee of Makushin Volcano (M) and oscillatory-type wake patternsdownwind of the Mount DuttomAghileen Pinnaclesregion (D) and the Frosty Peak region (F). Only peakswith elevations exceeding 2000 m, however, were generating distinctive vortex trails. We further note thateven though the two vortex streets formed in the lee ofUnimak Island eventually merged, they maintainedseparate identities for over 350 km.a. Cloud heights Vizualization of the wakes was made possible by theclearly defined stratocumulus cloud streets in the vicinity of the eastern Aleutian Islands. The cloud basewas at approximately 300-600 m according to reportsmapped onto surface meteorological charts (Fig. 4),with the greater height in rough agreement with theradiosonde data obtained around 0000 GMT 6 April(Fig. 5a). In the latter case, the cloud tops were presumably below the base of the inversion at 1000 m andtheir vertical extent coincidental with the layer of 100%humidity observed between 500 and 1000 m. The uniformity of the cloud patterns over the BeringSea would indicate that there was little turbulence inthe incident winds blowing roughly parallel to thecloud streets. Some upstream influence occurred within100 km of the island barriers and in all leeward areasthere was an apparent increase in the level of turbulence. As suggested by Lyons and Fujita (19'68), theextensive clear areas in the near-wake regions wereprobably produced by the downward turbulent mixingof drier air above the inversion with the saturated airbelow. The fact that the clouds directly associated withthe vortex streets reformed much closer to the landthan elsewhere would suggest that turbulent mixingwas suppressed in the vicinity of the street patternsor that there was a horizontal convergence of moist airwithin the wake which was not evaporated by the infusion of drier air. This contrasts with the large cloudfree areas in the lee of Unalaska Island where strongvertical mixing was taking place. The origin of the thinaltocumulus cloud over parts of the Island Chain isuncertain but may have been indicative of locallystrong downward motions to a higher secondary condensation level.b. Winds and the effective obstacle diameter The surface meteorological charts indicate that winddirections most favorable to the vortex street generationlasted for approximately 24 h beginning between 06001200 GMT 5 April. At the time of the satellite photograph, reported surface winds were from the northnorthwest at about 15 m s-~ and had developed withinan area between a southeastward moving low pressuresystem (~ 980 mb) and an accompanying quasi-stationary high pressure system (~1026 mb) centered a fewhundred kilometers northwest of Unimak Island. Between 1800-2400 GMT 5 April, the low pressure systemwas. nearly stationary but by 1200 GMT 6 April thewind directions had begun to shift rapidly with the878 MONTHLY WEATHER REVIEW Vonu~.105 Fro. 4. Six-hourly surface meteorological charts for the wake region on 5 April 1976 at 1200 GMT (a) and at 1800 GMT (b).approach of the next low pressure cell. The radiosonde the satellite imagery of Fig. 3a was obtained. Corredata of Fig. 5b shows that the wind direction over this sponding wind speeds on the other hand varied con24 h period was uniform with height and in accord siderably with height and time.with the ship observations was from about 340-T when Gaster's (1969) experiments with slender cones haveJULY1977 R.E. THOMSON, J. F. R. GOWER AND N. W. BOWKER 879~.5~.01.51.00.50oIt/ /it //;:., \ ~\ '\ i'x '"'"'""~"'~.ii~t \~: ". I x~i t I r~ . I .// !~ /i'/ ~;~" ? ' ",, I;. X~ '~,. --~... ~ ' ~. "~. / 5~ ~, , 'l~ , ~'-.~, -IO 0 0 50 100 TEMPERATURE ~C) RELATIVE HUMIDITY (%)4.54.0S,5$.02.52.01.51.00.5I I 20 $~0 DIFIECTIDN(a) (b)SPEED (MS-I) Fro. 5. Radiosonde data (WBAN 33) on four separate occasions at Cold Bay, Alaska, April 1976: (a) temperature andrelative humidity, (b) wind speed and wind direction. (+) 00 GMT April 5; (X) 1200 GMT April 5; (-) 00 GMT April 6;(El) 1200 GMT April 6.demonstrated that the vortex shedding frequency at aparticular "elevation" along the cone was controlledby the local diameter. On this basis, we have determinedthe free stream speed U0 and the effective diameter dfor each barrier at the 750 m level, midway throughthe cloud layer. These values are contained in Table 1.'We should point out, however, that our choice of d isnot completely objective since it has the further stipulation that the topographic area must also penetratethe inversion in order to be