MONTHLY WEATHER. Editor, JAMES E. CASKEP, JR Closed May IS, 1954

Transcription

1 ~~ DEPARTMENT OF COMMERCE SINCLAlR WEEKS, Scrtary WEATHER BUREAU P. W. REICHEISWPER, Chid MONTHLY WEATHER REVIEW Editor, JAMES E. CASKEP, JR. Volum 82 MARCH 1954 Closd May IS, 1954 Numbr 3 bd Jun IS, 1954 i? * ESTIMATION OF FRICTION OF SURFACE WINDS IN THE AUGUST 1949, FLORIDA HURRICANE RUSSELL E. JOHNSON Hydrolcqic Srvics Division, U. S. Wathr Burau, Washington, D. C. [Manuscript rcivd Jun 3, 1953; rvisd March 4, ABSTRACT Th quations of motion ar adaptd for us in computing th tangntial and normal componnts of friction in a modl hurrican. Valus of th componnts of friction ar stimatd from surfac data of th August 1949 Florida hurrican. Th computations ar basd upon man prssur and wind profils dscribing th front and rar portions of th storm, within 28 to 7 mils from th cntr, as it movd through th Lak Okchob rgion. Th tangntial componnt of friction appars to b gratr than th normal componnt in th rgion to th rar of th cntr, whil in advanc of th cntr th opposit is gnrally obsrvd. All friction curvs show a continuous incras of friction with wind spd. INTRODUCTION In coopration with th Corps of Enginrs, U. 5. Army, th Hydromtrological Sction of th Unitd Stats Wathr Burau has bn invstigating surfac winds of hurricans, with particular intrst in th rgion of Lak Okchob, Fla. On phas of th invstigation was concrnd with th forcs rsisting surfac winds. Although th frictional forcs lud xact masurmnt, thir importanc to th bhavior of surfac winds is radily apparnt. A familiar approach to th problm of computing friction is through th thory of th mixing lngth, assuming that th mixing lngth can b dtrmind and that th vlocity distribution, spcially along th vrtical, is known. This mthod is discussd in dtail by Rossby and Montgomry [l]. Sinc th hurrican data availabl to th Sction wr markd by an absnc of uppr air obsrvations, furthr considration of th mixing-lngth thory was ncssarily liminatd. Th quations of motion, thrfor, wr dvlopd in a form suitabl for us with hurrican surfac data to comput friction. Thir dvlopmnt and th rsults subsquntly obtaind ar prsntd in this papr. THE EQUATIONS OF MOTION Th quations of horiontal motion may b writtn -.-"-Ly--F, dua- bp dt bs whr, is th spd along th path, s; Ta, radius of curvatur of s, is positiv for cyclonic curvatur; t is tim;f th Coriolis paramtr; a th spcific volum; p th prssur; n, a normal to s, is dirctd opposit to th Coriolis forc; and F, and F, ar th componnts of friction, tangnt and normal, rspctivly, to th path. For convninc in a study of friction th abov quations ar rwrittn Friction is dfind hr as th sum of all forcs which ar -.

