organising committee - springer978-1-4615-3750... · 2017-08-27 · organising committee j. jimenez...
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ORGANISING COMMITTEE
J. Jimenez (Director) Departamento de Mecanica de Fluidos Esc. Teen. Sup. Ing. Aeronauticos PI. Cardenal Cisneros 3 28040 -Madrid SPAIN
P. Huerre Dept. Mecanique Ecole Polytecnique, Departamentale 36 91128 Palaiseau cedex FRANCE
A. Lifian Departamento de Mecanica de Fluidos Esc. Teen. Sup. Ing. Aeronauticos PI. Cardenal Cisneros 3 28040 -Madrid SPAIN
Y. Pomeau Groupe de Physique Statistique de l'ENS 24, Rue Lhomond 75231 Paris Cedex 05 FRANCE
P. Saffman Applied Mathematics (217-50) California Institute of Technology Pasadena, CA 91125 USA
357
LECTURERS
G. Ahlers Lehrstuhl fur Theoretische Physik IV Universitat Bayreuth Postfach 101251 8580 Bayreuth GERMANY
J .C. Antoranz Dpto. Fisica Fundamental Univ. Educacion a Distancia Apto. 50487 28080 Madrid SPAIN
Roberto Benzi Universita di Roma Dip. di Fisica Via Orazio Raimondo 1-00173 Roma ITALY
T. Bohr Niels Bohr Institute Blegdamsvej, 17 2100 Copenhagen DENMARK
H.R. Brand FB 7 Department of Physics University of Essen D 4300 Essen 1 GERMANY
H. Chate Institut de Recherche Fondamentale DPh-G/PSRM, CEN Saclay F 91191 Gif-sur-Yvette cedex FRANCE
J-M. Chomaz CNMR 42 Av. G. Coriolis 31057 Toulouse FRANCE
P. Clavin Laboratoire de Recherche en Combustion Universite de Provence Centre Saint Jerome 13397 Marseille Cedex 13 FRANCE
R.J. Deissler Center for Nonlinear Studies Los Alamos National Laboratory Los Alamos, N .M. 87545 USA
Stephan Fauve Ecole Normale Superieur Lyon 46 allee d'ltalie 69364 Lyon Cedex 07 FRANCE
359
H. Fiedler Technische Universitat Berlin Hermann-Fottinger Institut Strasse des 17 Juni D-1000 Berlin 12 GERMANY
M. Gharib Dept. of AMES, R-011 Univ. California San Diego La Jolla, CA. 92093 USA
J.D. Gibbon Mathematics Department Imperial College London, SW7 2AZ UNITED KINGDOM
J .A. Hernandez Ramos Departamento de Mecanica de Flufdos Esc. Teen. Sup. Ing. Aeronauticos PI. Cardenal Cisneros 3 28040 -Madrid SPAIN
E. Hopfinger Institut de Mechanique de Grenoble B.P.68 38402 S.-Martin d'Heres Cedex FRANCE
M. Jensen Nordita Blegdamsvej, 17 2100 Copenhagen DENMARK
J.e. Lasheras Department of Mechanical Engineering University of Southern California Los Angeles, CA 90089-1191 USA
360
M. Lesieur Institut de Mechanique de Grenoble B.P.53X 38041 Grenoble Cedex FRANCE
J.L. Lumley Sibley School of Mechanical and Aerospace Engineering Upson and Grumman Hall Cornell Bniversity Ithaca, NY 14853-7501 USA
L. Kleiser DFLVR Institute for Theoretical Fluid Mechanics Bunsenstrasse 10 D-3400 Gottingen GERMANY
R. MacKay Mathematics Institute University of Warwick Coventry CV 4 7 AL UNITED KINGDOM
J.M. Massaguer E.T.S. Ingenieros Telecomunicaci6n Universidad Politecnica de Cataluiia Jordi Girona Salgado 31 08034 Barcelona SPAIN
O. Metais Institut de Mechanique de Grenoble B.P.53X 38041 Grenoble Cedex FRANCE
P. Moin Mechanical Engineering Department Stanford University Stanford, CA 94305 USA
D. Papailiou Dept. Mechanical Engineering University of Patras llio 26001 Patras GREECE
C. Perez Garda Dpto. Ffsica Facultad de Ciencias U niversidad de Navarra E-31080 Pamplona SPAIN
A. Pumir Laboratoire de Physique Statistique Ecole Normale Superieure 24, Rue Lhomond F-75231 Paris Cedex 05 FRANCE
W. Reynolds Mechanical Engineering Department Stanford University Stanford, CA 94305 USA
Renzo llicca Dept. AMTP Silver Street Cambridge, CB3 9EW UNITED KINGDOM
Jean-Pierre llivet Observatoire de Nice, BP139 06003 Nice Cedex FRANCE
Erika Roesch Max-Planck Inst. fUr Stromungsforschung Bunsenstr. 10 D-3400 Gottingen GERMANY
A. Roshko Aeronautics Department California Institute of Technology Pasadena, CA 91125 USA