counted.c. Wavelengths and widths of eddy rows The wavelengths as a function of distance along thewake have been plotted in Fig. 6a. Downwind of MountVsevidof (V) the wave. length was uniform at about75 km (4-200/o) but in the other vortex patterns showedconsiderably more variation. Along the wake of theShishaldin group (S), for example, there appeared tobe a decrease in wavelength up to a distance of 250 kmfollowed by a slight increase in wavelength throughoutthe remaining portion of the wake. Typical values forthe two Unimak Island vortex streets at 200 km downstream were 75 km (4-20%) for the Shishaldin groupand 50 km (4-20%) for the Pogromni group (Table 1).For the sake of analysis, vorticities beyond the apparentcoalescent region of these two vortex streets at around370 km have been considered applicable to theShishaldin wake only. The lateral separation h between eddy rows has beenplotted in Fig. 6b. In the lee of Mount Vsevidof (V), hfirst increased to a maximum of about 45 km (4-20%)at a downstream distance of around 300 km and thendecreased. The width of the vortex street from thePogromni group increased gradually and that from the880 MONTHLY WEATHER REVIEW VOLUrtE105 TABLE 1. Characteristic values for the vortex streets of the eastern Aleutian Islands and Alaskan Peninsula at 1800 GMT April5, 1976. "Topographic region" refers to the predominant mountain peak (height H) in each group of peaks having an associatedwake with d the effective width of each group at the 750 m level.~ is a typical longitudinal distance between eddies in a particularrow and/, the distance between rows; L is the total length and mthe number of wavelengths; U0 is the incident or free stream speedof the wind. As a comparison, values for Kiska Island in the western Aleutian Islands are also shown (Lyons and Fujita, 1968). Inthis case d was measured at the 100 m level. The parentheticalvalue for d excludes the contribution from Roundtop Mountain(see Section 4).Topographic region H d a ~ L U 0(location) (m) (kin) (kin) (km) (km) rn (ms-l)Pavlof Volcano(Alaskan Peninsula) 2518 18 65. 25 370 2 10Shishaldin Volcano(Unimak Island) 2857 32 75 35 630 7 I0 (23)Pogromn[ Volcano(Unimak Isalnd)2002 13 50 30 370 6 10Mount Vsevidof(LInimak Island)2109 17 75 35 390 5 10Kiska Island 1216 18 85 25 475 3 10Shishaldin group remained nearly uniform up to theregion of their coalescence, after which there was asharp decrease in the width of the vortex street. Aswith representative values for the wavelengths, thewidths of the vortex sheets in Table 1 have beendetermined at downstream distances of 200 km.d. Calculated properties of the flow field Table 2 gives the characteristic parameters for the.vortex streets based on the 9bserved quantities inTable 1. The average ratios/~/d for the Shishaldin andVsevidof groups can be seen to fall within the range(1) and are typical of local values obtained along thewake. An anomalously high value of 1.0, however, occurred in the area of mergence between the Shishaldinand Pogromni vortex streets. Moreover, the local valuesof h/a for the Pogromni Volcano vortex street werehighly variable and generally inconsistent with (1)an aver'age of all possible ratios yields 0.66. Similarly,local values of h/a for the vortex street associated withPavlof Volcano typically exceeded the range (1), although the value in Table 2 was indicative of the welldefined portion of the wake. For want of a better alternative, we have usedUe/Uo-~0.75 in accordance with Chopra and Hubert(1965) to obtain the dddy propagation speed Ue. Determination of the remaining quantities is then based onthe formulas of Section 2 assuming/S= 1.75X 10-3. The numerical values listed in Table 3 have beenderived from theoretical results apphcable to classicalK~rman vortex streets using the data in Tables 1 and2. For a derivation of the appropriate equations werefer the reader to Chopra and Hubert (1965) and toWilkins (1968). Finally, quantities pertaining to the'~~ 5ox 0Ig~ ,oo[ o O x Xx x X x x x XA A X A DO 0o,% oO -IIO0' 200 300 400 5 0 6 0 DOWNSTREAM DISTANCE (km)o>150IOO50 x s x ~ x ~ x Xi i i i i i05-I oo o 0 O- ~0+ + O 0 100 l~00 :5OO 4_ 0 DOWNSTREAM DISTANCE (kin) '~00Fro. 6. Wavelength a (a) and separation h (b) between vortexrows as a function of downstream distance from the mountainbarrier for the vortex streets of Fig. 3a: (X) Shishaldin group;(/x) Pogromni group; (c) Vsevidof group; (q-) Pavlof group.Solid circles give the total width of combined wake downstreamof Unimak Island.remaining wake patterns in Fig. 3a have been listed inTable 4, with an approximate eddy viscosity obtainedfrom Table 2. In connection with the quantities inTable 3, it should be noted that laboratory experiments TABLE 2. Calculated values from Table 1 that characterize thevortex streets and associated flow field. U~ is the propagation speedof the eddies taken here as 0.75 Uo, T the period of the eddy pair 'formation and n the frequency of formation, K the eddy viscosity;R the Reynolds number based on K; and S the Strouhal number(see Section 2).Topogra'phic U, T = 1/n Kregion ~/fi (m s-~) (h) (m~ s-t) R SPavlof Volcano 0.38 7.5 '2.4 1.5 XI0a 120 0.21Shishaldin Volcano 0.47 7.5 2.8 1.8X10a 183 0.32 (128) (0.23)Pogromni Volcano 0.60 7.5 1.9 1.2 X10a 112 0.19Mount Vsevidof 0.47 7.5 2.8 1.8 x10a 97 0.17Kiska Island 0.30 7.5 3.1 1.9 x 10~ 100 0.16JULY1977 R.E. THOMSON, J. F. R. GOWER AND N. W. BOWKER 881 TABLF~ 3. Calculated values for the vortex streets based on the theory for idealized Kgrm~.n vortex streets and the results of Tables 1and 2. The drag coefficient C~> ~ hid; the circulation r = 2a (U0-- U~) coth Orh/a); the drag per unit height D = (pr2/2ra) + (pKh/a)(2 U~-U0); the rate of energy dissipation per unit mass ~=P~/(8rr2to)[1--exp(--r2/2Kto)], where r=20 km and to= T/2; the decaye-folding time t~=r-4K where r=20 km; and T* is the age of the oldest observed eddy. F D ~ te T*Topographic region CD (m~ s-~) (kg s-2) (J kg-~ s-~) (h) (h)Pavlof Volcano 1.4 3.9 X 10~ 4.4X 10~ 11.1 X 10-4J 18.4 13.7Shishaldin Volcano 1.1 4.2 X l0t 4.5 X 10~ 11.2 X 10-4j 15.9 23.0 (L5)Pogromni Volcano 2.3 2.6X l0t 2.6X 10~ 6.4x 10-~J 23.9 > 13.7Mount Vsevidof 2.1 4.2 x 10~ 4.5 X 10* 11.2 x 10-4J 15.9 14.5Kiska Island 1.4 7.0X 10* 10.9X 10* 27.4X 10-~J 14.6 14.7with bluff bodies indicate that only 66% of the initiallygenerated circulation actually becomes available toform an individual vortex (e.g. Mair and Maull, 1971).On this basis, the estimates of I' in this table may betoo large by a factor of 1.5, and the subsequent estimates of the drag and energy dissipation too large bya factor of about (1.5)~.4. Discussion and conclusions Contrary to most previously observed atmosphericwakes, the patterns of Fig. 3a appear to have beenassociated with groups of mountain peaks rather thanwith isolated islands. Such an interpretation is consistent with the occurrence of two distinct vortexstreets in the lee of Unimak Island and the threesmaller wakes in the lee of the southwestern tip of theAlaskan Peninsula. Vizualization of the flow fields in thiscase was made possible by an extensive cover of wellstructured stratocumulus cloud streets lying along thewind between 500 to 1000 m MSL. An inversion havinga base altitude of about 1000 m over the topographicrelief apparently ensured that the incident winds wereforced around the higher mountain barriers. The estimated age of the oldest eddies in each vortex trail TABLE 4. Characteristic values for the non-vortex wakes in thelee of the eastern Aleutian Islands and Alaskan Peninsula at 2008GMT April 5, 1976.//is the height of the highest peak within eachgroup producing the wake, d the effective diameter at an elevationof 750 m, U0 the incident wind speed; K a typical eddy viscosityfrom Table 2 and R the Reynolds number.Topographic region // d U0 K (Location) (m) (km) (m s-~) (m~ .s-1) RMount Dutton (Alaskan Peninsula) 1473 7 10 1.6X 10~ 44Frosty Peak (Alaskan Peninsula) 1763 8 10 1.6X10a 50Akutan Peak (Akutan Island) 1890 7 10 1.6X 10a 44Makushin Volcano (Unalaska Island) 2036 14 10 1.6X 10a 87 (Table 3) was consistent with the maximum duration Of northerly winds that could have initiated the wake patterns. a. Flow characteristics Based on derived values for the kinematic eddyviscosity, the Reynolds numbers for the flows associatedwith the four vortex streets were well within the stablerange (2) for K&rm&n-type vortex streets that formbehind circular cylinders. The results of Tables 2 and4 indicate, moreover, that the critical Reynolds numberfor these particular atmospheric conditions was around92, midway between the value of 87 for the quasisteady Makushin wake and 97 the well-defined Vsevidofwake. This value is at least consistent with Gaster'sexperiments which showed that the critical value ofthe Reynolds number increased as the taper of thecones decreased. Although the taper of the mountainpeaks is about two orders of magnitude smaller thanthat of the laboratory cones, vertical motions in theunstable air below the inversion would