2 74 REVIEW WEATHER MONTHLY MARCH 1964 du to friction and viscosity. In addition to th friction arising from flow ovr a rough ground surfac, it includs th ffcts of latral ddy viscous forcs, whthr acclrativ or rtardativ, imposd by adjacnt air currnts. METHOD OF CALCULATING THE FRICTION IN A MODEL HURRICANE Th solution of quations (2) for a modl hurrican, charactrid by a stady stat of man flow, circular symmtry, and constant latitud, is givn in this sction. It is sn from th working modl, shown in figur 1, that ds = -&sin (3) dn = - drcos 9 whr r, th distanc from th cntr, is dirctd outward, and is th dflction angl of th wind as masurd from th normal of r to th tangnt of th trajctory s. Sinc th man flow has bn assumd to b stady, In accordanc with Yats [2], th radius of curvatur of 8 spiral may b writtn dr r8=t d4 whr p, a normal to th tangnt of th spiral, is drawn from th origin as shown in figur 1. From figur 1 it is sn that qlr=cos (6) Diffrntiating quation (6) with rspct to r and substituting th rsult into quation (5) givs r, = cos r " 1 d sin 9 - dr Substitutionfrom quations (3), (4), and (7) into quations (2) givs FIOUXE 1.-Hurrican modl. pc=valu of a circular isobar. r=distancc from th cntr, dirctd positiv outward. s=path of air particl, dirctd positiv in th dirction of motion. O=Ddction angl of th wind across a circular isobar. n=normal to 8, dirctd opposit to th Coriolis forc. p=a normal to tangnt of path, drawn from cntr. INSTRUMENTATION Th Corps of Enginrs maintains mtorological obsrvation stations at svn hurrican gats on th shor of Lak Okchob and thr wind-rcording stations on stl-girdr pylons within th lak. Th station locations ar shown in figur 2. Estrlin-Angus multipl pn rcordr tracs ol th wind spd and dirction wr availabl for th lak stations. Dins anmomtrs at th hurrican gats providd continuous hracsofwind spds and dirctions xcpt for Hurrican Gat No. 3 whr wind spds only wr availabl. Th hurricangat stations also providd barograph tracs. Th hights of anmomtrs ar givn blow in tabl 1. Th watr surfac is about 14 ft. msl and th land surfac 14 to 16 ft. msl. TABLE 1."Anmomtr hight at obsrvation stations at Lak Okchob

3 ~ ~~~~ -E 1954 MONTHLY WEATHER REVIEW METEOROLOGICAL INSTALLATIONS ON LAKE OKEECHOBEE. FLORIDA FIQUUE Z.-Map of Lak Okhob ma showing locstion of obsrvation stations. ESTIMATION OF FRICTION IN THE AUGUST 1949 FLORIDA HURRICANE Th mthod prsntd for calculating th friction was drivd by assuming a symmtrical hurrican with stady man flow and no variation in latitud. Ths assumptions wr convnint in ordr to arriv at an xact mathmatical xprssion for th friction. Although th assumptions may b rasonably wll satisfid in natur by a quasi-stationary hurrican showing littl chang in intnsity, no hurrican is xpctd to satisfy th assumpdons prfctly. Bcaus an idal systm is lacking, cbmputd valus of friction must proprly b rgardd as Bstimats. Although th data of this hurrican wr th bst &?ailabl to th Hydromtorological Sction, thy wr not ntirly satisfactory. Insufficint synoptic data ld to th us of obsrvat,ional historis of th 1 stations at Lak Okchob. Th basic data wr xtractd at 1-minut intrvals from rcording charts. Bcaus of th fluctuations in wind spd and dirction, ach wind datum was xtractd as a IO-minut avrag valu. Th dflction angls of th windwr masurd with rfrnc to circls having thir origin at th rotation cntr. Th locations of th stations rlativ t,o th hurrican cntr, whos path is tracd in figur 3, wr dtrmind for succssiv 1-minut positions of th cntr for th tims corrsponding to thos of th data xtractd from th station rcording charts. Th station- FiOURE 3."Sction Of SUf8C chart for 33 OMT, August 27, 1949, showing cun'mt POSftion and path Of hurricm. location data usd with th station rcords dtrmind th wind spds, dflction angls, and prssurs for positions in th hurrican. Thus, ach station furnishd data for svral positions in th front and rar portions of $h storm. Th data usd for th front wr obsrvd during a 5-hour priod as th storm movd 85 to 9 mils northwstward toward Lak Okchob. Th cntral prssur of th storm rmaind narly constant within th rang to 28.2 inchs. Th data usd for th rar wr obsrvd during a 5-hour priod in which th storm progrssd about 65 mils in th rgion byond th Lak and th cntral prssur ros from about 28.2 to 28.4 inchs. Th data obsrvd at ach 1-minut position of th storm ar plottd in figurs 4-6. For any givn station ths plottd points will of cours b spacd farthr apart th fastr th movmnt of th storm cntr and th closr th station lis to th path of th cntr. Man curvs basd only upon ths plottd points would thrfor b biasd in favor of thos stations which, bcaus of thir locations, providd a gratr numbr of obsrvations

4 76 MONTHLY WEATHER REVIEW MARCH 1954 FIQUBIE &-Man wind spd proflls, ach compard with a Rankin Vortx, for front and rar aras of hurrican of August 1948.

