GS and SGS Coherent Structures in Homogeneous Isotropic Turbulence

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1 15 th CFD Symposum <C04-> GS and SGS Coherent Structures n Homogeneous Isotropc Turbulence Ο M. Ashraf Uddn Intellgent Modelng Laboratory, The Unersty of Tokyo, Yayo, Bunkyo-ku, Tokyo , Japan. E-mal: auddn@cebeer.s.u-tokyo.ac.jp Nobuyuk Tanguch Insttute of Industral Scence, The Unersty of Tokyo, Komaba, Meguro-ku, Tokyo , Japan. E-mal: ntan@s.u-tokyo.ac.jp Mamoru Tanahash Dept. of Mechancal and Aerospace Engneerng, Tokyo Insttute of Technology, -1-1 Ookayama, Meguro-ku, Tokyo , Japan. E-mal: mtanahas@mes.ttech.ac.jp Tosho Myauch Dept. of Mechancal and Aerospace Engneerng, Tokyo Insttute of Technology, -1-1 Ookayama, Meguro-ku, Tokyo , Japan. E-mal: tmyauch@mes.ttech.ac.jp Tosho Kobayash Insttute of Industral Scence, The Unersty of Tokyo, Komaba, Meguro-ku, Tokyo , Japan. E-mal: kobaya@s.u-tokyo.ac.jp Abstract: GS (grd-scale) and SGS (subgrd-scale) coherent structures n homogeneous sotropc turbulence are dentfed by a pror test. GS and SGS elocty felds are obtaned by flterng the elocty feld for Re λ =64.9 usng two classcal flters for LES: Gaussan flter and sharp cutoff flter, and the most mportant flter wdth s consdered as the length of Kolmogoro mcroscale n the feld wth a constant multplcaton. Coherent structures n the GS feld,.e., structures larger than flter wdth are consdered as grd-scale coherent structures and others are subgrd-scale coherent structures. Second narant Q of the elocty gradent tensor s used for dentfcaton of these structures n GS and SGS felds. By sualzng the contour surfaces of second narant Q, t s shown that GS and SGS felds tself contan lots of dstnct tube-lke coherent structures n homogeneous sotropc turbulence. The characterstc of GS and SGS coherent structures s somewhat smlar to structures, whch ndcates that the feld may contan mult-scale structures n turbulent flow. 1 INTRODUCTION Drect numercal and large-eddy smulatons ( and LES) hae been wdely used to study the physcs of turbulence. Howeer, drect numercal smulaton for hgh Reynolds number flow requres formdable computng power, and s only possble for low Reynolds numbers. Generally, ndustral, natural or expermental confguratons nole Reynolds numbers that are far too large to allow drect numercal smulaton, and the only possble method s large-eddy smulaton. Turbulent flow s completely nonlnear and complex and t has been shown n recent years that turbulent flows contan arous types of ortcal structures, more strctly coherent structures, but the lack of the proper knowledge about these structures preents the deelopment of turbulence theory and turbulent model. Durng the past decades, the studes on the coherent structures n turbulence hae been the subjects of consderable nterest among turbulence researchers. The study on these coherent structures s promsng not only for understandng turbulence phenomena such as entranment and mxng, scalar dsspaton, heat and mass transfer, chemcal reacton and combuston, drag and aerodynamc nose generaton, but also for modelng of turbulence. In the theoretcal study, t s beleed that tube-lke structure s a type of eddy or ortex, whch s the canddate of fne scale structure, partcularly, n the small-scale motons n turbulence. (1)()(3)(4)(5) Nowadays, from drect numercal smulaton of turbulence, (6)(7)(8)(9)(10)(11)(1)(13) fne scale tube-lke coherent structures n homogeneous turbulence are obsered, and the sualzaton of these small-scale structures n the turbulent flow becomes possble. In the recent studes, by drect use of local flow pattern, (10)(11) the cross-sectons of tube-lke coherent fne scale structures are nestgated from database of homogeneous sotropc turbulence n whch the crosssectons are selected to nclude the local maxmum of second narant of the