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After-dinner speech by Ryszard Herczynski, 6.9.2001
Let me start by thanking Konrad Bajer and Keith Moffatt for this op-portunity to speak to you. Both Konrad and Keith are members of thesame Cantabrigian family. Konrad obtained his Ph.D. from Moffatt,Keith from Batchelor, George from the 'Pater Familiae', G.I. Taylor.This sounds already like a biblical story: Abraham begat Isaac, Isaacbegat Jacob, Jacob begat Judas and his brethren, and so on.
Only Taylor had never got Ph.D., apart the usual honorary ones.There was no Ph.D. degree when G.I. graduated from Cambridge Uni-versity nor did he have a mentor in fluid mechanics. G.I. chose for himselfthis subject, and excelled in asking pertinent and important questions.Thus, already in his 1917 paper, in the language of the day, he wroteabout singularities occurring in turbulence, the very subject you cameto discuss in Zakopane.
And it was here in 1963 that the Sixth Fluid Dynamics Symposiumwas held, organised by the Polish Academy of Sciences. That meeting,38 years ago, was a rather modest affair, but it was a turning point of akind. It was the first conference in the series to be attended by scientistsfrom the West. Western participants were greeted without applause butwith deep satisfaction. We all understood the importance of breakingthe imposed isolation of Polish mechanics. That scientist who had thecourage to cross the Iron Curtain first was George Batchelor. He drovefrom England in a huge, old car, with his entire family and his doctoralstudent, Keith Moffatt.
I had met George and Keith two years earlier, when I came to Cam-bridge for a year-long visit. As a child, I read sentimental stories aboutCambridge, about Newton and the apple. These stories I kept in mindduring the war, and the real Cambridge fully confirmed my almost myth-ical expectations. It was then a tranquil, welcoming place. A studentgoing to London or elsewhere for a weekend would leave his or her bicy-cle at the railway station, without a chain or padlock, and would be sureto find it waiting in the same place upon return. Since then, Cambridgehas become a major tourist attraction, and tranquility has become a rarecommodity. To preserve their normal rhythm of life, colleges are forcedto limit the number of visitors. Some charge admission, other close theirgates to outsiders altogether. The old atmosphere of openness and trustis giving way to the brave new world.
And the perspectives are bleak. No computer is needed to estimatethat if every citizen of, say, the United States and Russia were to visitCambridge once in his or her lifetime, and for one day only, twenty thou-sand American and Russian tourists would arrive there every day. The
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K. Bajer and H.K. Moffatt (eds.), Tubes, Sheets and Singularities in Fluid Dynamics, 361-363.© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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only visible shield is mass culture which ignores past art, past architec-ture, and to an even greater extent ignores science and places where itwas and still is born. Fortunately most US and Russian citizens - andalso most citizens around the world - are as little interested in seeingCambridge, UK, as are their Presidents, Mr. Bush and Mr. Putin. ThusGod save Cambridge and let us pray for the spread of mass culture.
More seriously, Cambridge and some other old universities symbol-ise for me the best tradition of pursuing science and learning. GeorgeBatchelor and G.I. are examples of high ethical standard of scientists. Itseems that these traditions and standards are now challenged, that scien-tific curiosity gives way to demands for speedy careers, that publicationof results preceded by careful analysis of previous accomplishments andending with a thorough discussion, as still found in the papers of JFM,are replaced by notes formulating results whose importance should betaken for granted. The cumulative character of science, its main achieve-ment since the Baconian revolution, is thus endangered.
My stay in Cambridge triggered, I dare to think, close relations be-tween George and the Polish fluid mechanics community. Of course,I can hardly claim credit for this because it was mainly the work ofGeorge and his group and of Wladek Fiszdon and his team in Poland. Iam happy that these relations are still maintained.
Many years after the conference in Zakopane, I asked George if, being25 again, he would still choose fluid mechanics, this classical and (asone may say) nearly fossilised branch of physics, as his field of research?The answer came immediately, in his usual style. Yes, if G.I. Taylorwere around.
My question shows that I missed the point that the art of our tradelies in part in finding new ways of asking the same questions. Eventhe question raised by Newton about the falling apple is not yet fullyanswered. The fluid mechanics you are discussing here, although I knowlittle about it, seems to me the most attractive subject, both in its scopeand its methods. It would be, of course, great to have some new Taylorto pave the way forward. I believe that he will come. Perhaps he isalready among you.
All this goes to say that we should not tire of unsolved problems, norof asking the same questions, ‘why’ and ‘how’. These are the apparentlynaive questions that annoying children ask over and over again. Until,that is, they learn to take things for granted. But it is a true gift to retaina childlike wonder and curiosity, and to derive an undiminished pleasurefrom figuring things out. This is the gift G.I. was blessed with. Let mewish you a meeting that keeps this spirit of doing science alive, withmany naive questions and hopefully some not entirely naïve answers.
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My own life in fluid mechanics has been bi-polarised to some extentbetween Warsaw and Cambridge; but Fluid Mechanics is of course aworld-wide activity, and it is a particular pleasure for me to see suchstrong representation at this meeting from so many countries of theworld - USA, Japan, Australia, France and many others. Welcome toPoland and to Zakopane, and I wish you all every success in your con-tinuing efforts to bring deeper understanding to fluid dynamics, in allits richness and diversity.
Extract from reply by Keith Moffatt
The choice of Zakopane for this Symposium brings back very happymemories of a previous (1963) meeting in Zakopane that I was privi-leged to attend. This was one of the early biennial meetings on FluidMechanics organised in Poland by Wladek Fiszdon and his colleagues atIPPT (Warsaw), that did so much to sustain scientific contact betweenEast and West during the long Cold War years.
My research adviser, George Batchelor, came by car from Cambridgeto Zakopane with his wife and three children, and offered me the lastspace in the car, which I gladly accepted. It was a memorable jour-ney! The Proceedings of the meeting (Arch. Mech. Stosowanej, vol. 2,1964) remind me that Richard Herczyriski (whom I thank for his kindremarks) lectured on Knudsen number effects in rarefied gases, and thatGeorge Batchelor lectured on diffusion from a point source in a turbu-lent boundary layer (a beautiful piece of work that is perhaps not as wellknown as it should be). I lectured myself on corner eddies in Stokes flow(which I am glad to see reappear in a three-dimensional geometry atthis Symposium!). It is salutary to recognise that so many fluid dynam-ical problems, particularly those involving turbulence, that were alreadyunder investigation 40 years ago, remain still unsolved to this day; it isperhaps a tribute to the structural stability of our subject! The frontiersof research move slowly, but we may hope that this Symposium will dosomething to accelerate the process.
I'd like to thank Konrad Bajer for the immense care that he hastaken in all the arrangements for the Symposium, and for his personalattention to detail which I know we have all appreciated, and which hasensured its outstanding success, both scientifically and socially.