Miguel A. Rubio Dpto. Ffsica Fundamental Univ. Educaci6n a Distancia Apto. 50487 28080 Madrid SPAIN
C. Simo Dept. Matematicas Aplicadas y AnaIisis Facultad de Matematicas Universidad de Barcelona Plaza de la Universidad Barcelona SPAIN
C. Van Atta Department of Applied Mechanics and Engineering Sciences (R-013) University of California, San Diego La Jolla, Ca. 92093-0413 USA
M.G. Velarde Facultad de Ciencias Univ. Educaci6n a Distancia Apto. 60141 28071 Madrid SPAIN
D. Walgraef Service de Chimie-Physique Universite Libre de Bruxelles Campus Plaine, C.P. 231 B-1050 Bruxelles BELGIUM
I. Wygnanski Faculty of Engineering Tel-Aviv University Ramat-Aviv Tel-Aviv, 69978 Israel ISRAEL
361
N. Zabusky Dept. Mechanical and Aerospace Eng. College of Engineering Rutgers University, P.O. Box 909 Piscataway, N J 08855-0909 USA
Stephane Zaleski Lab. Physique Statistique Ecole Normale Superieure 24 Rue Lhomond 75231 Paris cedex 05 FRANCE
362
W. Zimmerman Lehrstuhl fur Theorische Physik U niversitat Bayreuth Postfach 101251 8580 Bayreuth GERMANY
PARTICIPANTS
J.C. Agiif IBM Scientific Centre Paseo Castellana 4 28046 -Madrid SPAIN
Roque Corral Departamento de Mecanica de Flufdos Esc. Teen. Sup. Ing. Aeromiuticos PI. Cardenal Cisneros 3 28040 -Madrid SPAIN
Owen E. Cote Air Force Office of Scientific Research European Off. Aerospace Res. & Dev. 233 Old Marylebone Rd. London NW1 5TH UNITED KINGDOM
M. de la Torre Dpto. Ffsica Fundamental Univ. Educacion a Distancia Apto.50487 28080 Madrid SPAIN
C. Dopazo Dept. Mecanica de Fluidos E. T .S.1. Industriales Marfa Zambrano 50 Polfgono Actur 50015, Zaragoza SPAIN
Miguel A. Fernandez Sanjuan Dpto. de Ffsica ETS Arquitectura Universidad Politecnica de Madrid 28040 Madrid SPAIN
M. Gaster Engineering Department Cambridge University Cambridge, CB3 9EW UNITED KINGDOM
F. Higuera Departamento de Mecanica de Flufdos Esc. Teen. Sup. Ing. Aeronauticos PI. Cardenal Cisneros 3 28040 -Madrid SPAIN
P. Juvet Mechanical Engineering Department Stanford University Stanford, CA 94305 USA
Carlos Martel Departamento de Mecanica de Flufdos Esc. Teen. Sup. Ing. Aeronauticos PI. Cardenal Cisneros 3 28040 -Madrid SPAIN
363
Roy E. Reichenbach Aeronautics and Mechanics Branch US Army European Res. Off. 233 Old Marylebone Rd. London NWI 5TH UNITED KINGDOM
Ezequiel del Rio-Fernandez Dpto. Fisica Fundamental Univ. Educacion a Distancia Apto. 50487 28080 Madrid SPAIN
Maurice Rossi Mecanique Theorique Universite de Paris VI Tour 66- 4, Place Jussieu 75230 Cedex 05, Paris FRANCE
J aume Timoneda Matematicas Aplicadas i AmUisis Univ. de Barcelona Gran VIa 585 08091 Barcelona SPAIN
364
Douglas A. Varela 15 Flag St. Massachusetts Institute of Technology Cambridge, MA 02139 USA
P.D. Weidman Department of Mech. Engineering University of Colorado Boulder, Co. USA
J. Zufiria IBM Scientific Centre Paseo Castellana 4 28046 -Madrid SPAIN
INDEX
Absolute instabilities, 23, 24-25, 58, 63 Acoustic excitation, 89, 90-91, 93 Active control of shear flow, 58 Aliasing errors, 124, 125 Analytic function theory, 135 Anisotropic diffusion terms, 321, 322, 326 Annular chaos, 242 Anti-Fourier transforms, 195 Argon laser technique, 16 Artificial compressibility, 177 Axial forcing
in laminar, co-flowing forced jets, 95, 96, 99,101,102,107
in round jets, 89, 90 Axisymmetric forcing, 97, 100, 343 Azimuthal forcing
in laminar, co-flowing forced jets, 95, 96, 97,99,100,102,105,107
puffs and, 343
Barber-pole instabilities, 251 Benard problem, 247-256, see also Parallel
flows Benney-Lin equations, 278 Betchov-Da Rios equations, 257-260 Bifurcations, 89, 350
in dynamical systems theory, 211, 218-219 Hopf, 320, 322-323, 327 noise effect on, 183-188 nonlinear oscillators and, 289-292,
293-294, 295 pattern formation and, 319, 320, 322-323,
325,326,327 puffs and, 275, 345 subcritical instabilities in, see Subcritical