elocty gradent tensor on the axs of the fne scale tube-lke coherent structures. In these studes, they hae shown that mean dameter of the coherent fne scale structures s about 10 tmes of Kolmogoro mcroscale (η) and the maxmum of mean azmuthal elocty s about a half of r.m.s of elocty fluctuatons (u rms ) and that the Reynolds numbers dependence of these characters s ery weak. The same analyses hae been appled to turbulent mxng layer (14) and showed that the characterstcs of tube-lke coherent structures n homogeneous sotropc turbulence and fully deeloped turbulent mxng layer obey the same scalng law. Snce the educed fne scale structures n ther study hae smlar mean azmuthal elocty profles and dstnct axes, they descrbed these structures as coherent fne scale structures n turbulence. The characterstcs of ortcal structures n turbulent channel flows (15) and MHD turbulence (16) also show the smlar behaor of tube-lke structures n homogeneous sotropc turbulence. These results suggest that the exstence of coherent fne scale structure n turbulence s unersal. 1

2 Although s the most exact approach to turbulence smulaton but too expense and s possble relately n smple flow felds whle large-eddy smulaton (LES) s less expense and can smulate ery complex flow felds n turbulence. Wth LES method, large-scale moton s drectly calculated but small-scale needs to be modeled by subgrdscale (SGS) model. Concernng the subgrd-scale model, t seems qute mportant to know what happened n the fltered feld for LES from the actual turbulence ncludng appearance or dsappearance of the tube-lke ortcal structures n resoled or unresoled feld. Therefore, the purpose of ths study s to flter elocty feld for obtanng the GS (grd-scale) and SGS (subgrd-scale) elocty felds n turbulent flow usng classcal flters for LES. Then we dentfy the grd-scale and subgrd-scale coherent structures and dscuss the statstcs of GS and SGS coherent structures n homogeneous sotropc turbulence. LARGE-EDDY SIMULATION.1 Data Base In ths study, data of decayng homogeneous sotropc turbulence has been used, whch s conducted by Tanahash et al. (10) and s calculated by usng 18 3 grd ponts. Reynolds number based on u rms and Taylor mcroscale, λ of the data s Re λ = GS and SGS Velocty Felds To obtan the grd-scale (GS) and gubgrd-scale (SGS) elocty felds, we hae drectly fltered the aboe elocty feld usng two classcal flters: Gaussan flter and sharp cutoff flter for LES. In LES, a elocty component u can be decomposed nto two components, one component s n the range of low wae-number of energy spectrum, large scale of moton, called GS component and s denoted by u, and the other component s n the range of hgh waenumber of energy spectrum, small scale of moton, called SGS component and s denoted by u. Ther relaton can be expressed as: u = u + u (1) The flterng s represented mathematcally n physcal space as a conoluton product. (17) The fltered part u of the arable u s defned formally by the relaton: u ( x) G( x x ) u( x ) dx =,, () D n whch G s flter kernel functon and s the flter wdth n -drecton. The dual defnton n the Fourer space û k of u(x) can be obtaned by multplyng the spectrum ( ) by the spectrum Ĝ ( k) of the kernel G(x) such that, ˆ ( k) = Gˆ ( k) uˆ ( k), k = 0, ± 1, ±,... u (3) The functon Ĝ s the transfer functon assocated wth the kernel G..3 Classcal Flters for LES In ths study, two classcal flters are used for performng the spatal scale separaton. For a flter wdth n -drecton, these flters n physcal space (PS) and Fourer space (FS) are wrtten as follows: (I) Gaussan flter: G 6 6x ( ) = x exp π ( ) ( ) k k = exp (PS) (4a) G ˆ 4 (FS) (4b) (II) Sharp cutoff flter: πx sn G( x ) = (PS) (5a) πx π 1, k Gˆ ( k ) = (FS) (5b) π 0, k > Usng the aboe two flters for LES n the Fourer space, one set of data s fltered and the exact GS elocty feld, u are