List of Participants
Postal and Internet addressess can be found on theconference website, www. igf. fuw. edu. p l / IUTAM
AUSTRALIACHONG, Min S.HIGGINS, Keith
CHINAXIE, Xi-Lin
DENMARKNORDLUND, Åke
FRANCEFARGE, MarieFRISCH, UrielGOMEZ, ThomasLE DIZÈS, StéphaneROSSI, MauriceSCHNEIDER, KaiVERGA, Alberto D.
GERMANYHORNIG, GunnarMAYER, ChristophPAGE, Steffen
JAPANFUKUMOTO, YasuhideHATTORI, YujiKIDA, ShigeoNAKAKI, Tatsuyuki
POLANDBAJER, KonradBRANICKI, MichalCICHOCKI, BogdanEKIEL-JEZEWSKA, MariaHERCZYNSKI, RyszardKUDELA, HenrykLEWTAK, RobertLIPNIACKI, TomaszMROWIEC, AgnieszkaPERADZYNSKI, ZbigniewREGUCKI, Pawe!SLIWA, Cezary
chong@mame. mu .oz.au
khigg@mame .mu. oz . au
gh@tp4. ruhr-uni-bochum. de
cm@tp4. ruhr-uni-bochum. de
365K. Bajer and H.K. Moffatt (eds.), Tubes, Sheets and Singularities in Fluid Dynamics, 365-366.© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
366
RUSSIA
AKHMETEV, Peter M.KUIBIN, Pavel A.KUZNETSOV, Evgenii A.MURAVNIK, Andrey B.OKULOV, Valery L.PANKRASHKIN, KonstantinPODVIGINA, OlgaRUBAN, Victor P.ZHELIGOVSKY, Vladislav
SPAIN
BRUN, CédricJIMÉNEZ, Javier
UK
BARENGHI, Carlo F.COWLEY, Steve C.COWLEY, Stephen J.GIBBON, John D.MOFFATT, KeithPRIEST, Eric R.RICCA, Renzo L.
UKRAINE
GOURJII, Alexandre A.MALYUGA, Vladimir S.
USA
BAYLY, Bruce J.BHATTACHARJEE, AmitavaCONSTANTIN, PeterKRASNY, RobertLEONARD, AnthonyPELZ, Richard B.PULLIN, Dale I.ZABUSKY, Norman
Author Index
Bold face indicates contributions tothis volume
Aarts, R.G.K.M., 138, 283Abernathy, F.H., 36Abid, M., 24Adams, C.S., 74Adrian, R.J., 242, 246Akhmetiev P., 156Alekseenko, S.V., 60, 86Amari, T., 124Anderson, C.R., 11Andersson, H.I., 180Andersson, P., 30, 239Andreotti, B., 24Anselmet, F., 66Anthore, R., 343, 348Antonsen Jr., T.M., 210Aref, H., 11, 54, 80, 92Arnol'd, V.I., 150, 168, 293, 316Aschwanden, M.J., 114Azzalini, A., 217
Bajer, K., 31, 36, 124Balachandar, S., 246Barenghi, C.F., 69, 74, 98, 144Barnes, J., 11Bartenwerfer, M., 354Bassom, A.P., 31, 36Batchelor, G.K., 179, 190Bauer, G.H., 74Bayly, B.J.,48, 157, 162, 168,210Beale, J.T., 282, 293, 328, 316Bechert, D.W., 354Beimfohr, S., 348Benjamin, R.F., 200Berger, M.A., 144, 156Berggren, M., 30, 239Berkooz, G., 239Bernard, P.S., 11Beronov, K.N., 30
Betchov, R., 30Bhattacharjee, A., 124,317, 328Bialynicka-Birula, Z., 99, 102Bialynicki-Birula, I., 99, 102Biskamp, D., 124Blackwelder, R.F., 239Blaizot, J., 124Blawzdziewicz, J., 348Bliss, D.B., 48Blondin, J.M., 199Boersma, J., 86Bonazza, R., 199Boratav, O.N., 316, 328, 282Bossis, G., 348Bostel, F., 343, 348Brachet, M.E., 282Brady, J.F., 348Brandenburg, A., 304Brenner, H., 360Brøns, M., 60Brouillette, M., 199Bulanov, S.V., 124Bungey, T.N., 124Buntine, J.D., 18Burgers, J.M., 18, 26
Cabral, H.E., 80Cadot, O., 24Caffarelli, L., 282Caflisch, R., 304Cambon, C., 210Cantwell, B.J., 18, 247, 260Casci, C., 36Castilla, M.S.A.C., 80Chan, D.C., 180Cheng, W.P., 260Chen, S.Y., 180Chern, I.-L., 200Chernyshev, S.A., 48Chertov, M., 210Childress, S., 168Chong, M.S., 18, 260Chorin, A.J., 11, 90, 293
367K. Bajer and H.K. Moffatt (eds.), Tubes, Sheets and Singularities in Fluid Dynamics, 367-373.© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
368
Christiansen, J.P., 54Cichocki, B., 348, 349Colella, P., 199Constantin, P., 282, 285, 293, 304, 316,
328Corrsin, S., 173Cottet, G.-H., 11, 54Couder, Y., 24Cowley, S.C., 124Craig, I.J.D., 124Crow, S.C., 316
Dahler, J.S., 348Dahm, W.J.A., 11Danalia, I., 66Daubechies, I., 216Daube, O., 60Davis, A.M.J., 354Davis, R.H., 348Davis, S.H., 354Del Álamo, J.C., 239Delbende, I., 19, 24, 30Do Waele, A.T.A.M., 138Dimotakis, P.E., 179Dmitruk, P.A., 114Doering, C.R., 24, 304Donnelly, R.J., 74Donoho, D., 216Doolen, G.D., 180Douady, S., 24Draghicescu, C., 11Draghicescu, M., 11Driscoll, T.A., 30Dusek, J., 66Du, Y., 168
Eckelmann, H., 239Ekiel-Jezewska, MX. , 343, 348Eloy, C., 48Escudier, M., 60Evans, N.W., 156
Faler, J.H., 86Falkovich, G., 210Farge, M., 211, 216, 217Fefferman, C., 282, 304, 316Felderhof, B.U, 348Fernholz, H.H., 239Feuillebois, F., 343, 348, 349Field, G.B., 144Finley, P.J., 239Finn, J.M., 168Fisher, G.H., 114Flanders, H., 150Flores, O., 239Flugge, S., 293
Fokas, A.S., 24, 304Forbes, T.G., 124, 132,304Freedman, M.H., 74, 144Frenkiel, F.N., 180Frisch, U., 168, 283, 316, 328Fukumoto, Y., 37, 48
Galloway, D.J., 168Galluccio, S., 210Galsgaard, K., 114, 124Garcia-Villalba, M., 239Germaschewski, K., 316Gharakhani, A., 54Ghoniem, A.F.,54Gibbon, J.D., 24, 295, 304Gibson, C.H., 179Gilbert, A.D., 31, 36, 168, 266Girimaji, S.S., 190, 210Goldstein, D., 199Gomez, D.O., 114Gomez, Th., 261, 266Gomilko, A.M., 355, 360Goto, S., 181, 190Gourjii, A.A., 87, 92Grauer, R., 304, 316Green, A.E., 283Green, R.M., 124Greene, J.M., 283Greengard, L., 11Gronig, H., 200Guckenheimer, J., 1 1Gudiksen, B., 114Gulak, Y., 199, 283, 328Gupta, S., 199Gurzhi, A.A., 92Gyr, A., 283
Haas, J.-F., 199Hamilton, J.M., 239Hamraoui, M.El., 54Happel, J., 360Hardin, J.C., 86Hatakeyama, N., 180Hattori, Y., 37Hawley, J., 199He, G.W., 180He, Z.-X., 74, 144Henningson, D.S., 30, 239Herczyriski, R,., 361Heyvaerts. J., 114Higgins, K., 13Hills, C.P., 360Hinsen, K., 348Hitchcock, D., 199Hites, M.H., 239Hocking, L.M., 354
AUTHOR INDEX 369
Holmes, P., 11, 239Hornig, G., 124, 133, 138, 151, 156Hosokawa, I., 190Huang, M.J., 190Hunt, J.C.R., 190Hunt, R.E., 125Hussain, A.K.M.F., 86, 138, 239, 246, 283Hut, P., 11Hwa, T., 340
Imshennick, V.S., 124Itano, T., 239Itzykson, C., 156