bifurcations Billows, 143, 145, 146, 147-148, 149, 150,
151, 152, 337, see also Waves Biot-Savart law, 203, 266 Blasius theory, 27, 277 Blooming jets, 89, 94 Bluffbodies, 43, 49, 51-53 Boltzmann equations, 339 Boundary layers
DNS of, 123, 128-130, 167, 170-172,332 dynamical systems theory and, 211-219
see also Dynamical systems theory
Boundary layers (cont'd) in laminar, co-flowing forced jets, 101 in thermal turbulence, 167-170, 175 vortex shedding and, 17 in wall jets, 68, 73
Boussinesq equations, 155, 160, 162, 170, 177, see also Non-Boussinesq conditions,
Braid regions DNS of, 145, 146 in laminar, co-flowing forced jets, 100,
102, 104 Brown-Rebollo concentration probe, 4-5 Brunt-Vaisala frequencies, 14, 161 Bubble formation, 133-141
core bursting and, 207 equations in, 134 evolution of disturbances in, 137-138 one-dimension solutions to, 138-139 two-dimensional evolution and, 139-141 uniform state instabilities in, 135-137
Buoyancy, 19, 162, 168,247,250 Burgers vortices, 201, 202, 203
Cantor sets, 230, 299 Cartesian coordinates, 159, 249, 276 Cauchy transformations, 262 Central manifold theory, 191 CGL equations, see Complex
Ginzburg-Landau equations Channel flows, 135-137, 140,141,334 Chaotic advection, 3 Chaotic attractors, 290, 297 Chaotic dynamics, 111, 112 Chaotic repellors, 299 Closed flows, 251-255 Closure model, of bubble formation, 134 Coanda effect, 59 Codimension-two bifurcation theory, 287 Coherent chaos, 297-302 Coherent motion, 81, 82 Coherent structures, 58, 68, 203, 211, 354
DNS of, 143-152,332,333 Complex Ginzburg-Landau (CGL) equations,
309-316 lattice theorem for, 311-312,315
Contractible chaos, 242 Convective chaos, 302-304
365
Convective instabilities, 58, 136, see also Nonlinear convective
instabilities Cooperative instabilities, 203 Core bursting, 202, 207 Corrsin-Oboukov theory, 157,158,159 Couette flow, 169, 170, 176,250-251,277,
345, see also Taylor-Couette flow Coupled map lattices, 297-307
coherent to incoherent chaos in, 297-302 convective chaos and, 302-304 power laws in, 304
Cylinders, 51-53, 115, 117 Dense fluidized beds, 133-141, see also
Bubble formation Desingularization, 204 DiffusiW, 155, 156, 157, 158, 162 Direct numerical simulation (DNS), 123-130,
352 of coherent structures, 143-152, 332, 333 as experiments, 331-339 of intermittency, 221,222 minimal flow unit in, 123, 128-130 outflow boundary conditions and, 125-128 of puffs, 341 ofRBC, 170-172, 176 spatial discretization in, 124-125
Dissipation, 222, 230, 310, 353, 354 noise effect on, 183-188
Double helices, 17 Doubly periodic channel flows, 247, 248, 249,
250,252,254 Drag
in dynamical systems theory, 211, 218-219 external excitation and, 79, 82, 83, 86
Duffing oscillator, 287 Dynamical systems theory, 211-219, 234
energy transfer model in, 213 equations in, 212-213 physical interpretation of, 214-217 Proper Orthogonal Decomposition in,
211-212, 218 wall region flow implications in, 213-214
Eckhaus instabilities, 321 Eddies, 349
in dynamical systems theory, 214, 217 in Kolmogorov spectra, 221 in large scale vortices, 33 in mixing transitions, 4, 9, 10 in thermal convection, 173
E.D.Q.N.M. calculations, 158, 159 Einstein convention, 276 Electro-convection, 183, 184 Energy transfer model, 213 Enstrophy, 261-263,353 Equilibrium hypothesis, 33, 38 Equivalent iterative map, 292-294 Euler equations, 243, 309, 351
in fIlamentation, 207 invariants of, 257, 259, 260-263 puffs and, 344
366
Euler equations (cont'd) in reconnection, 206 vortex line stretching and, 265, 266, 269
Expansion theorem, 260 External excitation, 67-86
in forced flows, 67, 75-86 in unforced flows, 67, 68-75, 76, 78, 82, 84,
85,86 Extrusive filamentation, 206
Fary-Milnor theorem, 260 Fencheltheorem, 260 Filamentation, 202, 206-207, see also Vortex
