Longwave Instabilities and Patterns in Fluids

1. Auflage 2017
ISBN: 978-1-4939-7588-4
Verlag: Springer

Buch, Englisch, 456 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 8276 g

Reihe: Advances in Mathematical Fluid Mechanics

This book summarizes the main advances in the field of nonlinear evolution and pattern formation caused by longwave instabilities in fluids. It will allow readers to master the multiscale asymptotic methods and become familiar with applications of these methods in a variety of physical problems.

Longwave instabilities are inherent to a variety of systems in fluid dynamics, geophysics, electrodynamics, biophysics, and many others. The techniques of the derivation of longwave amplitude equations, as well as the analysis of numerous nonlinear equations, are discussed throughout.



This book will be of value to researchers and graduate students in applied mathematics, physics, and engineering, in particular within the fields of fluid mechanics, heat and mass transfer theory, and nonlinear dynamics.

Zielgruppe

Research

Autoren/Hrsg.

Nepomnyashchy, Alexander

Shklyaev, Sergey

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Mathematische Modellierung
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre

Inhaltsverzeichnis

Introduction.- Convection in Cylindrical Cavities.- Convection in Liquid Layers.- Convection in Binary Liquids. Amplitude Equations for Stationary and Oscillatory Patterns.- Instabilities of Parallel Flows.- Instabilities of Fronts.- Longwave Modulations of Shortwave Patterns.- Control of Longwave Instabilities.- Outlook.- A. Solvability Conditions for an Inhomogenous Linear Boundary Value Problem.- B. Types of Bifurcations.- C. Stationary Pattern Selection.- D. Regular Wave Patterns.- E. Resonant Perturbations.