## Theory and Applications of Viscous Fluid FlowsThis book is the natural sequel to the study of nonviscous fluid flows pre sented in our recent book entitled "Theory and Applications of Nonviscous Fluid Flows" and published in 2002 by the Physics Editorial Department of Springer-Verlag (ISBN 3-540-41412-6 Springer-Verlag, Berlin, Heidelberg, New York). The physical concept of viscosity (for so-called "real fluids") is associated both incompressible and compressible fluids. Consequently, we have with a vast field of theoretical study and applications from which any subsection could have itself provided an area for a single book. It was, however, decided to attempt aglobaI study so that each chapter serves as an introduction to more specialized study, and the book as a whole presents a necessary broad foundation for furt her study in depth. Consequently, this volume contains many more pages than my preceding book devoted to nonviscous fluid flows and a large number (80) of figures. There are three main models for the study of viscous fluid flows: First, the model linked with viscous incompressible fluid flows, the so-called (dynamic) Navier model, governing linearly viscous divergenceless and homogeneous fluid flows. The second is the sü-called Navier-Stokes model (NS) which is linked to compressible, linearly viscous and isentropic equations für a polytropic viscous gas. The third is the so-called Navier-Stokes-Fourier model (NSF) that gov erns the motion of a compressible, linearly viscous, heat-conducting gas. |

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### Contents

1 | |

11 | |

Some Features and Various Forms of NSF Equations 35 | 34 |

Some Simple Examples | 57 |

4 | 60 |

The Limit of Very Large Reynolds Numbers | 89 |

Low Mach Number Asymptotics | 165 |

Some Viscous Fluid Motions and Problems | 191 |

Some Aspects of a Mathematically Rigorous Theory 277 | 276 |

A FiniteDimensional Dynamical System Approach | 387 |

for Developed Turbulence | 435 |

449 | |

485 | |

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### Common terms and phrases

amplitude analysis approximation assume asymptotic behavior Bénard bifurcation boundary conditions chaotic Chap classical coefficients components compressible flow compressible fluid consequence considered constant convection coordinate Couette flow cylinder deck derive the following dimensionless domain dynamical system eigenvalue Ekman layer Euler existence expansion finite flat plate fluid dynamics Fluid Mech Fourier free surface function Galerkin approximations global gradient Guiraud Hopf bifurcation infinity initial conditions inner instability inviscid Iooss layer limiting process linear low Mach number low Reynolds number Marangoni Marangoni effect matching mathematical model equations modes motion Navier equations nonlinear NSF equations number flow observe Oseen outer paper parameter perturbation phase space plane pressure Rayleigh reader can find region relation rotating Sect singular so-called stability steady-state Stewartson Stokes strange attractor temperature theory thermal thermal convection turbulence unsteady-state variables velocity vector viscous viscous fluid flows vorticity wall wave number weak solutions zero Zeytounian