filaments Finite amplitude instabilities, 274-278 Finite-difference simulations, 124-125, 126 Floquet multipliers, 235, 291, 295 FLOSIAN, 146 Flow behind a backwards-facing step, 143,
149-150,152 Flow visualizations, see also specific types
of {iQrtler instability, 29 oflaminar, co-flowing forced jets, 99 of large scale vortices, 34 of mixing transitions, 3, 9 of vortex shedding, 13
Fluctuations, 319,320, 324-327 Forced flows, 67, 75-86 Fourier modes
in bubble formation, 137 in coupled map lattices, 301, 307 DNS of, 124, 125, 146 in dynamical systems theory, 212, 217 external excitation effect on, 82 RCs and, 194, 195 L.E.S. of, 156, 157 in mixing transitions, 9 in parallel flows, 250, 256 pattern formation and, 320 in Ruelle-Takens route, 236 in shell model, 222 vortex line stretching and, 266
Fractals, 230, 348-349 Frechet derivatives, 276 Free-shear flows, 68, 75, 97
DNS of coherent structures in, 143-152
mixing transitions in, 3-10, see also Mixing transitions
Free-shear layers, 3,5,8,96,99 Froude numbers
in bubble formation, 134 L.E.S. of, 161, 162 vortex shedding and, 13-14, 19
Galerkin projections, 211, 212 Galerkin truncations, 255-256 Gaussian distributions, 176
L.E.S. of, 159-160, 162 Gaussian white noise, 325, 326 Gaussian window, 137 Gauss linking number, 261
Ginzburg-Landau equations, 25, 191, 278, 319, see also Complex Ginzburg-Landau equations
Gledzer model, 222 Global instabilities, 58 Gortler instabilities, 23-31
forcing effects on, 29-30 forcing means used in, 28 geometry with counter-profile, 27-28,29,
31 geometry without counter-profile, 27, 29,
31 Gravity,161 Green's function, 23
Hairpin vortex filaments, 145, 146, 149 Hamiltonian systems, 207, 225, 259-260, 348,
351,353,354 Hard turbulence, see Strong turbulence Hartree approximations, 325 Hasimoto transformations, 258, 260 Heisenberg parameters, 213, 214, 215 Helical-pairing instabiliw, 143, 147-149, 151,
152 Helicity
in Betchov-Da Rios equations, 259-260 in Euler equations, 260-262 in homogeneous fluids, 17 puffs and, 345 in round jets, 89, 90, 91, 93
Helmholtz oscillator, 97, 287-295 equivalent iterative map and, 292-294 intermittency in, 289-292, 294
Heteroclinic cycle, 219 Hexagonal convective cells (HCs), 191-197
under non-Boussinesq conditions, 191-192, 194-196, 197
stationary defects in, 196-197 High-order upwind-based schemes, 125 Hilbert-Schmidt theory, 211 Hill spherical vortices, 201 Homogeneous fluids, 13, 14-17 Homogeneous turbulence, 335, 349 Hopfbifurcations, 320, 322-323, 327 Horseshoe vortices, 28 Hot-wire anemometry, 335, 337
of Gortler instabilities, 26, 30 in mixing transitions, 3 in round jets, 90, 94 of vortex shedding, 18,21,52-53 in wall jets, 68,75
Hydrodynamical turbulence, 297 Hyperbolic attractors, 234, 244 Hyperbolicity, 233, 237 Hyperbolic-tangent velocity profile, 143, 144 Hypersonic re-entry vehicles, 334 Hysteresis
in Gortler instability, 24,29 in nonlinear oscillators, 288, 290, 291
Icosahedral lattices, 325 Incoherent chaos, 297-302
Individual instabilities, 203 Infinitesimal perturbations, 134, 135 Inflow boundary conditions, 125-128 Inhomogenuos chemical reactions, 297 Instabilities, see specific types Instantaneous Lyapunov exponents, 222 Intermittency, 221-230, 355
dynamical systems theory on, 202, 218 fractal structure of, 230 L.E.S. of, 155-164, see also Large-eddy
simulation Lyapunov exponents and, 221, 222,
225-230 in nonlinear oscillators, 287, 289-292, 294,
295 shell model of, 221, 222-225
Intrusive filamentation, 206 Inviscid theory, 309,310, 313
in laminar, co-flowing forced jets, 99, 100 in mixing transitions, 5 in thermal convection, 169, 170
Isotropic turbulence, 349 DNS of, 124, 125, 126, 127, 152,335 L.E.S. of, 155, 156-160, 161, 162, 163 pattern formation and, 321, 322
