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 TheoryThe 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-Görtler 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.
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 TheoryThe 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-Görtler 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.
1: Classical Hydrodynamic Stability Theory
2: High-Reynolds-Number Analysis of Parallel and Shear Flow
Instabilities
3: Boundary-Layer Receptivity
4: Weakly Nonlinear Stability Theory
5: Coherent Structures and Self-Sustaining Processes in Shear Flows
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.
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