obtaned. After generatng u, we subtract the GS elocty feld from elocty feld and obtan the SGS elocty feld. That s, the SGS elocty feld can be obtaned by the relaton (from Eq.1): u = u u (6) Flter wdth plays ery mportant role wth flter functons n ths process. The characterstc flter wdth s commonly used as the length, approxmately proportonal to the grd nteral n the preous researches. (18)(19)(0) The structures represented by the GS and SGS eloctes consequently depend both on the grd nteral and on the type of flter employed. In the preous studes, (10)(11) t s shown that the mean dameter of the coherent fne scale eddy s about 10 tmes of Kolmogoro mcroscale (η) n turbulent flows. Therefore, n ths study, the most mportant flter wdth,, s consdered as the length of Kolmogoro mcroscale n the feld wth a constant multplcaton. Snce we are dealng wth homogeneous sotropc turbulence, the flter wdth s same n each drecton and hereafter t s denoted by..4 Profles of the, GS and SGS Velocty Felds In the preous study, (1) usng seeral flter wdths and dfferent Reynolds numbers, t s shown that flter wdth depends on the Reynolds number of the flow, regardless of the flter employed. In ths study, to obtan the GS and SGS elocty felds from feld for Re λ =64.9, we hae consdered flter wdth =10η, where η s obtaned from the elocty feld. In order to understand the GS elocty feld from the elocty feld, we compared elocty wth fltered elocty n Fg.1. For ths purpose we hae randomly chosen one-dmensonal elocty profle n x 1 drecton and hae plotted u 1( x 1 ) and ( x ) 1 1 u for =10η n Fg.1. In all cases we

3 .0 GS-Gaussan u Fg. 1 Sample of fltered and unfltered elocty felds Slope -5/3 GS-Gaussan E(k) E(k) kη 10 1 Slope -5/3 SGS-Gaussan S 10 - kη 10 1 Fg. Three-dmensonal energy spectra of elocty fluctuatons. and GS felds, and SGS felds. obtaned these one-dmensonal profles for the aboe two flter functons: Gaussan and sharp cutoff flter. Although =10η s a small alue, but the profles n Fg.1 suggest that the generaton of GS elocty feld as well as SGS elocty fled from ths Re λ case s well usng both flter functons. Three-dmensonal energy spectra of fltered and unfltered elocty fluctuatons for ths flter wdth, =10η are presented n Fg., whch s calculated by the defnton wrtten as follows: E ( k ) = uˆ ( ) uˆ ( k) 1 1 k < k k+ 1 k (7) In each case, the GS and SGS spectra are obtaned by usng Gaussan and sharp cutoff flter, and then compared wth the spectrum. The spectrum shows the power decay close to k -5/3. In the preous study, (10) usng database, t s shown that the energy dsspaton rate s domnated by the fne scale eddes n homogeneous sotropc turbulence, whch s beyond the dscusson of ths paper. Wth the sharp cutoff flter, the SGS felds contan the elocty due to all the structures wth wae number k > π. On the other hand, full range of wae numbers contrbutes to the SGS elocty n the case of Gaussan flter. Fg. reeals ths dfference n behaor for GS and 3 Fg. 3 Contour surfaces of the second narant of the elocty gradent tensor (Q=3) n the feld. Vsualzed regon s the whole calculaton doman. Second narant s normalzed by Kolmogoro mcroscale and r.m.s of elocty fluctuatons. SGS spectra usng dfferent flters for LES. Ths fgure clearly ndcates that, when sharp cutoff flter s used, the GS spectrum exactly collapsed wth spectrum n the range of low wae numbers ( k π ), whle SGS spectrum s restrcted n the hgh wae number range, and the contrbuton of subgrd scale s entrely due to the hgh wae numbers. The behaor of these spectra also confrms the accuracy of the flterng process. When Gaussan flter s used, the subgrd scales account for a fracton of the total () knetc energy. Moreoer, SGS energy has a sgnfcant contrbuton from the low wae numbers (.e., the large scales) as we can see n Fg.. Howeer, wth ths small, t seems that GS felds contrbute to the large part of energy dsspaton rate for all flter functons. 