Jacobian matrices, 225, 252, 253
KAM theory, 238 Kapitza instabilities, 278 Kaplan-Yorke dimension, 225, 226 Karhunen-Loeve expansion, see Proper
Orthogonal Decomposition Karman vortex streets, 111-119, 350
control of, 115-119 differential equations in, 112, 114-115,
117,118,119 model for, 113-115
Kelvin-Helmholtz instabilities DNS of, 143, 144, 146, 147-148, 149, 151 in large scale vortices, 43 mixing transitions and, 3, 5, 7, 9 in vortex shedding, 14, 17, 19
Kinetic energy, 352, 353 DNS of, 130, 143 L.E.S. of, 157-158, 159, 161, 162, 163, 164
Knotted vortices, 260, 261, 262 Kolmogorov spectra, 349, 351, 352, 354-355
coupled map lattices and, 304 intermittency and, 221-230, see also
Intermittency L.E.S. of, 157, 159, 164 mixing transitions and, 5, 9 vortex dynamics and, 201, 202, 204
Korteweg-DeVries equations, 207 KPP problem, 345 Krutzsch instability, 203
Lagrangian derivatives, 260, 265 Laminar, co-flowing forced jets, 95-107
axial forcing in, 95, 96, 99, 101, 102, 107
367
Laminar co-flowing forced jets (cont'd) azimuthal forcing in, 95, 96, 97, 99, 100,
102,105,107 Laminar flows, 3, 58, 75, 207, 334, see also
Laminar, co-flowing forced jets Landau equations, 63 Langevin equations, 304 Laplace terms, 302, 313 Large coherent structures, 68 Large-eddy simulation (L.E.S.), 155-164
of isotropic turbulence, 155, 156-160,161, 162, 163
of stably stratified turbulence, 155, 156, 160-163
of viscosity, see under Viscosity Large scale vortices, 33-49
stationary boundary conditions in, 58-59 turbulence memory and, 33, 34, 38 vortex decay in, 33, 38 vortex dipoles in, 43, 44 vortex generation in, 33, 38, 43, 45, 46, 48,
49 vortex pairing in, 33, 38, 43
Laser-induced fluorescence technique, 29 Lattice theorem, 311-312, 315 Law of the wall, 73, 74, 354 Legendre transforms, 112, 225, 303 L.E.S., see Large-eddy simulation LIA, see Localized induction approximation Linear instabilities, 206 Linearly tapered cylinders, 51-53 Linear oscillations, 287 Linear stability theory, 302 Local instabilities, 58 Localized induction approximation (IJA),
257-258,259-260,263 Lorenz model, 255 Lyapunov eigenvectors, 222, 227, 229 Lyapunov exponents, 226-227, 234
bifurcations and, 277 in coupled map lattices, 297, 299, 300,
301,304 instantaneous, 222 intermittency and, 221, 222, 225-230 Karman vortex streets and, 111 in Ruelle-Takens route, 235 s-waves and, 279
Macho turbulence, 237, see also Strong turbulence
Magnetic energy, 262 Melting theory of two-dimensional solids, 326 Miller integrators, 288 Minimal flow unit, 123, 128-130 Mixing layers, 3, 202, 350
DNS of, 123, 128, 143, 144-145 external excitation effect on, 68 Ruelle-Takens route and, 237 stationary boundary conditions and, 57,
59-64 tearing and, 203
Mixing transitions, 3-10, 123
368
Mixing transitions (cont'd) DNSof,333 small scale structures and, 4, 7-8, 9 streamwise vortices and, 3, 6-7, 9 vortex pairing and, 3, 8
Mode-locking strips, 239, 240 Modulational stability, 314 Moses method, 347, 350 Moving equilibrium, 33 Moving-front solutions, 279 Mushroom-type vortices, 145
Navier-Stokes equations, 52, 243, 309-310, 316,347,350,352
bifurcations and, 183, 188, 273, 274, 275 DNS of, 222, 336, 338, 339 in dynamical systems theory, 212, 214, 216 intermittency and, 221, 222, 224-225 L.E.S. of, 156 in mixing transitions, 9 in spatially developing mixing layers, 144 in temporal mixing layers, 146, 149 in thermal convection, 250, 251 vortex dynamics and, 201, 202 vortex line stretching and, 265, 266,
268-269 Nematic liquid crystal, 183, 184,320 NLSE, see Nonlinear Schrodinger equation Noise, see also White noise
in coupled map lattices, 299 dissipation and, 183-188 DNSand,338 in dynamical systems theory, 218
Nonaxisymetric oscillating instabilities, 14 Non-Boussinesq conditions, 191-192, 194-196,
