## Turbulence in FluidsThis is the 4th edition of a book originally published by Kluwer Academic Publishers. It is an exhaustive monograph on turbulence in fluids in its theoretical and applied aspects, with many advanced developments using mathematical spectral methods (two-point closures like the EDQNM theory), direct-numerical simulations, and large-eddy simulations. The book is still of great actuality on a topic of the utmost importance for engineering and environmental applications, and presents a very detailed presentation of the field. The fourth edition incorporates new results coming from research work done since 1997. Many of these results come from direct and large-eddy simulations methods, which have provided significant advances in problems such as turbulent mixing or thermal exchanges (with and without gravity effects). Topics dealt with include: an introduction to turbulence in fluid mechanics; basic fluid dynamics; transition to turbulence; shear-flow turbulence; Fourier analysis for homogeneous turbulence; isotropic turbulence; phenomenology and simulations; analytical theories and stochastic models; two-dimensional turbulence; geostrophic turbulence; absolute-equilibrium ensembles; the statistical predictability theory; large-eddy simulations; and a section that explores developments towards real-world turbulence. |

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### Contents

II | 1 |

III | 4 |

IV | 13 |

V | 14 |

VI | 16 |

VII | 20 |

VIII | 21 |

X | 24 |

LI | 221 |

LII | 223 |

LIII | 227 |

LIV | 236 |

LV | 238 |

LVI | 243 |

LVII | 245 |

LVIII | 250 |

XII | 26 |

XIII | 32 |

XIV | 41 |

XV | 44 |

XVI | 52 |

XVII | 55 |

XVIII | 62 |

XIX | 69 |

XX | 73 |

XXI | 74 |

XXII | 76 |

XXIII | 91 |

XXIV | 108 |

XXV | 118 |

XXVI | 120 |

XXVII | 135 |

XXVIII | 136 |

XXIX | 145 |

XXX | 151 |

XXXI | 155 |

XXXII | 158 |

XXXIII | 160 |

XXXIV | 161 |

XXXV | 163 |

XXXVI | 166 |

XXXVII | 167 |

XXXVIII | 169 |

XXXIX | 179 |

XL | 182 |

XLI | 184 |

XLII | 186 |

XLIII | 190 |

XLIV | 193 |

XLV | 196 |

XLVI | 202 |

XLVII | 205 |

XLVIII | 209 |

XLIX | 216 |

L | 220 |

LIX | 253 |

LX | 264 |

LXI | 265 |

LXII | 270 |

LXIII | 277 |

LXIV | 284 |

LXV | 292 |

LXVI | 303 |

LXVII | 306 |

LXVIII | 311 |

LXIX | 314 |

LXX | 322 |

LXXI | 325 |

LXXII | 330 |

LXXIII | 339 |

LXXIV | 343 |

LXXV | 346 |

LXXVI | 349 |

LXXVII | 354 |

LXXVIII | 357 |

LXXIX | 366 |

LXXX | 372 |

LXXXI | 379 |

LXXXII | 386 |

LXXXIII | 393 |

LXXXIV | 403 |

LXXXV | 419 |

LXXXVI | 420 |

LXXXVII | 428 |

LXXXVIII | 440 |

LXXXIX | 452 |

XC | 455 |

XCI | 467 |

XCII | 483 |

XCIII | 489 |

XCIV | 508 |

XCV | 545 |

### Common terms and phrases

anticyclonic atmospheric barotropic boundary layer calculation Chapter closure coherent vortices compressible convection corresponding courtesy cyclonic decay density developed diffusion direct-numerical dissipation downstream eddy viscosity Ekman layer energy spectrum enstrophy evolution experimental Figure Fluid Dynamics Fluid Mech Fourier space Gaussian geostrophic Grenoble hairpins homogeneous turbulence horizontal imensional incompressible initial instability inviscid isosurfaces isotropic turbulence Kelvin–Helmholtz kinetic energy kinetic-energy Kolmogorov Kraichnan Large-eddy simulation lence Lesieur longitudinal vortices Mach number Métais mixing layer mode motion Navier–Stokes equations nonlinear numerical simulations Orr-Sommerfeld equation p+q=k passive scalar perturbation Phys plane potential vorticity predictability pressure pseudo-spectral methods random Reynolds number Rossby number Rossby waves rotation scales shear flows sional small-scale spanwise spatial statistical stratified structure subgrid subgrid-scale t)dk temperature temporal mixing layer theory three-dimensional turbulent flow Turbulent Shear Flows two-dimensional turbulence upstream vector velocity field velocity profile vortex vortex rings wake wave number zero