have increasedthe effective taper of the mountainous regions to bringthem more in line with Gaster's models. Moreover,the increase in wind speed with height partially com. pensated for the relatively rapid vertical decrease inthe width of the mountain barriers; as with the coneexperiments, therefore, the local Reynolds number wasa slowly changing function with distance "up" thebarrier. (Typically, R increased by less than 10% between the altitudes of 750 and 1000 m for the fourmountainous regions generating vortex streets.) The vortex street associated with the Vsevidof group of peaks had a Reynolds number of about 100 and most closely resembled the stable and laminar vortex streets observed behind cylindrical models in the lab oratory (c.f. Gaster, 1969). Similarly, the vortex trails behind the Pogromni and Pavlof groups closely re sembled laboratory patterns over a considerable portion of their length, suggesting that for Reynolds numbers at least as large as 120 the observed vortex streets in the wake of the Aleutian Islands were also stable and laminar. In comparison, the vortex street downwind of Shishaldin Volcano were somewhat irregular, with poorly formed vortices on the left side of the wake882 M O N T H L Y W E A T H E R R E V I E W Vo~xJ~m 105(looking downwind) but well-structured vortices onthe right side. Ostensibly, this unsymmetrical structurewas related to the fact that the relatively high Reynoldsnumber of 183 for the flow approached the transitionvalue from laminar-like to partially turbulent vortexstreets. On the other hand, it is also possible thatstructure of the Shishaldin vortex street was due to theoblong shape of the 750 m contour presented by thethree mountain peaks in this region and to the factthat the lowest elevations occurred on the left side ofthe incident wind direction. The mountain barrier maytherefore have been behaving more as an irregularlyshaped plate than a circular cylinder. Since the Reynolds numbers for the wakes in thelee of Makushin Volcano, Frosty Peak and MountDutton were below the critical value, only laminar-likestreaming took place. Nevertheless, the presence inthese wakes of long sinusoidal oscillations that increased in amplitude downstream would suggest thatfor Reynolds numbers as low as about 40 the incidentflow was unstable to small disturbances. In this particular group of wakes, however, only the one behindFrosty Peak appeared to develop into a pattern resembling a vortex trail. With the exception of the Shishaldin wake, theStrouhal numbers in Table 2 for the vortex streets ofFig. 3a were within the laboratory range (8). If, however, we assume that the contribution from the lowerpeak, Roundtop Mountain, was not a factor in theformation of the Shishaldin wake, we find d~23 km,R ~ 123 and. S ~ 0.23 (numbers in parentheses in Tables2 and 3) which are in closer agreement with the otherobserved values. Furthermore, the associated drag coefficient of ~ 1.5 would appear to be more realistic. Onthe other hand, if we consider that the conically shapedRoundtop Mountain reaches an altitude of 1910 m andhas a base diameter of 5 km at the 750 m level it is0.40m. 0.30figz 0.~0fig~ 0,10~10 I I I I00 150 200 250 3~0 REYNOLDS NUMBER, R FIO. 7. Strouhal number versus Reynolds number for the vortexstreets of Fig. 1: X (see Table 2); Kishka Island (/x); MadeiraIsland (~); Johnston Atoll (~1); and Cheju Island (O). Thedashed line approximates a best-fit of Roshko's (1954) experimental results [-cf. Eq. (2.7)-1.difficult to justify its omission, nor will doing so accountfor the irregularity of the vortex street. Another difficulty with respect to the Strouhal number is that thevortex shedding frequency here is not an independentlymeasured parameter but is related to the Reynoldsnumber via ~. This accounts for the straightline relationship between the open data points in Fig. 7 inwhich S is plotted against R for both mesoscale andlaboratory-scale vortex streets. In contrast, Tsuchiya(1969) was able to obtain a value for n based upon twosatellite images taken within slightly less than onevortex shedding period. The extreme values for hisranges of S and R have been included in Fig. 7 and forlarge R can be seen to agree closely with the laboratoryresults.b. Wake formation According to various laboratory investigations, thereexist two different mechanisms for vortex formationand shedding in the stable Reynolds number range(Papailiou and Lykoudis, 1974). The first involvesvortex formation by an instability that grows downstream within a laminar wake, while the second mechanism involves a "double vortex street" laminar instability in which the vortices are shed near theobstacle. ]-Gaster (1969, 1971) on the contrary hasattributed the existence of these two modes to nonuniformities in the incident flow.