5 MUCH 1954 WEATHER MONTHLY REVIEW w w 45 $ 4 * 35 3 I- 25 d 2 : 15 IO I T 5 45 ;5 -I IA I5 5 IO g 5-5 -I - 5: -1 -I 5 -I FIGURE &-Man dflction angl profils for front and rar aras of hurrican of August within th part of th storm rprsntd by th curvs. With th purpos of allowing all stations to hav qual influnc on th curvs, intrpolations wr mad from a tabulation of th 1-minut obsrvational data for ach station in ordr that vry station might b rprsntd by data, obsrvd or intrpolatd, at vry mil distanc from th cntr. During th 1-minut tim intrvals btwn obsrvd data, changs wr vry small and linar intrpolations within ths small incrmnts appar to b bhly satisfactory. Th complt tabulation of obsrvd and intrpolatd data was usd to comput arithmtic avrags of prssur, wind spd, and dflction angl for vry mil distanc from th cntr. Thus, qual wight was givn to all stations in dtrmining th man profils shown in figurs 4-6. Although th data of tjh svral stations on which ach of ths curvs is basd wr obsrvd ovr a 5-hour priod, t,h avrag tims of th data corrsponding to th points on a curv all fall within a priod of only about 234 hours. Sinc th cntr of th hurrican passd within 28 mils of vry station at Lak Okchob it was possibl to construct th curvs for th rgion outsid th 28-mil radius. Continuation of ths man curvs within th 28-mil radius was not prmittd in viwof a bias introducd by th dcras in th numbr of obsrving stations with narnss to th cntr. Extn- sion of th curvs byond 6 or 7 mils from th cntr was not possibl bcaus of th uncrtain position of th cntr whn it was locatd out at sa and latr bcaus of th filling which occurrd aftr th cntr had movd byond Lak Okchob. It can b sn from figur 3 that th storm cntr movd ovr th northastrn part of th Lak and, hnc, most of th data wr from th lft sid of th storm. At all stations th winds wr influncd by both land and watr in proportions which varid with ach chang in th rlationship of th wind pattrn to th land-watr distribution. Th mixd influnc of land and watr in various proportions contributd to th scattr of obsrvd wind valus. In figur 5 th sparation of points plottd for th rar of th storm into two groups according to wind spd is du to rlativly larg diffrncs in th proportional influnc of land and watr. Sinc th winds wr undr a mixd influnc, it was not possibl to mak a comparativ analysis of pur-watr and pur-land winds. By using th man curvs, figurs 4-6, with quations (8), th man friction was stimatd at a sufficint numbr of distancs from th rotation cntr to dfin th friction curvs shown in figur 7. In th computations th air was considrd saturatd at 75O F. and th latitud was takn as 27' N.

6 78 MONTHLY WEATHER REVIEW F 8.75 :- 2.5 : ( F a 1.5 ylj tq I w 1.26 I (I 1. F, s Normol componnt of mon friciion..maech 19% m 2.75 ; 2.5 k 2.25 i I 2." $ - 1, i (.75 5.so I I UI 25 ')\ -,* 3 " SO I IO I5 o DISTANCE FRONT \ ) FROM CENTER ROTATION (Milsr) REAR FIGTJBE 7.-Distribution of man friction in front and rar aras of hurrican of August \ \ $ 1. 1.,75 -,25 u, E & 2.5 L.I a 2.25 * c ".2. L I- o p 1.5 LL f 1.25 W 3 In6.75.so oc) " 5 IO I5 2 MEAN MEAN WINDSPEED IMilES pr now) E 2.5 : 2.25 m 2.m :!.75 c 1.5 p Y 1.25 'W Lo =.75 SO,25 FIGUBE 8.-Rlatiom of componnts of man friction to man wind spd for front and rar araa of hurrican of August 1849.

