Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances [electronic resource] /
International Centre for Mechanical Sciences.
Steinrück, Herbert.editor.
A survey of asymptotic methods in fluid mechanics and applications is given including high Reynolds number flows (interacting boundary layers, marginal separation, turbulence asymptotics) and low Reynolds number flows as an example of hybrid methods, waves as an example of exponential asymptotics and multiple scales methods in meteorology.
Description based upon print version of record.
Title Page; Copyright Page; PREFACE; Table of Contents; Introduction to Matched Asymptotic Expansions; 1 Introduction; 2 Flow around a thin elliptical airfoil ε  4.4 Turbulence asymptotics5 Conclusions; Bibliography; Asymptotic Methods For PDE Problems In Fluid Mechanics and Related Systems With Strong Localized Perturbations In Two-Dimensional Domains; 1 Introduction; 2 Infinite Logarithmic Expansions: Simple Pipe Flow; 3 Some Related Steady-State Problems in Bounded Singularly Perturbed Domains; 3.1 Oxygen Transport From Capillaries to Skeletal Muscle; 3.2 A Nonlinear Elliptic Problem; 4 Slow Viscous Flow Over a Cylinder; 4.1 Summing Logarithmic Expansions: A Linear Biharmonic Problem; 4.2 A Convection-Diffusion Problem
5 The Fundamental Neumann Eigenvalue in a Planar Domain with Localized Traps6 Conclusion; Bibliography; Exponential Asymptotics and Generalized Solitary Waves; 1 Introduction; 1.1 Stieltjes Integral; 1.2 Fourier Integral; 1.3 Airy Functions; 1.4 WKB Solutions and Stokes Phenomenon; 2 WaveScattering and Reflection; 2.1 Forced Harmonic Oscillator; 2.2 Balanced Flow and Slow Manifold; 2.3 Waves in a Variable Medium; 3 Borel Summation: Forced Nonlinear Harmonic Oscillator; 3.1 Case (a); 3.2 Case(b): Outer expansion; 4 Generalized Solitary Waves; 4.1 Korteweg-de Vries equation; 4.2 Linear spectrum
4.3 Reformulation as a dynamical system4.4 Case (1); 4.5 Case (2); 4.6 Case (3); 5 Fifth-order Korteweg-de Vries equation; 5.1 Formulation and outer expansion; 5.2 Inner expansion and Borel summation; 5.3 One-sided oscillations; 5.4 Higher-order terms; 6 Coupled Korteweg-de Vries Equations; 6.1 Internal waves; 6.2 Outer expansion; 6.3 Inner expansion and Borel summation; 6.4 Weak coupling approximation; Bibliography; Exponential Asymptotics and Stokes Line Smoothing for Generalized Solitary Waves; 1 Introduction; 2 Generalized Solitary Waves and the 5KdV
2.1 Initial Asymptotic Analysis and Late Terms2.2 Optimal Truncation and Stokes Smoothing; Bibliography; Multiple scales methods in meteorology; 1 Overview; 2 Fluid mechanical conservation laws; 2.1 Pure fluid dynamics; 2.2 Equations of state; 2.3 The influence of gravity; 2.4 The effects of Earth's rotation; 2.5 Adiabatic motions and the concept of potential temperature; 2.6 Summarizing the equations; 3 Introduction to multiple scales asymptotics; 3.1 Exact solutions for the linear oscillator; 3.2 Dimensionless representation and small parameters
3.3 Regular perturbation analysis for small mass and damping
Includes bibliographical references.
A survey of asymptotic methods in fluid mechanics and applications is given including high Reynolds number flows (interacting boundary layers, marginal separation, turbulence asymptotics) and low Reynolds number flows as an example of hybrid methods, waves as an example of exponential asymptotics and multiple scales methods in meteorology.
Mechanics.
Mechanics, Applied.
Partial differential equations.
Fluids.
Theoretical and Applied Mechanics.
Partial Differential Equations.
Fluid- and Aerodynamics.
Courses and lectures /