Fluid Dynamics
Part 4: Hydrodynamic Stability Theory
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Product details:
- Publisher OUP Oxford
- Date of Publication 3 July 2023
- ISBN 9780198869948
- Binding Hardback
- No. of pages368 pages
- Size 253x175x25 mm
- Weight 836 g
- Language English
- Illustrations 101 line figures 400
Categories
Short description:
This is Part 4 of a book series on fluid dynamics which is devoted to hydrodynamic stability theory. This theory aims at predicting the conditions under which a flow which is smooth and regular (a so-called laminar flow) undergoes a transition to a more complicated and apparently erratic state known as turbulence.
MoreLong description:
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-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.
Table of Contents:
Classical Hydrodynamic Stability Theory
High-Reynolds-Number Analysis of Parallel and Shear Flow Instabilities
Boundary-Layer Receptivity
Weakly Nonlinear Stability Theory
Coherent Structures and Self-Sustaining Processes in Shear Flows
