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This book presents the new discovery of the origin of turbulence from Navier-Stokes equations. The fully developed turbulence is found to be composed of singularities of flow field. The mechanisms of flow stability and turbulent transition are described using the energy gradient theory, which states all the flow instability and breakdown resulted from the gradient of the total mechanical energy normal to the flow direction. This approach is universal for flow instability in Newtonian flow and non-Newtonian flow. The theory has been used to solve several problems, such as plane and pipe Poiseuille flows, plane Couette flow, Taylor-Couette flow, flows in straight coaxial annulus, flows in curved pipes and ducts, thermal convection flow, viscoelastic flow, and magnet fluid flow, etc. The theory is in agreement with results from numerical simulations and experiments. The analytical method used in this book is novel and is different from the traditional approaches. This book includes the fundamental basics of flow stability and turbulent transition, the essentials of the energy gradient theory, and the applications of the theory to several practical problems. This book is suitable for researchers and graduate students.

Fluid mechanics --- ingenieurswetenschappen --- vloeistoffen --- Navier-Stokes equations.

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The 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.

Navier-Stokes equations. --- Navier-Stokes, Equations de --- Differential equations, Partial. --- Partial differential equations --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Navier-stokes equations

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Numerical solutions of differential equations --- Partial differential equations --- Fluid mechanics --- Navier-Stokes equations --- Vortex-motion. --- Numerical solutions. --- Navier-Stokes equations - Numerical solutions.

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This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyse turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers and physicists.

Turbulence. --- Navier-Stokes equations. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Flow, Turbulent --- Turbulent flow --- Turbulence --- Navier-Stokes equations

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Navier-Stokes equations. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow