## The Navier-Stokes Equations: A Classification of Flows and Exact Solutions, Volume 13The Navier-Stokes equations were firmly established in the 19th Century as the system of nonlinear partial differential equations which describe the motion of most commonly occurring fluids in air and water, and since that time exact solutions have been sought by scientists. Collectively these solutions allow a clear insight into the behavior of fluids, providing a vehicle for novel mathematical methods and a useful check for computations in fluid dynamics, a field in which theoretical research is now dominated by computational methods. This 2006 book draws together exact solutions from widely differing sources and presents them in a coherent manner, in part by classifying solutions via their temporal and geometric constraints. It will prove to be a valuable resource to all who have an interest in the subject of fluid mechanics, and in particular to those who are learning or teaching the subject at the senior undergraduate and graduate levels. |

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### Contents

Steady flows bounded by plane boundaries | 11 |

Steady axisymmetric and related flows | 45 |

Unsteady flows bounded by plane boundaries | 89 |

Unsteady axisymmetric and related flows | 128 |

195 | |

### Common terms and phrases

algebraic analogue angular velocity arbitrary asymptotic axial axis Beltrami flows Berker body force boundary conditions boundary layers bounded centre-line channel circular cylinder classical combinatorics constant continuity equation core corresponding decay dynamics equations 1.19 Ergodic theory exact solutions example finite flux g(oo generalisation geometry given groups Hiemenz increases inflow injection inviscid motion Navier-Stokes equations no-slip condition numerical solutions obtained ordinary differential equations oscillating outflow parameter plane boundary plate Poiseuille Poiseuille flow porous pressure gradient problem radial velocity radius Reynolds number rotating disk Rott satisfied identically self-similar Serrin shear stress shown in figure solid-body rotation solution branch solution of equation stagnation flow stagnation point stagnation-point flow steady flow Stokes stream function streamlines surface symmetric Terrill and Thomas theory three-dimensional tions two-dimensional uniform unsteady various values velocity components velocity profiles viscous viscous fluid vortex vorticity Wang Watson whilst