Description

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This is the fourth volume in a four-part series on fluid dynamics:

Part 1. Classical Fluid Dynamics
Part 2. Asymptotic Problems of Fluid Dynamics
Part 3. Boundary Layers
Part 4. Hydrodynamic Stability Theory

The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field.

Part 4 is devoted to hydrodynamic stability theory which aims at predicting the conditions under which the laminar state of a flow turns into a turbulent state. The phenomenon of laminar-turbulent transition remains one of the main challenges of modern physics. The resolution of this problem is important not only from a theoretical viewpoint but also for practical applications. For instance, in the flow past a passenger aircraft wing, the laminar-turbulent transition causes a fivefold increase in the viscous drag.

The book starts with the classical results of the theory which include the global stability analysis followed by the derivation of the Orr-Sommerfeld equation. The properties of this equation are discussed using, as examples, plane Poiseuille flow and the Blasius boundary layer. In addition, we discuss 'inviscid flow' instability governed by the Rayleigh equation, Kelvin-Helmholtz instability, crossflow instability, and centrifugal instability, taking the form of Taylor-G rtler vortices.

However, in this presentation our main attention regards recent developments in the theory. These include linear and nonlinear critical layer theory, the theory of receptivity of the boundary layer to external perturbations, weakly nonlinear stability theory of Landau and Stuart, and vortex-wave interaction theory. The latter allows us to describe self-sustaining nonlinear perturbations within a viscous fluid.

About the Author

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Anatoly Ruban, Imperial College London, Jitesh Gajjar, University of Manchester, Andrew Walton, Imperial College London Anatoly I. Ruban is Professor and Chair in Applied Mathematics and Mathematical Physics at the Imperial College London. He was formerly Professor of Computational Fluid Dynamics in the Department of Mathematics at the University of Manchester, from 1995 to 2008. In 1991 he received the Doctor of Science degree in Physics and Mathematics. In Moscow, he served as Head of the Gas Dynamics Department in the Central Aerohydrodynamics Institute in Moscow from 1978-1995 after earning his PhD in Fluid Mechanics in 1977. Jitesh S.B. Gajjar is currently Professor of Applied Mathematics at the University of Manchester. He obtained his undergraduate and PhD degrees from Imperial College (1977-1984), then worked as a Research Scientist at BMT Ltd before taking up a lecturing post at Exeter University in 1985. He moved to Manchester in 1991. His research expertise is in fluid mechanics and he has published extensively including co-authoring Fluid Dynamics vol. 1 with Anatoly Ruban. Andrew G. Walton is a Senior Lecturer in the Mathematics Department at Imperial College London. He graduated from University College London with First Class Degree in Mathematics and Astronomy and was awarded the Faculty Medal for the Physical Sciences. In 1989 he worked as a Research Scientist at Old Dominion University, Virginia, and NASA Langley Research Center, Virginia, before completing his PhD in Fluid Dynamics in the Mathematics Department at University College London under the supervision of Professor F. T. Smith FRS in 1991. He then worked as an Associate Research Assistant, including the role of Analyst/Programmer in the Mathematics Department at University College London, and was appointed Lecturer in the Mathematics Department at Imperial College London in 1992.