3 GS AND SGS COHERENT STRUCTURES In order to dscuss about GS and SGS coherent structures, we notce the tube-lke coherent fne scale eddy by sualzaton of flows n the feld. The concept usually assocated wth an eddy s that of a regon n the flow where the flud elements are rotatng around a set of ponts. Identfcaton of the eddy or ortex from /LES database s a ery dffcult and complex task, requrng consderable computatonal efforts wth proper dentfcaton method. There are seeral methods for dentfcaton of the ortcal structures n turbulence wth sgnfcant dfferences () and most of them show threshold dependence. As we dscussed n the ntroducton, drect local flow pattern (3) can educe coherent structures n (10)(11)(1)(14) seeral flow felds, whch shows unersal characterstcs n turbulence. In our preous study, (13) usng the aboe method we hae dentfed the coherent fne scale eddes and ts axes wthout usng any thresholds and then dscussed the spatal dstrbuton of coherent fne scale eddes by sualzaton of axes n homogeneous sotropc turbulence. In ths study, we use the same method to dscuss about GS and SGS coherent structures n homogeneous sotropc turbulence. Fg.3 shows the contour surfaces of normalzed second narant of the elocty gradent tensor Q n the feld for Re λ =64.9. The second narant of the elocty gradent

4 I I I(c) II II II(c) Fg. 4 Contour surfaces of the second narant of the elocty gradent tensor n GS and SGS felds obtaned from feld usng (I) Gaussan flter and (II) sharp cutoff flter. Vsualzed regon s same as n Fg.3. GS feld (Q=), SGS feld (Q=1) (c) GS (Q=) & SGS (Q=1) felds tensor s defned as: Q 1 = ( S S W W ) j j j j, (8) where S j and W j are the symmetrc and asymmetrc part of the elocty gradent tensor A j. In Fg.3, the sualzed regon s whole calculaton doman and the leel of the sosurface s selected to be Q =3. Hereafter, denotes the normalzaton by Kolmogoro mcroscale η and root mean square of elocty fluctuatons, u rms, and for all cases η and u rms are obtaned from the feld. The normalzaton of Q by η and u rms s due to the fact that the dameter and the maxmum azmuthal elocty of tube-lke fne scale structures can be scaled by η and u rms (10) Fg.3 shows that lots of coherent tube-lke structures are randomly orented n homogeneous sotropc turbulence. Howeer, f we ncrease or decrease the alue of Q, we can also show dstnct tube-lke structures n turbulence, lttle bt dfferent from Fg.3, whch means the sualzaton of fne scale structures sgnfcantly depends on the alue of threshold of Q. (13) Fg.4 shows the contour surfaces of second narant of the elocty gradent tensor Q n GS and SGS felds obtaned by usng Gaussan and sharp cutoff flters wth flter wdth =10η. The sualzed regon and ewpont n Fg.4 s same as n Fg.3 for all cases. The leel of the 4 sosurface for all cases n Fg.4 s selected to be Q = for GS felds and Q =1 for SGS felds. As we dscussed aboe, the sualzaton of coherent structures depends on the threshold alue of Q and we do not concern the strength of the structures, therefore, n ths sualzaton we consdered these dfferent alues for Q for dfferent felds only to show the ortcal structures n GS and SGS felds by sualzaton. Fg.4 clearly ndcates that GS and SGS felds contan lots of dstnct tube-lke structures somewhat smlar to felds, whch can best be defned as coherent structures or eddes n turbulence. (13) It s also clear that the sze or length of GS structures n all cases seems to be larger than SGS structures. It s known from the classcal dea of flud dynamcs that seeral small-scale structure together form a large-scale structure,.e., seeral small (SGS) structures entrely le nsde a large (GS) structure n the order of ts sze. Howeer, Fg.4(c) clearly ndcates that GS (green) and SGS (red) structures are qute dstnct and unque n turbulence. 4. CHARACTERISTICS OF GS AND SGS COHERENT STRUCTURES 4.1 Identfcaton Scheme Snce for sualzaton of flows n Fgs.3-4, we use poste second narant Q and we can see the exstence of

5 many tube-lke coherent structures n, GS and SGS felds n homogeneous sotropc turbulence. Obously these tube-lke structures contan at least one local maxmum of Q on ts axs. Wth ths local Q maxmal, Tanahash et al (10) hae clarfed the statstcs of coherent fne scale structures n homogeneous sotropc turbulence. Ths method can best be used to study on the GS and SGS coherent structures n turbulence. Usng ths method, we can obtan a pont on the cross-secton on the axs of coherent structures wth local Q maxmum. The dentfcaton method conssts of the followng steps: Step : Ealuaton of Q at each collocaton pont from the results of, GS and SGS felds. Step : Probablty of exstence of poste local maxmum of Q near the collocaton ponts s ealuated at each collocaton pont from Q dstrbuton. Because the case that a local maxmum of Q concdes wth a collocaton pont s ery rare, t s necessary to defne probablty on collocaton ponts. Step (c): Collocaton ponts wth non-zero probablty are selected to surey actual maxma of Q. Locatons of maxmal Q are determned wthn the accuracy of 10-6 n terms of relate error of Q by applyng a 4 th order Lagrange-nterpolaton polynomal to, GS and SGS data. Step (d): A cylndrcal coordnate system (r,, z) s consdered by settng the maxmal pont as the orgn. The z drecton s selected to be parallel to the ortcty ector at the maxmal pont. The elocty ectors are projected on ths coordnate and azmuthal elocty u s calculated. Step (e): Pont that has small arance n azmuthal elocty compared wth the surroundngs s determned. If the azmuthal eloctes at r =1/5 computatonal grd space show same sgn for all, that pont s dentfed as the center of the swrlng moton. Step (f): Statstcal propertes are calculated around the ponts. 4. Statstcs of Coherent Structures Fgs.5-7 show the mean azmuthal elocty profle of coherent structures n, GS and SGS felds for two flter functons. In these fgures, r represents the radus of the coherent structures, whch s determned by the dstance between the center and the locaton where the mean azmuthal elocty reaches the maxmum alue. Mean azmuthal elocty profles n all cases are normalzed by u rms and η, whch are obtaned from the feld. In Fgs.5-7, symbols represent an azmuthal elocty of a Burgers ortex, whch s wrtten as follows: Γ αr = 1 exp πr 4ν z αz, (9) =, (10) where Γ s the crculaton of the Burgers ortex tube and α s a stretchng parameter. Usng database, (10)(14) t was shown n the preous study that the mean azmuthal elocty profle of coherent fne scale structures n homogeneous sotropc turbulence and turbulent mxng layer could be approxmated by a Burgers ortex. They (10) Burgers' ortex () r Fg. 5 Mean azmuthal elocty profle of the coherent structures n the feld, normalzed by Kolmogoro mcroscale and r.m.s of elocty fluctuatons. Symbols represent elocty profle of a Burgers ortex and error bars denote arances of azmuthal elocty. also hae shown that the mean dameter of the coherent fne scale structures n homogeneous sotropc turbulence s about 10η and the maxmum of mean azmuthal elocty s about half of u rms, and these characterstcs of coherent structures are ndependent on Reynolds numbers of the flow. Fg.5 confrms these behaors of the coherent structures for ths Reynolds number case. Our nterest s to dscuss the characterstcs of GS and SGS coherent structures comparng wth the results, hence, we hae shown approxmaton of coherent structures n the GS and SGS felds wth that of the Burgers ortex n Fgs.6-7. The mean azmuthal elocty profle of GS-Gaussan coherent structures n Fg.6 shows a good agreement wth that of Burgers ortex n the whole range as t as n feld. In Fg.7, the agreement of mean azmuthal elocty