Hydrodynamic StabilityThis book begins with a basic introduction to three major areas of hydrodynamic stability: thermal convection, rotating and curved flows, and parallel shear flows. There follows a comprehensive account of the mathematical theory for parallel shear flows. A number of applications of the linear theory are discussed, including the effects of stratification and unsteadiness. The emphasis throughout is on the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, the theory is related to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems, for which hints and references are given, not only provide exercises for students but also provide many additional results in a concise form. |
Contents
III | 1 |
IV | 4 |
V | 8 |
VI | 14 |
VII | 22 |
VIII | 27 |
IX | 32 |
X | 34 |
XLIII | 267 |
XLIV | 280 |
XLVII | 285 |
XLVIII | 290 |
XLIX | 295 |
L | 305 |
LI | 311 |
LII | 317 |
XI | 37 |
XII | 44 |
XIII | 50 |
XIV | 52 |
XV | 59 |
XVI | 62 |
XVII | 63 |
XVIII | 69 |
XIX | 71 |
XX | 82 |
XXI | 88 |
XXII | 108 |
XXIII | 116 |
XXIV | 121 |
XXV | 124 |
XXVI | 126 |
XXVII | 131 |
XXVIII | 144 |
XXIX | 147 |
XXX | 153 |
XXXI | 158 |
XXXII | 164 |
XXXIII | 180 |
XXXIV | 196 |
XXXV | 202 |
XXXVI | 211 |
XXXVII | 239 |
XXXVIII | 245 |
XXXIX | 251 |
XL | 256 |
XLI | 263 |
XLII | 265 |
Common terms and phrases
A₁ Airy functions amplitude asymptotic asymptotic expansions basic flow Bénard convection bifurcation Blasius boundary layer boundary conditions boundary layer c₁ coefficients consider constant curve of marginal cylinders derived eigenfunctions eigenvalue relation experimental exponentially flow is stable Fluid Mech given by equation gives Hence hydrodynamic hydrodynamic stability initial-value problem instability integral inviscid fluid k₁ Kelvin-Helmholtz instability laminar Landau equation linear theory marginal curve marginal stability Math method nonlinear normal modes obtain ordinary differential equations Orr-Sommerfeld equation oscillation outer expansions parallel flows perturbation plane Couette flow plane Poiseuille flow R₁ Rayleigh Rayleigh number Reid rotating satisfy shear layer shown in Fig sinh solutions of equation steady Taylor number Taylor vortices theoretical tion turbulence two-dimensional disturbances U₁ unstable mode viscous wavenumber waves weakly nonlinear Wronskian z₁ zero α˛ ди дх