Fluid Dynamics : Part 4: Hydrodynamic Stability Theory

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Fluid Dynamics : Part 4: Hydrodynamic Stability Theory

Ruban, Anatoly/ Gajjar, Jitesh/ Walton, Andrew

ウェブストア価格 ¥18,120（本体¥16,473）
Oxford University Press（2023/07発売）
外貨定価 US$ 90.00
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製本 Hardcover:ハードカバー版／ページ数 368 p.
言語 ENG
商品コード 9780198869948
DDC分類 532.5

Full 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.

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