Jeffrey, D.J., 348Jeong, J.-T., 239, 241, 246, 354Jiménez, J., 24, 216, 229, 239, 241, 246Johansson, A.V., 239John, F., 293Jones, V.F.R., 144
Kambe, T., 180Kardar, M., 340Kato, T., 282, 293, 316, 328Katrahov, V.V., 340Kawahara, G., 36, 190Kendall, T.M., 246Kerns, E.T., 348Kerr, R.M., 282, 304, 316Kettle, S.F.A., 282Kevlahan, N., 216Khesin, B.A., 150Kida, S.,11 , 18, 36, 138, 171, 181, 190,
210, 281, 283, 328Kim, H.T., 239Kim, J., 239, 246Kinzelbach, W., 283Kiprijanov, I.A., 340Kivotides, D., 74Klapper, I., 124, 304Klimchuk, J.A., 114Kline, S.J., 239Knio, O.M., 54Knüppel, O., 80Kohn, R., 282Kolmogorov, A.N., 171, 179, 260, 266, 316Kolokolov, I., 210Konovalyuk, T.P., 92Konstantinov, M.Yu., 92Kop’ev, V.F., 48Koplik, J., 74Korkina, E.I., 168Kotelnikov, A., 199Koumoutsakos, P.D., 11Kouzoubov, A., 354Krasny, R., 3, 11
Kristoffersen, R., 180Kudela, H., 49, 54Kuibin, P.A., 60, 81, 86Kuznetsov, E.A., 305, 316, 334
Ladd, A.J.C., 348Lamb, H., 199, 360Landahl, M.T., 239Larchevêque, M., 261, 266Lau, Y.-T., 168Leadbeater, M., 74Lecoq, N., 343, 348Le Dizès, S., 19, 24, 25, 30, 48Lee, L.C., 124Lee, M.J., 239Leibovich, S,, 60, 86Leighton, D.T., 348Leonard, A., 11, 54, 180, 201, 210Leray, J., 283Lesieur, M., 180Lessen, M., 24Levine, H., 74Lim, T.I., 54Lim, T.T., 11Lindsay, K., 3, 11Linker, J., 124Lipniacki, T., 93, 98Ljapin, V.M., 340Loc, T.P., 60Longcope, D.W., 114, 124Luchini, P., 354Luciani, J.F., 124Ludwig, H.-G., 114Lumley, J.L., 180, 239Lundgren, T.S., 24, 179, 180, 190, 210, 266Lu, S.S., 246L’vov, V.S., 316
MacKay, R.S., 48Madelung, O., 102Mahalov, A., 48, 217Majda, A.J., 282, 293, 304, 316, 328Makihara, T., 181Malham, S.J.A., 304Malherbe, J.M., 124Malyuga, V.S., 355Mansour, N.N., 260, 239Manzo, F., 354Marble, F.E., 36Marliani, C., 304, 316Martin, S.F., 124Masmoudi, K., 348Massey, W.S., 156Maurer, J., 74Ma, W.W., 61, 66Mayer, C., 151, 156
370
Mayer, E.W., 24McClymont, A.N., 124Medina, E., 340Meiburg, E., 54Meinhart, C.D., 246Meiron, D.I., 282, 328Melander, M., 283Meleshko, V.V., 92Mellor, C., 124Meneguzzi, M., 24, 282, 283Métais, O., 180Metcalf, T.R., 114Metzler, S.P., 239Mikic, Z., 114, 124Milano, L. J., 114Mirman, R., 283Miskis, M.J., 354Misra, A., 180Miura, H., 190Mloduchowski, T., 99Moauro, V., 80Moffatt, H.K., 18,48,74, 124,125, 138,
144, 150, 156, 168, 283, 293, 360, 363Mo, G., 348Moin, P., 190, 239Mokhtarzadeh-Dehghan, M. R., 246Mollo-Christensen, E., 239Monastyrsky, M.I., 156Monin, A.S., 316Moore, D.W., 11, 36, 48, 86, 190Morf, R.H., 328, 282,283Morikawa, G.K., 80Moser, R., 216Moser, R.D., 239Munn, R.E., 180Muravnik, A.B., 335, 340
Nagib, H.M., 239Nakagawa, H., 246Nakaki, T., 75, 80Negrini, N., 80Neukirch, T., 124Nezu, I., 246Ng, C.S., 317, 328Niccum, D.L., 66Nickel, B.G., 328, 282Nickels, T.B., 11, 54Nicolaenko, B., 217Nirenberg, L., 282Nitsche, M., 3, 11Nordlund, Å., 107, 114, 124Nore, C., 24
Obukov, A.M., 173Ohkitani, K., 18, 293, 295, 304Okulov, V.L., 55, 60, 86
Olia, W.M., 80Olshanetsky. M.A., 124O'Neil, K.A., 80Onishi, Y., 348Ooi, A., 13Orlandi, P., 24, 239Orszag, S.A., 282, 283, 328Osterlund, J.M., 239Ott, E., 168Ottino, J.M., 11, 92OuldSalihi, M.L.,54Overholt, M.R., 180Overman II, E.A., 199
Paillet, P., 24Parisi, G., 340Parker, E.N., 114, 124, 132Parnell, C.E., 124Pearson, C.F., 36Pellegrino, G., 216,217Pelz, R.B., 269, 282, 316, 328Peng, G., 199Perry, A.E., 18, 260Peradzyriski, Z., 145, 150Petschek, H.E., 124, 132Pevtsov, A. A., 114Pinelli, A., 240,241, 246Podolsky, D.I., 329, 334Podvigina, O.M., 305Poggi, D., 241, 246Pohožaev, S. I., 340Politano, H., 261,266,282Ponce, G., 283Pope, S.B., 180, 190, 210Porporato, A., 246Porter, D.H., 180, 190, 266Porter, L.J., 114Pouquet, A. , 180, 190,261,266,283Powell, K.G., 24Pozzi, A., 354Prestridge, K., 200Priest, E.R., 114,115, 124, 132,304Prochazka, A., 18Proctor, M.R.E., 168Pullin, D.I., 18, 171, 180Pumir, A., 283
Rado, A., 124Rasmussen, J . J . , 329, 334Ray, J., 199Reddy, S.C., 30Regucki, P., 49Retakh, V.S., 156Reyl, C., 210Reynolds, W.C., 239Rhines, P.B., 36
AUTHOR INDEX 371
Ricca, R.L., 69, 74, 86, 98, 139, 144, 283Richardson, S., 354Rickard, G.J., 124Ridolfi, L., 246Rieutord, M., 114Rightley, P.M., 200Robinson, A.C., 18Robinson, S.K., 240, 241, 246Rogers, M., 216Rokhlin, V., 11Rom-Kedar, V., 11Rosenhead, L., 11Rossi, M., 19, 24, 30Ruban, V.P., 316, 329, 334Ruzmaikin, A., 156
Saffman, P.G., 18, 48, 54, 60, 86, 180Sakai, J., 124Samtaney, R., 199Samuels, B.C., 69, 74, 98, 144Sangani, A.S., 348Sbeih, K., 11Schatzle, P.R., 11Schindler, K., 124Schmidt, D.S., 80Schmitz, R., 348Schnack, D.D., 114Schneider, K., 211, 216, 217Schoppa, W., 239, 246Schrijver, C.J., 114, 124Schwarz, K.W., 74, 98Schwarz, W.H., 180Scott, J.F., 210Serrin, J., 293Shankar, P.N., 360Shariff, K., 11, 54Shtork, S.I., 60, 86Siggia, E.D., 190, 283Simens, M.P., 234, 239Singh, P.J., 24Skrbek, L., 74Skubachevskii, A.L., 340Sliwa, , 99, 102Smart, J.R., 348Smith, C.R., 240,241,246Smith, J., 124Somov, B.V., 124Sondergaard, R., 260Sørensen, J.N., 55, 60Soria, J., 260Sotiropoulos, F., 60Soward, A.M., 36, 293Stalp, S.R., 74Steele, G., 304Stein, R.F., 114Strykowski, P.J, 66Sturrock, P.A., 114
Sturtevant, B., 199Sudan, R.N., 114Sulem, P.-L., 282, 283Swearingen, J.D., 239Sweet, P.A., 124, 132Swenson, E.V., 80Syrovatsky, S.I., 124Szewczyk, A., 30Szymczak, P., 349
Tabeling, P., 74Tabor, M., 124Takaki, R., 86Takaoka, M., 11, 138Tanaka, M., 36, 190Taylor, G.I., 283, 354, 358Tel, T., 168Tennekes, H., 180Titov, V.S., 124Toh, S., 239Tomkins, C.D., 246Townsend, A.A., 239, 266Trefethen, A.E., 30Trefethen, L.N., 30Truesdell, C., 293Tryggvason, G., 11Tsai, C.-Y., 48Tse, F., 217Tsinober, A., 283Tuck, E.O., 354Tur, T.J., 124
Uchida, Y., 114
Vainshtein, S.I., 168Van Ballegooijen, A.A., 114Vanderbilt, D., 283Van Heijst, G.J.F., 92Van Hoven, G., 114Ventikos, Y., 60Vergassola, M., 210Verzicco, R., 24Vincent, A., 24, 282Voelkl, T., 179, 180Voigt, L.K., 55, 60Von Karman, T., 192Vorobieff, P., 200Vulpiani, A., 210
Waele, A.T.A.M., 283Wajnryb, E., 348Waleffe, F., 48, 239Walker, J.D.A., 246Wang, C.Y., 354Wang, X., 328
372
Wei, T., 180Wherrett, B.S., 283Widnall, S.E., 48Wiggins, S., 11Wilcoxon, R.K., 66Williamson, C.H.K., 66Willmarth, W.W., 180, 246Wilson, II.J., 348Winckelmans, G.S., 54, 199Winiecki, T., 74Wood, D.H., 86Woodward, P., 266Woodward, P.R., 199, 180, 190Wray, A.A., 190Wray A.A., 216
Yamamoto, K., 190Yanase, S., 36, 190Yang, X., 200Young, W.R., 36Yuan, Y.M., 242, 246
Zabusky, N.J., 191, 199, 200Zakharov, V.E., 316Zawadzki, I., 54Zeldovich, Ya.B., 168Zeng, S., 348Zeng, S.-M., 200Zhang, S., 191, 200Zhang, Y.-C., 340Zheligovsky, V.A., 305Zhou, H.L., 61, 66Zhou, J., 241, 242, 246Zoldi, C.A., 200Zuber, J.-B., 156
Xie, X.L., 61, 66
Yaglorn, A.M., 316
Topic Index
ABC flow, 305, 159Abelian group, 271Accelerated inhomogeneous flows (AIFs),
191Accelerated diffusion, 36Active regions, 112, 116Advection-diffusion, 31
similarity solution, 32Advection problem, 87Alfvén's theorem, 134Alfvén velocity, 112Analyticity strip, 277Anisotropy, 93, 305Annihilation of gradients, 31Anti-parallel vortex filaments, 329Anti-parallel vortex tubes, 270, 274Atwood number, 193Autocorrelation time, 109Autonomous flow, 234Average
angle of inclination, 109crossing number, 69, 71, 139dissipation, 109heating rates, 112
Axial velocity, 171Axial vortex structures, 55Axisymmetric
flow, 3mode, 46Navier-Stokes equations, 55structures, 61wave, 45
Azimuthal waves on a vortex ring, 3
Backscatter of energy, 201Baroclinic vorticity generation, 194Batchelor vortex, 19Bending
mode, 46waves, 38, 45
Bessel modes, 45Biaxial strain, 13Binary reconnection, 115, 121
Biot-Savart kernel, 4, 6, 8Blowup theorems, 272Borromean rings, 152Bose - Einstein condensation, 69, 71Boundary conditions, 112
on rough surface, 349Boundary driving, 112Boundary layer, 31Boundary-layer approximation, 128Boundary motions, 108
velocity, 109work, 111
Breaking of vortex lines, 305Buffer layer, 236Burgers vortex, 13, 21, 171, 262Bursting cycle, 241
,109 group, 271,274Canonical
momentum field, 331vorticity field, 331
Catastrophe theory, 305Cat's-eye, 15Cauchy
formula, 286, 301invariant, 305
Centre of symmetry, 270Chaotic
advection, 87, 209dynamics, 3Hamiltonian system, 6
Character, 271Chemical reaction front, 36Chern-Simons three-form, 154Chirality, 270, 281Chromosphere, 116Closure property of groups, 271Coherent
structures, 61, 213, 220, 305in turbulence, 305
vorticity, 211, 214Coherent Vortex Simulation (CVS), 215Collapse, 305
373
374
Collective dissipation, 109Commutivity, 270Complexity, 139
measures, 69, 73Compressible turbulence, 263Computer-assisted proof, 75Concentration, 34
contours, 34gradient, 34gradient enhancement, 36of fuel, 36
Conditional sampling methods, 242Connectivity, 110Conserved current, 100Constraints, 112Contact interactions, 347Continuity equation, 154Continuous family of wave functions, 101Converging flux model, 121Cooling function, 112Coriolis force, 44Corner
eddies, 355of a cubic cavity, 355
Corona, 116Coronal
activity, 111heating, 107, 111, 115tectonics, 115
Coronal Mass Ejections (CME), 122Correlation
dimension, 66functions, 305
Corrugations, 349Counter-current shear flows, 61Counter-flow, 94Creeping flow, 349Critical
layer, 48points, 270
Cross-helicity, 154, 156Cross-linkage, 152, 156Crow instability, 274, 305, 329Crystallographic groups, 270Calugareanu-White linking number, 139Current sheets, 110, 111, 115Curvature, 40, 126
D2 group, 275, 277D2h group, 277Degeneracy, 270, 271Degenerate point group, 279Density scale heights, 112Depletion of nonlinearity, 277Developed turbulence, 305Differential forms, 145, 146, 150Diffusion
accelerated, 36Diffusive reconnection, 130Dimension of the set of singular points, 273Dipole field, 37, 38, 40, 44Direct summation, 8Discrete groups, 269, 271Dissipation path, 110DNS, 177Double helix, 81Drag reduction, 349Driving and dissipation, 111Dynamical behaviour, 61
Eigenfunctions, 159, 305Eigenvalue, 305Eigenvectors, 175Ejections, 241, 244Electric
current density, 111field, 127
Ellipticinstability, 37, 38, 44vortex, 39
Elsasser variables, 298Emission measure images, 112Energy, 69, 305
conservation, 109, 305dissipation, 171, 305flux, 231gain, 26of the ground state, 143spectrum, 139, 318
Enstrophy, 139, 305Euler equations, 145, 147, 305, 317
compressible, 192Eulerian, 163Evolution equations, 127Exponentially decaying spectrum, 305Extended series, 278Exterior
derivative, 146, 148, 149product, 145
Fan reconnection, 115, 120Fast dynamo problem, 158Fast reconnection, 107, 115Fast Wavelet Transform, 213Filament method, 278
simulations, 274Finite-time
blow-up, 269singularities, 269
Finite timesingularities, 285
Finite-timesingularities, 318
TOPIC INDEX 375
Finite timesingularities, 329
Flame sheet, 36Flows
with a spatial symmetry, 305with discrete symmetries, 269
Fluidline, 188surface, 188
Flux sheet, 126Force-free, 111, 118
Euler equation, 305Fourier harmonics, 305Framing, 139Friction
