satellite pictures of mesoscale eddies

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SATELLITE PICTURES OF MESOSCALE EDDIES L. F. HUBERT and A. F. KRUEGER

U.S. Weather Bureau, Washlngton, D.C.

(Manuscript received July 30, 1962; revised September 18, 1962)

ABSTRACT

S:rtellite photographs of horizontal eddy patt,erns :Lrc presented and t,he conditions associated with their forma- tion are discussed. It is shown that some map tjc purely mechnnical eddies produced by an oh.stacle (islands) in the flow, others may be the result of inertial oscillation, and othcrs may be produced by inertial instability. Gravity waves on a low inversion are snggestcd to be the key mech:rnism producing instability.

1. DESCRIPTION OF THE OBSERVATIONS

Turbulent eddy motion in fluids has been thoroughly studied in connection wit'll I I I ~ ~ J - applictltions of h$ro- dynamics. Jn nleteorology, turbulent eddies, which are the basic mechtlnistrl of diffusion, :mtl cyclones w11ich are eddies on the planetary scalc, have heen identified : m l their (irking ~nechanisn~s arc rather well understood. Satellite pictures presented here show rnesosctlle eddies produced by obstacles in the airflow, some persisting great' distances downstream. Their long lifetime appears to be inconsistent with the rate of decay expected for solrlc types of eddies; therefore t'heir source of energy poses : r n interesting question.

This note has two object'ives-first, i t shows that' their interpretation as LLnlechmic:d eddies" or traveling pressure waves produced by an obstacle in the flow is probably inadequat'e t'o explain their persistence great distances tlownstrealrl; second, it suggests R rllech:misrn to explain their persistence. The term "tnechnnict~l eddies" is used here to tnetm perturbat'ions in t'he basic flow with sufficient inertia to mainttain eddying velocities superinlposed on the initial velocity field; thus, when the inertia is dissipated the eddy components disappear. A von KBrmBn vortex street is an example of this phenon~enon.

Figures I , 2 , and 3 show eddies in stratocunlulus clouds downst'rennl from SZadeira Island; figure 4 shows :r remarkable development of this pattern downstrean1 from the Canary Islands group. Figures 1, 3, ;rnd 4 tire TIROS pictures while figure 2 is from a 70-lnln. film exposed on Project Mercury flight 11A-4. This type of eddy has been recorded on quite tl few occasions by satellite photography,' but it' may well be a more common occurrence often invisible because no clouds delineate the pattern for our cameras. Such a case is shown on the MA-4 film, figure 2 , a n example of R pattern so poorly developed that i t was not seen on a TTROS J I I picture

I 9 comprchcnsive collcction of picturcs of cddirs in various slapcs of devrlopment is currently hcinp asscmhled hy 11. 31. Johnson, McteoroloFical Satellite Lahoratory.

t'uken ;It about the sitme tilne. All eddies examined in the Atlantic exhibit' the following characteristics:

1. Their scde is of the order of 100 ~ I I I . or slightly sllldler.

2 . The>- occup\- 21 band tlpprosinlately as wide as the obstacle (island or island group) in the flow.

:3. They lie d o w ~ ~ s t r e i t ~ ~ l fro111 the obstacle, sotnetimes for great distances. Where pictures are available the eddies nppe:u- inlnlediutel- downstream tts well.

4. The visible patterns are in strntocun~ulus clouds lying beneath :L strong inversion, usunlly below 1 knl. above sea level.

Although no detailed analysis is possible, dat'tl are Sufficient to show that wind in this surface stratum blows from the islands toward the eddies a t speeds typically less than 15 kt,. The feat'ure that aroused t'he authors' int'erest' WAS the fact t'tlat these eddies are still vigorous at great distances fronl the initit~ting obstacle, such that' if one post,ulates nlechanical eddies being carried tlownstreunl >Lt parcel speeds the disturbances tare vigorous for 10 to 20 hr. Observation of curling tobacco smoke or obstacle-produced eddies in a stream show that t'he spiral pattern is quickly obliterated when the eddy components cease (or :we converted t'o smaller and smaller scale eddies--"and so on to viscosity"). For that reason it appears reasonable to discount the possibility of eddy patterns carried passively downstream many hours after the eddy components themselves have ceased.

2. LIFETIME EXPECTANCY OF EDDIES Figure 4 shows remarkably well developed eddies more

than 500 km. downstrealll from the Clunwry Islands. If they were mechanical eddies carried dowrlst'retlln with w speed of 15 kt., these disturhances must have remained vigorous for 19 hr., and it is likely that' the wind speed was considerably less than 15 kt., tllerebJ- irtlplying even greater persistence. The following argument indicates that the loss of eddy momenturll is sufficient t'o destroy

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458 MONTHLY WEA‘l’HER REVIEW SOVEMRER 3962


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FIGURE 4."Complex eddy pattern downstrram from Cutlary Islands 1400 GMT .Jaly 2 , 1062. TIROS V pass 187.


where 7, is stress along the n-axis and the other terms have their usual meteorological lneaning. When the flow is disturbed the large-scale pressure gradient is unchanged but' the work done on the air by the obstacle creates perturbation pressures and speeds in the immediate vicinity, so we might rewrite (I) ,

where the primed quant'ities represent the pert'urbation quantities added to the steady, unprirned, quantities. If we consider here onl?- random small-scale eddies, any parcel of air might' remain under the influence of a transient eddy only briefly. Thus the term (fu') can reasonablF be ignored because of' the short' time any parcel can he subjected to this force as it' t'ravels through ench eddy. Compare, for example, the length of t'irne (say, several hours) that the steady (constant direct'ion) pressure gradient' ol a generating seabreeze must be applied before the wind turns parallel t o tlle coast. If fu' is neglected, and if the corresponding equation for steady flow is subtracted from ( 2 ) ,

Equation ( 3 ) represents tlle forces in the vicinitJ- of an obstacle which generate the eddy velocity, P , and the pressure term is quasi-steady in the inlrnediate vicinit~--a standing pattern produced by the interaction of the islands and the winds. As air parcels are carried tlownstrearrl these eddies could persist either because a similar pressure pattern moves downstrearn, or by virtue of their inrrtiu, without any accelerating pressure field. Both of these alternatives, appear to be physically unrealistic for the type of eddy pat tern of figure 4, for the following reasons.

Consider first tlle possibility of R traveling pressure pattern. Conditions are favorable for S O I I I ~ type of traveling pressure pattern because these eddies have been observed along with strong, low-level inversions. Gravity waves initiated by the wind irlrpinging on an obstacle would produce a wave-like pressure pattern because ol' the changing depth of the dense surl'ace layer. Furthennore, each nleso-High and 1,ow would have a lateral extent about the scale of thc obstacle tmd the wavelength nlight be of the same scale, thus rnatcl~ing the areal extent ol' the eddies.> Such a series of Highs and Lows would not produce an eddy pattern, however, because the eddies quite certainly reflect circular flow and at this srnall scale the eddy conlponents rrlust be Enleriau, that is, the pressure gradient' must be directed alony the flow. If' oue RSSUII I~S the cloud patterns represent' strearulines and attenlpts to draw a patt'ern of isobars that would produce Eulerian flow in this pattern he will construct R very complicated pressure field, particularly for the case of

2 For example, compare the wavelength and lateral extent of waves under Yery similar

figure 4. Because the pressure pattern is produced by the variable inversion height, this complicated pattern also represents the contour pattern of inversion heights which, under this alternative, are required to move downstream as a gravit3- wave with litt'le change of shape! Consideration of wave mechanics indicates t'he traveling pressure pattern explanation is riot' satisfactory because such a complicated wave pat'tern would change shape as it propagated.

Consider the alternative explanation, that' the pressure patt,errl remains quasi-st'ationary where it, is maintained by t'he influence of' the obstacle, but that the eddies are nlaintained by their inertia, without auy moving pressure field. The deceleration of' the cross-stream component is then:

111; 1 bTn - " ~ -

rlt-p bn (4)

An experirnental project IVBS carried out in 1953 to nleasure stress and its vertical variation in tlle trade winds by C'harnock et a1. [3]. Typical values from that work are used in the following, but it' should be borne in mind that, the eddy lifetime estirnate rllatle on this basis is an overest i r~~ate because r~~o~r~entunl loss along the I~orizontd is ignored.