7 MAECH 1954 MONTHLY WEATHER REVIEW 79 DISCUSSION Th darth of data from th innr rgions of th storm xcludd th most intrsting ons from this study. Only six stations xprincd th hurrican within th radius of maximum winds. On th basis of thir rports thman valus of windspd and dflction angl in front of th storm cntr wr gratst at a radius of 25 mils. In th rar of th cntr th gratst man valu of wind spd was indicatd at a radius of 22 mils. Unlik th forward portion of th storm, th rar portion was not markd by a radius having a pak valu of th man dflction angls. Th man dflction angls in th rar showd a continuous incras with distanc from th cntr until a constant valu was rachd at th 45-mil radius. In ach part of figur 5 a graph of th wind-spd distribution in th outr portion of a Rankin Vortx is includd for comparison. Th friction curvs in figur 7 show th variations of th tangntial and normal componnts of man friction with rspct to distanc from th rotation cntr of th hurrican. It would b xpctd that th tangntial componnt is gratr than th normal componnt. This was, in fact, found to b th cas in friction computations by Horiguti 131, whn t>h quations of motion wr applid to man data of th Okinawa typhoon of August Whil Horiguti s data wr of th rgion of th typhoon btwn 62 and 435 mils from th cntr, th data lading to th analysis givn hr wr from th rgion within 7 mils of a st orm cntr and wr tratd sparatly for th front and rar portions of th storm. In th prsnt analysis, th tangntial componnt again was found to b gratr than tlh normal componnt in th rgion to th rar of th cntr. But in front of th cntr, as shown in figur 7, th normal componnt gnrally appars to b th gratr. Th rlations of th tangntial and normal componnts of man friction to manwindspd ar prsntd in figur 8. Each curv shows a continuous incras of friction withwind spd. Th numbr bsid ach plottd point indicats th distanc from th storm cntr. Errors introducd in th computations by assuming horiontalflow, constant virtual tmpratur of surfac air, and a man latitud ar considrdngligibl. Th subjctivity in masuring slops of th basic curvs is rsponsibl for som rror in th rsults, but carful masurmnts hav kpt this rror small. Th rprsntation of th front and rar portions of th hurrican as parts of symmtrical systms in stady man stats, by man curvs, srvd in arriving at stimats of man friction. Although th man curvs hav a virtu in liminating local ffcts imposd upon th rprsntativ flow, thr may b an objction to comprhnsiv mans which obscur larg-scal dynamic influncs charactristic of diffrnt sctors of th storm. In computations of man friction th rsults can vary with th mannr of dfining th man flow. Hnc, thr is no critrion for judging rrors incurrd through th us of man flows. Without obsrvational data through th vrtical, thr is no way for dirct vrification of th rsults. With th aid of uppr air data th mthod prsntd in this papr may provid a mans of vrifying th standard thortical formula for computing friction. ACKNOWLEDGMENTS Th writr xprsss thanks for th hlpful commnts of mmbrs of th Hydromtorological Sction in th prparation of this articl. Spcial acknowldgmnt is du R. W. Schlomr of th Sction for his stimulating rol in discussions during th analysis of th data. Th figurs wr drawn by th Drafting Unit of th Hydrologic Srvics Division. REFERENCES 1. C.-G. Rossby and R. B. Montgomry, Th Layr of Frictional Influnc in Wind and Ocan Currnts, Paprs in Physical Ocanography and Mtorology, vol, 111, No. 3, Massachustts Institut of Tchnology and Woods Hol Ocanographic Institution, Cambridg, Mass., April R. C. Yats, A Handbook on Curvs and thir Proprtis, J. W. Edwards Go., Ann Arbor, Mich., Jun 1947, p Yosiki Horiguti, On th Typhoon of th Far East, Part 111. Winds in th Typhoon Ara, Mmoirs of th Imprial Marin Obsrvatory, Kob, Japan, vol. 111, No. 3, Jun 1928, pp (s pp ).