matrix, 343velocity, 230
Frozen-field evolution, 131Frozen-in vortex filament, 305, 329Fuel concentration, 36Full octahedral group, 270
Gaugefield, 154group SU(2), 154group U(1), 154invariant, 152, 153transformation, 155
Gaussiandistribution, 110vortex, 32
Gauss linking number, 139Generalised theorem of Kelvin, 331Granular scales, 112Granulation turn-over times, 112Green's function, 330Grooves, 350, 351Group
C21,, 271,274D2, 275,277£>2ft,277O,281Oh, 278Abelian, 271closure property of, 271crystallographic, 270degenerate point, 279discrete, 269, 271full octahedral, 270gauge , SU(2), 154gauge , U(1), 154non-symorphic space, 281of volume preserving mappings, 331order of, 271space, 270
Hairpin vortices, 242, 246Hamiltonian
formalism for vortex lines, 330functional, 330system, 4, 38
"hard" direction, 305Helical
pitch of the vortex lines, 55structures, 61symmetry, 55vortex, 81
Helicity, 69, 73, 133, 139, 150, 152, 156conservation laws, 145, 149conservation theorem, 145, 150total, 135transition of, 55
Helium II, 69Heteroclinic
orbit, 77tangle, 6
Hierarchyof current sheets, 109, 110of higher order invariants, 153
High symmetry, 318Hill's vortex, 171, 192Hopf bifurcation, 65Hopflink, 152Hybrid spectral finite-difference method, 15
Ideal magnetohydrodynamics (MHD), 152,297
Improper rotation, 271Inactive motions, 235Incoherent vorticity, 213, 214, 220Induced velocity, 81Induction equation, 116Inertial-range turbulence, 201, 210Inertial waves, 22Infinite curvature of vortex lines, 329Infinite energy, 297Integrable hydrodynamics, 305Interior derivative, 146Intermittency, 305Intermittent fine scales, 261Inverse superharmonic bifurcation, 65Inversion, 271Irreducible representations, 269, 271Irrotational strain, 126Iso-surfaces, 109Isotopies, 152
Jacobian, 158, 305
Kelvin waves, 38, 45, 46Kelvin-Helmholtz instability, 3, 25Kelvin's
376
circulation theorem, 134, 819, 331vortex ring, 37, 39, 44
Kelvin waves, 45, 46Kida
flow, 318symmetries, 319
Kinematic dynamo, 158, 202Kinetic, energy, 305
dissipation, 111on the group of volume preserving
mappings, 331Knot invariants, 152Kolmogorov spectrum, 202, 209, 305Krein’s theory, 38
Lagrangian, 163chaos, 164, 201functional, 329turbulence, 88
Lamb-Chaplygin vortex pair, 192Largo-eddy simulation, 171Laser Doppler Anemometry (LDA), 243Limit cycle, 65Linear interpolation, 305Line-length density, 94Linkage of magnetic flux, 152
total, 156Linking number, 69, 72, 139Local
approximate Hamiltonian, 329stretching map, 87winding number, 113
Localised Induction Approximation (LIA),94
Locally self-similar, 318Logarithmic layer, 230Longitudinal parameter, 332Long-scale
approximation, 332unstable regime, 332
Lorentz force, 126Low-pressure vortex, 181Lubrication, 343Lundgren’s
spiral vortex, 186transformation, 19
Lyapunov exponent, 164, 201, 202, 204,209, 210
Mach number, 191Magnetically dominated plasma, 111Magnetic
diffusivity, 127dissipation, 107, 108, 111dynamo, 202field, 125, 133, 151
field gradient, 128field line braiding, 107field topology, 125flux expulsion, 31flux function, 31flux tubes, 153helicity, 152induction equation, 127link, 139reconnection, 125
Magneticreconnection, 133
Magneticrelaxation, 139Reynolds number, 109, 134surface fi l l ing factor, 113
Magnetohydrodynamics (MHD), 133, 145,148, 149, 151
two-dimensional, 31Massey
higher products, 153triple product, 153, 154
Massively parallel supercomputers, 112Matching solutions, 33Material
curve, 4surface, 6, 8
Mathematica, 323Matrix representation, 271MDI magnetogram, 112Mechanical friction, 343Minimal flow, 234Mixed Lagrangian-Eulerian description, 305Mixing, 87
layer, 214Modelling of turbulence, 211Monolithic current sheets, 108Moore-Saffman-Tsai-Widnall instability, 37,
46Moore-Saffman vortex, 39Moore’s spiral vortex, 186Moving grid. 305Multipole approximation, 8Multi-Resolution Analysis, 212, 219“mushroom” structure, 195
Navier-Stokes equation, 127, 133N–body problem, 8Near-wall turbulent measurements, 242Noether-type symmetry, 331Nonlinear long-scale dynamics, 329Non-symmetric stretched vortices, 14Non-symorphic space group, 281Non-uniform reconnection, 119Norm, 305Nul l points, 115, 270Number of windings, 110
TOPIC INDEX 377
Numericalalgorithm, 305experiments, 107integration, 305resolution, 109simulations, 23, 57stability, 305
Observed scaling of coronal heating, 113Octahedral flows, 270, 278O group, 281 group, 278Ohm’s law, 133Opposing boundaries, 111Optimal perturbations, 26Order of the group, 271Orthogonal
dipoles, 270, 275wavelet, 212
Oscillating vortex pair, 6Outer boundary condition, 126
Pancake structure, 305Parameterisation of the vortex line, 332Parametric resonance, 38, 41
instability, 37Particle Image Velocimetry (PIV), 242Passive
scalar, 31, 179vector field, 129
Péclet number, 32Periodic rough surface, 349Petschek reconnection, 118Phase alignment, 242, 244Photosphere, 112, 115Photospheric velocity field, 112Physical knot, 139Piece-spline interpolation method, 91PIV, 242Planar flow, 3Plasma beta, 108Plasma physics, 151Poincaré section, 6Point singularity, 305Point vortex dynamics, 75, 87Potential, 111Pressure scale heights, 112Primary and secondary vortices, 242Primary mode, 45Principle of stationary phase, 162Probability density, 99Pseudo-spectral method, 278Pure gauge Yang-Mills field, 155Pure shear, 38, 39, 41
Quadrupole field, 38, 39, 41