I n general it is entirely proper to consider only terms b ~ , / b s ant1 d ~ , / b z even though the complete stress tensor contains six terrns. The four neglected terms all depend upon horizonttll variations of' stress which in turn are proportional to horizontal wind shear. Therefore, t'he neglect~etl terllls are usually an order of magnitude less than retained terms. Consider, however, tlle speed pro- files of eddies pictured here; within a few hu~~t l r ed meters aloug horizontal aze.5 the unperturbed basic current' must incwxse (or decrease) by :I large fraction (for reasons stated below) so that the tleceleration by friction may be grossly underestimated by neglect of the horizontal shear terrns. Quirlittltively i t is easy to understand this. In the undisturbed state, the flow can be considered llorizontully uniform so the 1n0111entur11 flus is dong the vertical only, proportional to the vertical wind shear. When horizontal eddies are superimposed, in addit'ion to the rnornent~u~rl lost to the earth's surface, there will also be a horizontal diffusion of nlotnentum to tlle hasic flow as lar</e as the vertical j u z , <f the horizontal shear is also laye. The values from Charnock et al. [3] will yield an estimate of the minirnunl value of frictiounl effect lettding to maximum Lifetime for eddies.

From their table 9, for t,he lowest 200 II I . Ar,=O.7 dyne c111.-~ (200 n1.)-1=0.8X dyne crr1.5 and taking p= 10-3 gI1l. ( 1 1 ~ 3 ,

Now if the undisturbed flow were as great us 15 kt., for eddies to be formed irnmediately downstream the per-

conditions, discussed by Bowley et al. [Z]. turbation speed 111ust' be of the order of 5 kt. (otherwise


MONTHLY WEATHER REVIEW 46 1

stream distuuce holu the islaud is probably approximately in gradient balance while the flow in the island wake is unbalanced. Such acceleration, if the scale is adequate, I I I : ~ ~ produce inertid oscillations. A simple and well knowrl exercise in dynamic nlet'eorology indicates that such osci1l:tt)ions t'nke the form of cycloids (Exner [4]). 'l'lresc are obtaincd l'rom an integration of the two horizontal equations of n-~otion assuming a constant pressure gradient and C'oriolis parameter. The resulting oscillations have wavelengths depending upon the strength of t11c mean flow, :tnd are of the order of about' 400 km. for speeds of 10 kt. Their period is half R pendulum day. The wavelength and horizont'al amplit'ude are smaller, however, if the oscillat'ions are set up in a non-linear pressure gradient' such that t'he lateral shear of the geo- strophic wind is cyclonic. (Ant'icyclonic shear increases h e wavelengt'h and anlplit'ude.) For example, a t 30' latit~ude l d f a perlddunl day is 24 lrr., but if' the 1:tt'eral sllear of the geost~ropl~ic wind is 1 kt). per 10 knl., the illnrtid period is reduced to 17 hr. The cycloid pat'tern of figure 3 lies in the scale range corresponding to a basic flow speed of about 10 kt'. and a period between 17 and 24 Ilr. It is, therefore, suggested t'llat the cycloidal pattern pictured Irere may well be the result of an inert>ial oscillation bec:tuse the scale of mot'iorr pictured ntutches the scale required by theory when reasonable values of the vllriablcs are inserted.

1 he strong inversion of this region is also favorable. Rossby [7] has indicated lor esalnple, tlliit vertical stabilit,y favors greater lttterttl lnising :uld consequently stronger inertial oscillations. For a Iron~oge~~eous single fluid layer he showed that only 7 percent' of t'he irlit'ial energy is :~vailable for inertial oscilliltiorls, while for rt st'rat'ified two-layer fluid 89 percent of the initial energy is tlvtrilable for inert,ittl oscillations. Thus, the extreme stnbilit'y in this part of the eastern Atlwnt'ic favors strong oscillations ttnd suggests that nrost of the nlotion may be restricted to the stable layer.

f ,

5. INSTABILITY EDDIES Stable inertial lnotiolr could produce t'lre pattern of

figure 3 and perhaps even cause the more circular patterns ol figures 1 and 2. Such IL hypothesis is not att'ractive when applied t'o figure 4 however, because t>he complex eddy pattern suggests a, random field of eddies. For that reason a hypotllesis is suggested that might explain the conversion of 1:tnlimtr flow, in and below t'lle inversion, into turbulent (horizontal eddies) flow.

Consider n sit'untion that is not fsvorable for stable oscillation (e.g., the initial disturbance might be too small or the pressure distribution unfavorable); the sequence of events leading to the complicated eddy pattern may be as Sollows :

1. Gravity w-aves are produced as t,he wind irnpinges on islands.

2. Because t h e strnt'urn beneath t'he inversion is shallow, t,he wave anlplitude is a large fract'ion of that depth so


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satellite pictures of mesoscale eddies

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