197,319 Nonlinear absolute instabilities, 23, 24-25 Nonlinear convective instabilities, 23-31, see
also Gortler instabilities Nonlinear instabilities
absolute, 23, 24-25 convective, see Nonlinear convective
instabilities DNS of, 124, 125 in filamentation, 206-207
Nonlinear oscillators, 287-295 equivalent iterative map and, 292-294 intermittency in, 287, 289-292, 294,295 Karman vortex streets and, 112, 115
Nonlinear Schrodinger equation (NLSE), 310 invariants of, 257, 258,260 s-waves and, 278, 279, 280-281
Nonlinear wavetrains, 138 Nontrivial orthogonal coordinates, 253 Nonvariational systems, 278-285 Nozzles
of laminar, co-flowing forced jets, 95, 96-97,99,100,101,104,105,107
of round jets, 89-90, 90, 91,93 of wall jets, 67, 68, 69-70,76,79,86
Numerical simulation, see Direct numerical simulation
Nusseltnumbers,167,168,170,171,173, 175,195
Oberbeck-Boussinesq approximations, 192 Oceanic measurements, 164 Ocean surface wave turbulence, 347 One-dimensional turbulence, 311, 347 Open flows, 248-250, 274-278 Orbits,235,239,242,292,353 Orthogonal coordinates, 253 Oscillatory instability, 253, 254, 255 Outflow boundary conditions, 125-128
Pade approximations, 124 Parallel flows, 247-256
poloidal field in, 252, 253-254, 256 subcritical bifurcations in, 273, 274-278 symmetry breaking in, 248, 254-256 three-dimensional, 248, 252-255 toroidal fields in, 252-253, 256 two-dimensional, 248
Passive control of shear flow, 57-59 Pattern formation, 319-327
flow field effects on, 320-322 fluctuations and, 319, 320, 324-327 spatial forcing in, 322-324
Peak-valley-counting technique, 8 Peclet numbers, 255-256 Penrosetilings, 325 Periodic attractors, 297 Periodic orbits, 235, 239, 242, 292 Plasma turbulence, 347 Plume bursting, 173, 174, 175 Poincare invariants, 353 Poincare return maps, 291 Poiseuille flows, 249, 250, 277, 321, 345 Poloidal fields, 252, 253-254, 256 Polymers, 59, 217, 218-219 Polynomial conservation laws, 258 Pomeau-Manneville intermittencies, 287 Porous disks, 34, 36, 37, 43 Potential energy, 161, 162 Power laws, 76,304 Prandtl numbers, 353
HCsand,l94 L.E.S. of, 157, 158-159, 162 in thermal convection, 247-256, see also
Parallel flows Preston tubes, 73, 74 Primary instabilities, 58 Proper Orthogonal Decomposition, 211-212,
218 Pseudo-heliciw, 257, 259, 263 Pseudo-spectral methods, 143, 146, 156 Puffs, 275, 341-345 Pulsating instabilities, 14
Rayleigh-Benard convection (RBC), 167, 167-177,350, see also Rayleigh numbers
bifurcations and, 183, 187 boundary layer in, 167-170 DNSof,170-172,176
Rayleigh-Bernard convection (RBC) (cont'd) under non-Boussinesq conditions,
191-192, 194-196 pattern formation and, 322, 324 in shear absence, 173-175, 176 shear induced, 172-173
Rayleigh numbers, 187, 188,192, 194,248, 255, see also Rayleigh-Benard convection
RBC, see Rayleigh-Benard convection RD equations, see Reaction diffusion
equations Reaction diffusion (RD) equations, 273, 274,
275-276 Recirculation zones, 14, 15, 21 Reconnection, 202, 204-206 Resonance regions, 239 Reynolds numbers, 309, 349, 350, 351, 352,
353,354,355 bifurcationsand,188,273,274,275,285 bluff bodies in, 51-53 in bubble formation, 134 DNS of, 123, 128, 143, 147, 331, 332,
333-334,335,338 in dynamical systems theory, 217 in Karman vortex streets, Ill, 113, 115,
116,350 in laminar, co-flowing forced jets, 95, 96,
99,101 large scale vortices and, 38 L.E.S. of, 156, 157,159 in mixing transitions, 3, 4, 5-6, 7, 8, 9, 10,
333 in parallel flows, 247, 253, 254 puffs and, 341, 342, 343, 344, 345 in reconnection, 204 in round jets, 89-94 thermal convection and, 170, 173 vortexdynamicsand,202 vortex line stretching and, 265, 269 vortex shedding at, 13-21, 51-53, see also
Vortex shedding vortex splitting at, 51-53 in wall jets, 67-86, see also External