Quantised vortices, 93Quantum vortex tangle, 93Quasi-static approximation, 22, 23Quasi-streamwise vortices, 233
Random-amplitude Fourier harmonics, 305Rankine vortex, 37, 39, 44, 46Rapid distortion theory, 22, 203Rapid reconnection, 126Rayleigh-Taylor flows, 191Recirculating bubbles in swirl flows, 55Reconnection, 3, 97, 115, 125, 133
line, 137processes, 296rapid, 126rate, 133saddle point, 130separator, 115spine, 115three-dimensional, 120
Reflection, 271Regular grid, 305Regularisation procedure, 329Regularised
Biot-Savart kernel, 3models, 330
Regularity of solutions of the hydrodynamicequations, 269
Relabelling of Lagrangian labels, 331Relaxation oscillation, 76Resistive scale, 110Resistivity, 109Resolution constraints, 111Resonance, 166Resonance band, 6Restricted Euler equation, 247Reynolds
number, 108, 134stress, 243
Ribs, 214Riccati equation, 299Richtmyer-Meshkov flows, 191Robinson, 241Rollers, 214Rotating
cavity, 55channel flow, 171
Rough surface, 346Roughness grooves, 349
41, 44Saddle point reconnection, 130Sawtooth profile, 354Scalar flux, 171Scaling
law, 113
378
laws derived from observations, 113of the photospheric motions, 109
Schmidt number, 32, 171Schrödinger equation, 99Second Chern class, 154Self-induced velocity, 81Self-similar
collapse, 278solutions, 116, 334variables, 305
Self-similarity, 305, 326Self-sustained oscillation, 3Separator, 121
reconnection, 115, 120Separatrices, 131Series solution, 351Shear layers, 25Shock-curtain, 191Sign-singular measure, 165Similarity
solution, 32variable, 34
Singular perturbation parameter, 33Singular point, 33
regular, 33irregular, 33
Singularity, 134, 285, 305formation, 296, 305formation in MHD, 295
Singularparabolic equations, 335potentials, 335
Slip velocity, 350Slowly varying, 160Smoothing, 305Sobolev space, 305“soft” direction, 305Solar flares, 115, 122Solenoidal field, 305Solvability condition, 45Space group, 270Spatially complex magnetic field, 111Spatial
point-wise singularity, 273resolution, 112, 305
Spectrum, 305of a passive scalar, 171
Spine reconnection, 115, 120Spiral
arm, 16vortex, 171, 262wind-up, 36
Spitzer conductivity, 112Stagnation flow, 134Statistical equations of hydrodynamics, 305Steady solution, 305Stirring process, 87
Stokes flow, 343, 344, 355Strained elliptic vortex, 6Straining flow, 126Strain rate / vorticity coupling, 276Stratified turbulence, 191Streamwise
momentum, 32vortices, 32
Stretching, 19, 26Subgrid-scale model, 171Subharmonic bifurcation, 65Sun, 115Superfluid
helium, 93turbulence, 69, 70
Supergranules, 116Superharmonic bifurcation, 65Super-weak collapse, 305Surface roughness, 349Suspension, 343Sweep, 241, 244Swirling jet, 19Swirl number, 21Synthetic emission measures, 107, 112
Taylor expansion, 305Taylor-Green vortex, 270, 277Temporal asymptotic behaviour, 61Tensor eddy-diffusivity, 178Third-order topological invariants, 151, 153Tilt angles, 110Topological
bounds, 139classification, 56crossing number, 139invariants, 72, 151measures of complexity, 151
Topology, 69, 117, 133of divergence-free fields, 151of magnetic field, 125
Toroidal / poloidal decomposition, 281TRACE satellite, 112Tracers, 31Trajectory, 163Transient growth, 26Treecode algorithm, 8Tubular vortices, 181Turbulence, 69, 181, 229Turbulent
flows, 19, 211kinetic energy, 231mixing, 172
Twisted torus, 152
Variational principle, 331Velocity
TOPIC INDEX 379
pattern, 111spectra, 237streaks, 233
Vertical resolution, 112Vinen equation, 93Viscous sublayer, 230Visiometrics, 191Von Karman wake, 192Vortex
blob method, 3breakdown, 55bursts, 19core, 3core oscillation, 3
Vortexbi-layers, 191
Vortexextraction algorithm, 212filament model, 318filaments, 69diffusing Gaussian, 32, 33lines, 69, 99, 305merging, 13pair, 4
Vortexprojectiles (VPs), 191
Vortexreconnection, 8, 70, 133, 285Reynolds number, 32ring, 4, 37, 96ring merger, 3, 8sheet, 25
sheet roll-up, 3structures, 201switch-over, 99tangles, 139tracking, 181tubes, 305
Vorticity, 36, 69, 133, 145, 147, 148, 305background, 36cancellation, 3filaments, 19isosurface, 8quantisation, 101transport equation, 15
Wall-bounded turbulence, 229Wall units, 230Wavelet, 211Weak field limit, 129Weber formula, 286Winding, 110Winding number of the vacuum, 155Wind-up of isolines, 36
spiral, 36WKBJ approach, 26, 33, 160Writhing number, 69, 72
X-Points, 116X-ray bright point, 121
Yang-Mills field, 155
MechanicsFLUID MECHANICS AND ITS APPLICATIONS
Series Editor: R. Moreau
Aims and Scope of the Series
The purpose of this series is to focus on subjects in which fluid mechanics plays a fundamental role.As well as the more traditional applications of aeronautics, hydraulics, heat and mass transfer etc.,books will be published dealing with topics which are currently in a state of rapid development,such as turbulence, suspensions and multiphase fluids, super and hypersonic flows and numericalmodelling techniques. It is a widely held view that it is the interdisciplinary subjects that will receiveintense scientific attention, bringing them to the forefront of technological advancement. Fluids havethe ability to transport matter and its properties as well as transmit force, therefore fluid mechanicsis a subject that is particularly open to cross fertilisation with other sciences and disciplines ofengineering. The subject of fluid mechanics will be highly relevant in domains such as chemical,metallurgical, biological and ecological engineering. This series is particularly open to such newmultidisciplinarydomains.
