Longwave instabilities and patterns in fluids
type: Item
instance of: scholarly article
title: Longwave instabilities and patterns in fluids
zbMATH Open document ID: 1384.76001
DOI: 10.1007/978-1-4939-7590-7
author: Sergey Shklyaev
author: Alexander A. Nepomnyashchy
published in: Advances in Mathematical Fluid Mechanics
publication date: 2017-11-28T00:00:00Z
review text: Longwave instabilities are inherent to a variety of systems in fluid dynamics (from the dynamics of the atmosphere and the ocean to the motion in microfluidic devices), geophysics (mantle dynamics, surges, avalanches), electrodynamics (electronic beams, plasma), biophysics (wetting and lubrication in biophysical applications, such as tear dynamics and flows in the respiratory system), and many others. The book consist of 9 chapters, a preface, 5 appendices and an index, whose contents are, in short, as follows. Chapter 1: Introduction, presents the phenomenon of pattern formation; shortwave and longwave instabilities; the complex Ginzburg-Landau equation; the classification of longwave amplitude equations. The chapter contains a list of 54 references. Chapter 2: Conservation in cylindrical cavities, deals with the free convection in a horizontal cylinder (derivation of the Allen-Cahn equation; basic properties of the Allen-Cahn equation; pattern coarsening as defects dynamics; stationary patterns in the presence of inhomogeneities; higher-order corrections; conservation in a non-Boussinesq fluid); mixed convection in a horizontal cylinder; convection in a vertical cylinder (Lyapunov functional; stationary solutions; stability of stationary solutions). The chapter contains a list of 20 references. Chapter 3: Convection in liquid layers, presents the Rayleigh-Bénard convection in a layer with poorly conducting boundaries; Bénard-Marangoni convection (poorly conducting boundaries; deformational instability: weakly nonlinear approach; deformational instability: strongly nonlinear approach; the role of the buoyancy effect); Marangoni oscillations and waves. The chapter contains a list of 116 references. Chapter 4: Convection in binary liquids: amplitude equations for stationary and oscillatory patterns, treats the problems of buoyancy convection; Marangoni convection (non-deformable surface; linear stability analysis; oscillatory mode; rhombic lattice; square lattice; he…
reviewed by: Ioan Pop
Mathematics Subject Classification ID: 76-02
Mathematics Subject Classification ID: 76Exx
Mathematics Subject Classification ID: 00A79
zbMATH DE Number: 6813553
zbMATH Keywords: Ginzburg-Landau equation
zbMATH Keywords: Allen-Cahn equation
zbMATH Keywords: mixed convection
zbMATH Keywords: Cahn-Hillard equation
zbMATH Keywords: front instability
zbMATH Keywords: parallel flow instability
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4939-7590-7
OpenAlex ID: W2772233913
Wikidata QID: Q125313991
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description: scientific article; zbMATH DE number 6813553