excitation Reynolds stresses
bifurcations and, 275 DNS of, 123, 127, 130 in dynamical systems theory, 211, 212,
213,214,216-217 external excitation and, 67, 71, 75, 79, 86 mixing transitions and, 6 parallel flows and, 250 puffs and, 344, 345
Riblets, flow over, 123, 129, 130 RNG theory, 351 Round jets, 89-94 Ruelle-Takens route, 233-244
criticisms of, 237-238 experimental observations on, 235-
236 uniform flows in, 233, 238-243
Runge-Kutta method, 137, 289
369
St. Venant's principle, 213 Schmidt numbers, 146, 337 Schwartz functions, 260, 262, 266 Secondary corrugation, 133 Secondary instabilities, 58 Shape instabilities, 253 Shear flows, 33, 123, 321, 349, see also
Free-shear flows stationary boundary conditions and, see
Stationary boundary conditions Shear instabilities, 247-256, see also Parallel
flows Shear layers, see also Free-shear layers
in large scale vortices, 43, 44, 47, 49 RBC in, 167-177, see also
Rayleigh-Benard convection in round jets, 89, 90, 91, 92, 93, 94 vortex shedding and, 17
Shear stresses, 73, 75, 79, 84 Shell models, 221, 222-225 Short-wave instabilities, 96, 203 Shroudedjets, 90, 91, 92, 94 Single helices, 17 Singularity formation, 202, 203-204 Sinuous instabilities, 14, 17-18 Sinusoidal driving force, 117, 118 Skin friction
DNSof,336 external excitation effect on, 67, 68, 73,
74,75,81,86 Skin-friction drag, see Drag Slugs
bifurcations and, 276 bubble formation and, 133, 135, 138, 139,
140, 141 Gortler instabilities and, 25 puffs and, 341, 342, 343
Small boxes, 274 Small scale structures, 4, 7-8, 9 Smoke-wire flow visualization, 52, 60 Soft turbulence, see Weak turbulence Spanwise forcing, 96, 99, 100 Spatial discretization, 124-125 Spatial forcing, 322-324 Spatially developing mixing layers, 127, 143,
144, 149-151, 152 Spectral simulations, 124-125, 126 Spheres,34,38,39,40,41,42,43
vortex shedding from, 13-21, see also Vortex shedding
Spiky turbulence, 310, 313, 315 Stable localized structures, see S-waves Stably stratified turbulence, 155, 156, 160-163 Stanton tubes, 73 Static control of shear flow, 58-59 Stationary boundary conditions, 57-65
control characteristics in, 62-63 feedback in, 57, 58, 61, 62, 64
Stochastic attractors, 234 Stochastic fields, 183,184,186,187,188,212 Stokes flow, 250, 344, 351 Straining field, 203, 204, 205
370
Strange attractors, 235,236,237,242,243, 244,348
defined,234 Stratified decay calculations, 156 Stratified fluids, 14, 19-21 Streamwise channels, 133 Streamwise forcing, 96, 97, 99, 100 Streamwise velocity, 67, 68, 76, 125, 214 Streamwise vortices
DNS of, 129, 130 Gortler instabilities and, 28 in laminar, co-flowing forced jets, 100,
101,102,104 mixing transitions and, 3, 6-7, 9 stationary boundary conditions and, 58
Strong turbulence, 309-316, see also Complex Ginzburg-Landau equations
Strouhal numbers in laminar, co-flowing forced jets, 95 in round jets, 89, 91 at stationary boundary conditions, 60, 63 in vortex shedding, 13, 17, 18, 19 in wall jets, 76
Stuart vortices, 146 Subcritical bifurcations, 273-286
in Gortler instabilities, 23, 24 parallel flow and, 273, 274-278 s-waves and, see S-waves
S-waves, 278-285 moving-front solutions of, 279-280 NLSE and, 278, 279, 280-281
Swift-Hohenberg equations, 324, 325 Swirl instabilities, 253, 254 Symmetry breaking
in parallel flows, 248, 254-256 pattern formation and, 319, 321
Taylor-Couette flows, 111,275,345,350, see also Couette flows
Taylor expansions, 112, 282 Taylor hypothesis, 125, 230 Taylor vortices, 277 Tearing, 203 Temporal mixing layers, 127, 143,146-149 Test Field Model closure calculations, 159 Thermal convection, 167-177,247-256, see
also Prandtl numbers, in thermal convection; Rayleigh-Benard convection
Thermal turbulence boundary layers in, 167-170, 175 shear absent in, 173-175 shear induced, 172-173