M. Lesieur: Turbulence in Fluids. 2nd rev. ed., 1990 ISBN 0-7923-0645-7O. Métais and M. Lesieur (eds.): Turbulence and Coherent Structures. 1991
ISBN 0-7923-0646-5R. Moreau: Magnetohydrodynamics. 1990 ISBN 0-7923-0937-5E. Coustols (ed.): Turbulence Control by Passive Means. 1990 ISBN 0-7923-1020-9A. A. Borissov (ed.): Dynamic Structure of Detonation in Gaseous and Dispersed Media. 1991
ISBN 0-7923-1340-2K.-S. Choi (ed.): Recent Developments inTurbulence Management. 1991 ISBN 0-7923-1477-8E.P. Evans and B. Coulbeck (eds.): Pipeline Systems. 1992 ISBN 0-7923-1668-1B. Nau (ed.): Fluid Sealing. 1992 ISBN 0-7923-1669-XT.K.S. Murthy (ed.): Computational Methods in Hypersonic Aerodynamics. 1992
ISBN 0-7923-1673-8R. King (ed.): Fluid Mechanics of Mixing. Modelling, Operations and Experimental Tech-niques. 1992 ISBN 0-7923-1720-3Z. Han and X. Yin: Shock Dynamics. 1993 ISBN 0-7923-1746-7L. Svarovsky and M.T. Thew (eds.): Hydroclones. Analysis and Applications. 1992
ISBN 0-7923-1876-5A. Lichtarowicz (ed.): Jet Cutting Technology. 1992 ISBN 0-7923-1979-6F.T.M. Nieuwstadt (ed.): Flow Visualization and Image Analysis. 1993 ISBN 0-7923-1994-XA.J. Saul (ed.): Floods and Flood Management. 1992 ISBN 0-7923-2078-6D.E. Ashpis, T.B. Gatski and R. Hirsh (eds.): Instabilities and Turbulence in EngineeringFlows. 1993 ISBN 0-7923-2161-8R.S. Azad: The Atmospheric Boundary Layer for Engineers. 1993 ISBN 0-7923-2187-1F.T.M. Nieuwstadt (ed.): Advances in Turbulence IV. 1993 ISBN 0-7923-2282-7K.K. Prasad (ed.): Further Developments in Turbulence Management. 1993
ISBN 0-7923-2291-6Y.A. Tatarchenko: Shaped Crystal Growth. 1993 ISBN 0-7923-2419-6J.P. Bonnet and M.N. Glauser (eds.): Eddy Structure Identification in Free Turbulent ShearFlows. 1993 ISBN 0-7923-2449-8R.S. Srivastava: Interaction of Shock Waves. 1994 ISBN 0-7923-2920-1J.R. Blake, J.M. Boulton-Stone and N.H. Thomas (eds.): Bubble Dynamics and InterfacePhenomena. 1994 ISBN 0-7923-3008-0
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MechanicsFLUID MECHANICS AND ITS APPLICATIONS
Series Editor: R. Moreau
R. Benzi (ed.): Advances in Turbulence V. 1995 ISBN 0-7923-3032-3B.I. Rabinovich, V.G. Lebedev and A.I. Mytarev: Vortex Processes and Solid Body Dynamics.The Dynamic Problems of Spacecrafts and Magnetic Levitation Systems. 1994
ISBN 0-7923-3092-7P.R. Yoke, L. Kleiser and J.-P. Chollet (eds.): Direct and Large-Eddy Simulation I. Selectedpapers from the First ERCOFTAC Workshop on Direct and Large-Eddy Simulation. 1994
ISBN 0-7923-3106-0J.A. Sparenberg: Hydrodynamic Propulsion and its Optimization. Analytic Theory. 1995
ISBN 0-7923-3201-6J.F. Dijksman and O.D.C. Kuiken (eds.): IUTAM Symposium on Numerical Simulation ofNon-Isothermal Flow of Viscoelastic Liquids. Proceedings of an IUTAM Symposium held inKerkrade, The Netherlands. 1995 ISBN 0-7923-3262-8B.M. Boubnov and G.S. Golitsyn: Convection in Rotating Fluids. 1995 ISBN 0-7923-3371-3S.I. Green (ed.): Fluid Vortices. 1995 ISBN 0-7923-3376-4S. Morioka and L. van Wijngaarden (eds.): IUTAM Symposium on Waves in Liquid/Gas andLiquid/Vapour Two-Phase Systems. 1995 ISBN 0-7923-3424-8A. Gyr and H.-W. Bewersdorff: Drag Reduction of Turbulent Flows by Additives. 1995
ISBN 0-7923-3485-XY.P. Golovachov: Numerical Simulation of Viscous Shock Layer Flows. 1995
ISBN 0-7923-3626-7J. Grue, B. Gjevik and J.E. Weber (eds.): Waves and Nonlinear Processes in Hydrodynamics.1996 ISBN 0-7923-4031-0P.W. Duck and P. Hall (eds.): IUTAM Symposium on Nonlinear Instability and Transition inThree-Dimensional Boundary Layers. 1996 ISBN 0-7923-4079-5S. Gavrilakis, L. Machiels and PA. Monkewitz (eds.): Advances in Turbulence VI. Proceedingsof the 6th European Turbulence Conference. 1996 ISBN 0-7923-4132-5K. Gersten (ed.): IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows atHigh Reynolds Numbers. Proceedings of the IUTAM Symposium held in Bochum, Germany.1996 ISBN 0-7923-4138-4J. Verhás: Thermodynamics and Rheology. 1997 ISBN 0-7923-4251 -8M. Champion and B. Deshaies (eds.): IUTAM Symposium on Combustion in Supersonic Flows.Proceedings of the IUTAM Symposium held in Poitiers, France. 1997 ISBN 0-7923-4313-1M. Lesieur: Turbulence in Fluids. Third Revised and Enlarged Edition. 1997
ISBN 0-7923-4415-4; Pb: 0-7923-4416-2L. Fulachier, J.L. Lumley and F. Anselmet (eds.): IUTAM Symposium on Variable Density Low-Speed Turbulent Flows. Proceedings of the IUTAM Symposium held in Marseille, France. 1997
ISBN 0-7923-4602-5B.K. Shivamoggi: Nonlinear Dynamics and Chaotic Phenomena. An Introduction. 1997