-] For Reynolds numbersbetween 200 and 10~, a "single vortex street" instabilitydevelops in each of the two vortex layers created on thecylinder. The rolling up of these layers then results ina periodic generation of secondary vortices. Furtherdownstream, a "double vortex street" is eventuallycreated and dominates the flow. The first mechanism appears to be applicable to thePavlof vortex street which did not develop into avortex street until far downstream. There was alsosome indication that the instability in the Frosty Peakwake eventually developed into a vortex street. Thesecond mechanism was most likely responsible for thevorte~ trails that formed immediately behind MountVsevidof and Pogromni Volcano. Vortices in each ofthese wakes would have been shed in alternating pairswith some exchange of circulation between adjacentrows taking place as the fluid moved downstream. Although the Reynolds number for the winds incident upon the Shishaldin group of peaks was slightlybelow the range for the single vortex street instability,this mechanism may have accounted for the fact thatonly the right-hand vortex layer developed into welldefined vortices. On the opposite side, the instabilitywas possibly too weak to deform into vortices. Such aninterpretation is further consistent with laboratory results in that the Shishaldin wake developed along thelines of a double vortex street instability far downstream. The latter development may also have beenresponsible for the coalescence of the Shishaldin andJULY1977 R.E. THOMSON, J. F. R. GOWER AND N. W. BOWKER 883Progromni vortex streets. An alternate explanation forthe spatial coalescence of the two Unimak vortexstreets, involving the generation of the combined vortextrail at an earlier time when the winds were more fromthe northeast, will be discussed presently.c. Vortex breakdown The spatial transformation of the Vsevidof vortexstreet into a "turbulent" trail occurred after roughlyfour wavelengths. This trail, bordered by stratocumuluscloud streets, then persisted an additional 150 kmbefore becoming lost in the general cloud structureover the North Pacific Ocean; degeneration of theadjacent Makushin Volcano wake into a turbulent-likecloud structure showed a somewhat similar kind ofbehavior. The possibility that the collapse of .theVsevidof wake was related to a low-frequency modulation analogous to that reported by Gaster (1969, c.f.his Fig. 8b) has been ruled out here since the modulation frequency Uo2/K, based on the kinematic eddyviscosity, was only about 0.06 s-L Therefore the lastvortex observed in Fig. 3a marked the full extent ofthis particular vortex street. The most spatially persistent vortex pattern at thetime of Fig. 3a was that in the lee of Unimak Island.Three clear areas in the cloud, two of them almostperfectly circular, presumably delineated the last vortices in the total wake. The larger of the two circular"vortices" had an estimated age of 16.5 h and a diameter of about 20 km, which is consistent with our choiceof r = 20 km in Table 3 with an e-folding time of 15.9 h.A similar crude estimate can be made for the Vsevidof- vortex street to show that the vortex diameter of 20km with an e-folding time of 15.9 h was consistent withthe width and age of the oldest eddy in the wake. Also,the downstream distance of 370 km for the region ofcoalescence for the two Unimak Island vortex streetscoincided with the maximum extent of the Vsevidofvortex street. Although the kortex streets in Fig. 3a appeared tobreak down by becoming unstable downstream, thereis an alternate explanation that should be mentioned.Using an eddy propagation speed of 7.5 m s-1 we findthat the distance of 370 km, corresponding to themaximum extent of the Vsevidof vortex street and thedownstream region of coalescence for the two UnimakIsland vortex streets, gives a lapsed time of 13.7 h.Subtracting this from the time of the satellite photograph yields 0630 GMT 5 April. If we then refer tothe weather maps for this time (0600 GMT) and alsointerpolate the radiosonde data from Fig. 5 between0000 and 1200 GMT, we find that the winds above analtitude of 500 m were directed along rather thanacross the eastern end of the Aleutian Island chainwith