profle for GS-sharp cutoff coherent structures wth Burgers ortex s good for relately small dstance (r<1η), that s, the Burgers ortex profle does not collapse wth mean azmuthal elocty profle for the large dstance. For Gaussan flter, the contrbuton of GS and SGS elocty felds are obtaned from the whole regon of elocty feld, whle sharp cutoff flter separates the elocty feld n GS and SGS felds at the cutoff wae number. Maybe, that s one reason of these dfferences n Fg. 6 and 7. Moreoer, flter sze =10η s relately small. For large flter wdth, the large-scale structures,.e., most of the coherent structures wth large dameter accumulate n the GS feld. Usng large flter wdth, we hae also seen (not shown) that the approxmaton of mean azmuthal elocty profle by Burgers ortex becomes qute good for relately large dameter tube lke coherent structures n GS sharp cutoff feld as well as n GS-gaussan fled. On the other hand, although not n hole range, but Fgs. 6 and 7 also show that the approxmaton of mean azmuthal elocty profle of SGS coherent structures n both SGS-Gaussan fled and SGS-sharp cutoff fled by Burgers, ortex s well n a certan range, and shows almost smlar behaor for both flter functons. These results suggest that mean azmuthal elocty profle of coherent structures n LES can be approxmate by that of a Burgers ortex as well as n. The comparsons of normalzed mean azmuthal elocty profle of coherent structures n, GS and SGS

6 Burgers' ortex (GS-Gaussan) GS-Gaussan r r 0.3 Burgers' ortex (SGS-Gaussan) SGS-Gaussan S r Fg. 6 Same as Fg.5, but GS feld and SGS feld obtaned by usng Gaussan flter. - - Burgers' ortex () r Burgers' ortex (S) r Fg. 7 Same as Fg.5, but GS feld and SGS feld obtaned by usng sharp cutoff flter. felds for dfferent flter functons are shown n Fg.8. Mean azmuthal elocty profle of GS structures for dfferent flter functons wth ths flter wdth, collapse wth profle at r=0η (Fg.8 ). On the other hand, mean azmuthal elocty profle of SGS structures for dfferent flter functons collapse each other at r=10η (Fg.8 ), but not wth profle. In all cases, the maxmum of mean azmuthal elocty of GS structures s hgher than structures, and of SGS structures s lower than structures. The maxmum of mean azmuthal elocty and dameter of coherent structures are about 0.6u rms and 15η n r Fg. 8 Comparson of mean azmuthal elocty profle ( ) of the, GS and SGS coherent structures. and GS felds, and SGS felds. In all cases, mean azmuthal elocty profle s normalzed by Kolmogoro mcroscale and r.m.s of elocty fluctuatons obtaned from feld. GS-Gaussan feld, and 0.8u rms and 0η n the GS-sharp cutoff feld. On the other hand, the maxmum of mean azmuthal elocty and dameter of coherent structures are about 0.u rms and 5η n SGS-Gaussan feld, and 03u rms and 7η n the SGS-sharp cutoff feld. The maxmum of mean azmuthal elocty for GS structures n the Gaussan feld s close to the feld, but the maxmum of mean azmuthal elocty for GS structures n the sharp cutoff feld s larger than the feld. In actual LES, GS structures can be dentfed but SGS structures need to be model by SGS model. Coherent structures hae hgh and thn energy dsspaton regons around them and these regons contrbute total energy dsspaton n turbulence. (4) Snce n SGS felds we can see the exstence of coherent structures somewhat smlar to feld, of course ery small n sze, ths result s ery worthy to deelop a structures base SGS model for LES. The probablty densty functons (pdf) of dameter of tube-lke coherent structures n, GS and SGS felds, whch are normalzed by η obtaned from feld are shown n Fg.9 for dfferent flter functons. It s clear that the peak of pdf of GS-structures n all cases do not concde wth each other or wth profle. Moreoer, the peak of pdf of GS structure n the GS-sharp cutoff feld shows hgher alue than n the GS-Gaussan feld for ths flter wdth. It s also reealed that the small dameter tube-lke coherent structure n GS feld s rare n all cases and large dameter of SGS structures reaches about 5η. Howeer, the collapse of pdf of dameter n the SGS felds s good, and the peak of pdf for SGS profle ncreases from the profle for all flter functons. Fg.10 shows the pdf of maxmum of mean azmuthal elocty of coherent structures n the same, GS and