ISBN 0-7923-4772-2H. Ramkissoon, IUTAM Symposium on Lubricated Transport of Viscous Materials. Proceed-ings of the IUTAM Symposium held in Tobago, West Indies. 1998 ISBN 0-7923-4897-4E. Krause and K. Gersten, IUTAM Symposium on Dynamics of Slender Vortices. Proceedingsof the IUTAM Symposium held in Aachen, Germany. 1998 ISBN 0-7923-5041-3A. Biesheuvel and G.J.F. van Heyst (eds.): In Fascination of Fluid Dynamics. A Symposiumin honour of Leen van Wijngaarden. 1998 ISBN 0-7923-5078-2
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FLUID MECHANICS AND ITS APPLICATIONSSeries Editor: R. Moreau
U. Frisch (ed.): Advances in Turbulence VII. Proceedings of the Seventh European TurbulenceConference, held in Saint-Jean Cap Ferrat, 30 June–3 July 1998. 1998 ISBN 0-7923-5115-0E.F. Toro and J.F. Clarke: Numerical Methods for Wave Propagation. Selected Contributionsfrom the Workshop held in Manchester, UK. 1998 ISBN 0-7923-5125-8A. Yoshizawa: Hydrodynamic and Magnetohydrodynamic Turbulent Flows. Modelling andStatistical Theory. 1998 ISBN 0-7923-5225-4T.L. Geers (ed.): IUTAM Symposium on Computational Methods for Unbounded Domains.1998 ISBN 0-7923-5266-1Z. Zapryanov and S. Tabakova: Dynamics of Bubbles, Drops and Rigid Particles. 1999
ISBN 0-7923-5347-1A. Alemany, Ph. Marty and J.P. Thibault (eds.): Transfer Phenomena in Magnetohydrodynamicand Electroconducting Flows. 1999 ISBN 0-7923-5532-6J.N. Sørensen, E.J. Hopfinger and N. Aubry (eds.): IUTAM Symposium on Simulation andIdentification of Organized Structures in Flows. 1999 ISBN 0-7923-5603-9G.E.A. Meier and P.R. Viswanath (eds.): IUTAM Symposium on Mechanics of Passive andActive Flow Control. 1999 ISBN 0-7923-5928-3D. Knight and L. Sakell (eds.): Recent Advances in DNS and LES. 1999 ISBN 0-7923-6004-4P. Orlandi: Fluid Flow Phenomena. A Numerical Toolkit. 2000 ISBN 0-7923-6095-8M. Stanislas, J. Kompenhans and J. Westerveel (eds.): Particle Image Velocimetry. Progresstowards Industrial Application. 2000 ISBN 0-7923-6160-1H.-C. Chang (ed.): IUTAM Symposium on Nonlinear Waves in Multi-Phase Flow. 2000
ISBN 0-7923-6454-6R.M. Kerr and Y. Kimura (eds.): IUTAM Symposium on Developments in Geophysical Turbu-lence held at the National Center for Atmospheric Research, (Boulder, CO, June 16–19, 1998)2000 ISBN 0-7923-6673-5T. Kambe, T. Nakano and T. Miyauchi (eds.): IUTAM Symposium on Geometry and Statisticsof Turbulence. Proceedings of the IUTAM Symposium held at the Shonan International VillageCenter, Hayama (Kanagawa-ken, Japan November 2–5, 1999). 2001 ISBN 0-7923-6711-1V. V. Aristov: Direct Methods for Solving the Boltzmann Equation and Study of NonequilibriumFlows. 2001 ISBN 0-7923-6831 -2P.F. Hodnett (ed.): IUTAM Symposium on Advances in Mathematical Modelling of Atmosphereand Ocean Dynamics. Proceedings of the IUTAM Symposium held in Limerick, Ireland, 2–7July 2000. 2001 ISBN 0-7923-7075-9A.C. King and Y.D. Shikhmurzaev (eds.): IUTAM Symposium on Free Surface Flows. Pro-ceedings of the IUTAM Symposium held in Birmingham, United Kingdom, 10–14 July 2000.2001 ISBN 0-7923-7085-6A. Tsinober: An Informal Introduction to Turbulence. 2001
ISBN 1-4020-0110-X; Pb: 1-4020-0166-5R.Kh. Zeytounian: Asymptotic Modelling of Fluid Flow Phenomena. 2002
ISBN 1-4020-0432-XR. Friedrich and W. Rodi (eds.): Advances in LES of Complex Flows. Prodeedings of theEUROMECH Colloquium 412, held in Munich, Germany, 4-6 October 2000. 2002
ISBN 1-4020-0486-9D. Drikakis and B.J. Geurts (eds.): Turbulent Flow Computation. 2002 ISBN 1-4020-0523-7B.O. Enflo and C.M. Hedberg: Theory of Nonlinear Acoustics in Fluids. 2002
ISBN 1-4020-0572-5
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FLUID MECHANICS AND ITS APPLICATIONSSeries Editor: R. Moreau
I.D. Abrahams, P.A. Martin and M.J. Simon (eds.): IUTAM Symposium on Diffraction andScattering in Fluid Mechanics and Elasticity. Proceedings of the IUTAM Symposium held inManchester, (UK, 16-20 July 2000). 2002 ISBN 1 -4020-0590-3P. Chassaing, R.A. Antonia, F. Anselmet, L. Joly and S. Sarkar: Variable Density FluidTurbulence. 2002 ISBN 1-4020-0671-3A. Pollard and S. Candel (eds.): IUTAM Symposium on Turbulent Mixing and Combustion.Proceedings of the IUTAM Symposium held in Kingston, Ontario, Canada, June 3-6, 2001.2002 ISBN 1-4020-0747-7K. Bajer and H.K. Moffatt (eds.): Tubes, Sheets and Singularities in Fluid Dynamics. 2002
ISBN 1-4020-0980-1P.W. Carpenter and T.J. Pedley (eds.): Flow Past Highly Compliant Boundaries and in Col-lapsible Tubes. IUTAM Symposium held at the Univerity of Warwick, Coventry, UnitedKingdom, 26-30 March 2001. 2003 ISBN 1-4020-1161-X
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