speeds of about 7.5 m s-~ at the 750 m level. Theseconditions, which prevailed for approximately 6 h priorto the formation of the last vortex in the Vsevidofwake, when combined with the effective mountaindiameter of 7.5 km, then give a Reynolds number of31. Since this was appreciably below the criticalReynolds number, the spatial termination of theVsevidof vortex street may simply reflect earlier windconditions in the overall wake development. Similarly,the temporal alteration of the Unimak Island patternfrom one to a pair of vortex streets may have derivedfrom earlier wind conditions. In this case, however,7.5 m s-~ winds blowing exactly parallel to the islandwould have seen an effective diameter of only 16 kmfor a Reynolds number of 67. Since this would notaccount for the single vortex street, the winds musthave been incident at a slight angle to the Shishaldinmountain group. Increasing the angle of attack by 10-north for example gives an effective diameter of 30 kmand a Reynolds number of around 125. Thus the wakein the lee of Unimak Island would have first developedas an unstable trail, then into a single vortex street asthe winds became progressively more northerly, andfinally into a pair of vortex streets as the wind directionchanged to northerly and northwesterly. The latter sequence of wind directions (and associatedvariable wind strength) may also account for the narrowness of the Vsevidof wake far downstream (Fig. 6b).At such earlier times in the formation of the vortexstreet, the effective width of the Vsevidof group ofmountain peaks and its associated wake would havebeen relatively narrow compared to later times whenthe wind was directed perpendicular to the islandchain. The spanwise diffusion of vorticity was apparently not enough to compensate for this effect. At latertimes, however, the winds were more constant in direction and the wake showed a definite downstreambroadening. In summary, the vortex streets analyzed in thispaper appear to be the atmospheric analog of Kf~rmgntype vortex streets that develop in the wake of bluffbodies in laboratory experiments. As noted by variousauthors in the past, the close similarity between thesetwo flows is somewhat surprising considering that thelaboratory patterns are small scale and are typicallyobserved behind regularly shaped bodies in homogeneous two-dimensional flows, while the atmospheric patterns are mesoscale and develop behind irregularlyshaped barriers in strongly stratified shear flows. Inmany respects, the results presented here supportpreviously obtained values for the kinematic eddyviscosity and characteristic properties of the mesoscalevortex streets. A number of features however are distinctive: 1) we have dealt with a group of fully delineated wake patterns that developed in the lee ofisolated mountain barriers; 2) the vortex streets wereformed in the presence of a comparatively weak inversion; 3) the vortex shedding frequencies weregenerally higher than previously reported; 4) a criticalReynolds number was determinable and found to be884MONTHLY WEATHER REVIEWVOLUME 105consistent with laboratory experiment with highlytapered cylindrical cones; and 5) the three distinctmechanisms for laboratory vortex street formation weredistinguishable in the development of the atmosphericwakes. Acknowledgments. We acknowledge the kind assistance of the U. S. National Climatic Center, Asheville,and Mr. F. Eddy of the Atmospheric EnvironmentService, Vancouver Airport, for providing us withatmospheric data. Our thanks also to Professor PaulLeBlond for his valuable comments during preparationof the manuscript and to MacDonald, Dettwiler andAssociates Ltd. for providing us with the satellitephotographs. REFERENCESAbernathy, F. H., and R. E. Kronauer, 1962: The formation of vortex streets. J. Fhdd Mech., 13, 1-20.Barkley, R. A., 1972: Johnston Atoll's wake. J. Mar. Res., 30, 201-216.Chopra, K. P., and L. F. Hubert, 1965: Mesoscale eddies in wake of islands. J. Atmos. Sci., 22, 652-657.Gaster, M., 1969: Vortex shedding from slender cones at low Reynolds numbers. J. Fluid Mech.; 38, 565-576. , 1971: Vortex shedding from circular cylinders at low Reynolds numbers. J. Fluid Mech., 46, 749-756.Gossard, E. E. and W. H. Hooke, 1975: Waves in the Atmosphere.Amsterdam, Elsevier, 221-222.Heffter, G. L., 1965: The variations of horizontal diffusion pa rameters and travel periods of one hour or longer. J. Appl. Meteor. 4, 153-156.Hendry, R., and C. 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