Thermohaline convection, 255 Thomson's circulation theorem, 17 Three-dimensional boundary layers, 128-130 Three-dimensional parallel flows, 248,
252-255 Three-dimensional small scale structures, 4,
7-8,9 Three-dimensional turbulence, 309, 311, 347,
348,352,354 Thual-Fauve solitions, 345
1broidal chaos, 242 1broidal fields, 252-253, 256, 343 n-Torus, 235, 237 ~Torus,235,237,239,240,241 3-Torus, 235, 236
uniform flows on, 233, 238-243 Translative instabilities, 149 Truly incompressible method, 177 Thrbulence memory, 33, 34, 38 Thrbulent coupled map lattices, see Coupled
map lattices Thrbulent patches, see Vortex patches Thrbulent puffs, see Puffs Thrbulent scalar, 155-164, see also
Large-eddy simulation Thrbulent wall jets, see Wall jets '!\vo-dimensional boundary layers, 128-130 '!\vo-dimensional parallel flows, 248 '!\vo-dimensional shear layers, 167-177, see
also Rayleigh-Benard convection '!\vo-dimensional turbulence, 309, 347, 353 '!\vo-dimensional wakes, 33-49, see also Large
scale vortices
Unforced flows, 67, 68-75, 76, 78, 82, 84, 85, 86, 143
SUB = behind a backwards-facing step, 143, 149-150,152
Uniform flows, 233, 238-243 Uniform state instabilities, 135-137 Uniform wavetrains, 138
van der Pol oscillators, 111, 287 Velocity
bubble formation and, 133, 135, 136 DNS of, 124, 125, 126, 127, 129, 147,336 external excitation and, 81, 82 intermittency and, 222 in Karman vortex streets, 113-114 in laminar, co-flowing forced jets, 97 L.E.S. of, 155, 156-157, 158, 159, 160-163 in round jets, 89, 90, 91, 92, 93 as vorticity substitute, 353 in wall jets, 68-75, 76-79, 84, 86
Vertical channels, 139 ViscosiW, 354
in dynamical systems theory, 219 intermittency and, 222 in Kolmogorov theory, 352, 355 large scale vortices and, 43, 49 L.E.S. of, 155, 156, 157, 158,162,163-164 mixing transitions and, 9 RBC and, 167, 169 stationary boundary conditions and, 59 vortex line stretching and, 266, 269 in wall jets, 67, 68, 70, 73, 84, 86, 169
Vortex decay, 33, 38 Vortex dipoles, 43, 44 Vortex dynamics, 201-207
defined,201 Vortex filaments, 203, 205, see also
Filamentation
Vortex filaments (cont'd) Betchov-Da Rios equations and, 257-260 DNS of, 145-146, 149
Vortex generation, 33, 38, 43, 45, 46, 48, 49 Vortex lines, 337
stretching of, 265-269, 354 Vortex loops, 101, 104,105, 106, 107 Vortex pairing
DNS of, 143, 144 Gortler instability and, 28 in large scale vortices, 33, 38, 43 mixing transitions and, 3, 8
Vortex patches, 207, 273, 274-275, 277, 285 filamentation of, 202, 206-207 fusion and fission of, 202-203
Vortex rings, 99-100, 203, 343 Euler equations and, 262 in laminar, co-flowing forced jets, 95, 96,
101,102,103,104 puffs and, 341, 345 reconnection and, 204 in round jets, 89
Vortex shedding, 13-21 in bluff body wakes, 51-53 in homogeneous fluids, 13, 14-17 instability mode frequencies in, 17-18 in large scale vortices, 34, 38 in stratified fluids, 14, 19-21
Vortex sheets, 204 Vortex splitting, 51-53 Vortex streets, 38, see also Karman vortex
streets Vortex tubes, 99-100
core bursting in, 202, 207 DNSof,337 Euler equations and, 261, 262-263 in laminar, co-flowing forced jets, 96, 101 reconnection in, 202, 204-206 singularity formation and, 204
Vorticity DNSof,150 in dynamical systems theory, 219 in laminar, co-flowing forced jets, 95-107,
see also Laminar, co-flowing forced jets
in round jets, 91 velocity as substitute for, 353
Vorticity links, 260-263
Wakes, 68,117,203, see also '!\vo-dimensional wakes
in homogeneous fluids, 13, 14-17 Karman vortex streets and, 115 in stratified fluids, 19-21
Wall jets, 67-86, 336, see also External excitation
Wall stresses, 80, 81, 86 Wave breaking, 206,207 Wavelengths, 138, 139 Wave patterns, 320, 322-324 Waves, 202, 203, see also Billows Wavetrains, 138
371