7 p p GS-Gaussan D SGS-Gaussan S do not concde each other or wth profle. The maxmum alue of mean azmuthal elocty profle s lower than u rms,.e., about half of alue. Usng large and dfferent flter wdth, we hae seen (not shown) that the pdf of SGS profle becomes ery close wth profle and the maxmum alue n the SGS fled neer exceed the maxmum alue n the feld. That s, the characterstcs of GS and SGS coherent structures sgnfcantly depend on the flter wdths. Ths behaor s nterestng to study on the coherent structure n actual LES or to deelop some LES modelng based on the coherent structures n turbulence. In the preous study, (10)(14) t was shown that the coherent fne scale structures could be scaled by Kolmogoro mcroscale and r. m. s of elocty fluctuatons. The aboe results n the present study also suggest that the GS and SGS coherent structures may possble to scale by η and u rms as well as n D Fg. 9 Probablty densty functon of dameter of coherent structures normalzed by Kolmogoro mcroscale. and GS felds, and SGS felds. p p GS-Gaussan.0.5,max.0.5,max SGS-Gaussan S Fg. 10 Probablty densty functon of the maxmum of mean azmuthal elocty of coherent structures normalzed by r.m.s of elocty fluctuatons. and GS felds, and SGS felds. SGS felds usng dfferent flter functons, whch s normalzed by u rms. It s reealed that, GS-Gaussan profle collapse wth profle well n the whole range. The profle n the GS-sharp cutoff feld s smaller than profle at small azmuthal elocty and larger than that at large azmuthal elocty of the tube-lke coherent structures. The maxmum alue of mean azmuthal elocty n GS and felds seems to be same. On the other hand, SGS profles of mean azmuthal elocty for both flter functons 7 5 CONCLUSIONS In ths study, GS and SGS coherent structures n homogeneous sotropc turbulence are dentfed. The GS and SGS elocty felds are obtaned by flterng the elocty feld usng classcal flters for LES. By sualzng the contour surfaces of second narant Q n GS and SGS felds as well as n feld, t s shown that GS and SGS felds tself contan lots of dstnct tube-lke coherent structures n homogeneous sotropc turbulence, whch ndcates that the feld contan mult-scale structures n turbulent flow. The characterstcs of these GS and SGS coherent structures are somewhat smlar to coherent structures. These GS and SGS coherent structures can be scaled by η and u rms as well as n. 6 REFERENCES (1) Townsend, A. A., On the fne-scale structure of turbulence, Proc. R. Soc. Lond., A08(1951), pp () Tennekes, H., Smple model for the small-scale structure of turbulence, Phys. Fluds, 11(1968), No. 3, pp (3) Lundgren, T. S., Straned Spral Vortex Model for Turbulent Fne Structure, Phys. Fluds, 5(198), pp (4) Pulln, D. I. and Saffman, P. G., On the Lundgren- Townsend Model of Turbulent Fne Scales, Phys. Fluds, A5(1993), pp (5) Saffman, P. G. & Pulln, D. I., Ansotropy of the Lundgren-Townsend Model of Fne-scale Turbulence, Phys. Fluds, A6(1994), pp (6) She, Z. S., Jackson, E. and Orszag, S. A., Intermttent Vortex Structures n Homogeneous Isotropc Turbulence, Nature, 344(1990), pp (7) Vncent, A. and Meneguzz, M., The spatal structure and statstcal propertes of homogeneous turbulence, J. Flud Mech., 5(1991), pp (8) Jmenez, J., Wray, A. A., Saffman, P. G. and Rogallo, R. S., The Structure of Intense Vortcty n Isotropc Turbulence, J. Flud Mech., 55(1993), pp (9) Vncent, A. & Meneguzz, M., The dynamcs of

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