Longwave instabilities and patterns in fluids
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; hexagonal lattice; the limit of small Lewis number; surfactant dynamics). The chapter contains 70 references. Chapter 5: Instabilities of parallel flows, contains waves on an inclined plane (small inclination angles; stability of traveling waves; vertical plane, moderate surface tension; strong surface tension); Kolmogorov flow (derivation of the amplitude equation; generalizations). The chapter contains a list of 64 references. Chapter 6: Instabilities of fronts, deals with combustion fronts; solidification fronts (amplitude equation; anisotropy-induced instability: convective Cahn-Hillard equation). The chapter contains a list of 61 references. Chapter 7: Longwave modulations of shortwave patterns, considers the problems of stationary patterns; hexagonal patterns; wave patterns (one-dimensional Ginzburg-Landau equation; 2D complex Ginzburg-Landau equation: spiral wave); interaction of longwave and shortwave instabilities. The chapter contains 70 references. Chapter 8: Control of longwave instabilities, deals with ime-periodic action (high-frequency parameter modulation; moderate-and low-frequency parameter modulation); spatial modulation of parameter; feedback control. The chapter contains a list of 108 references. Chapter 9: Outlook, examines the influence of lateral boundaries; evaporative convection (longwave instabilities in viscoelastic liquids and biofluids; isothermal vibrational instabilities in large aspect ratio containers; reaction-diffusion-convection systems). The chapter contain a list of 85 references. This book represents an important and interesting contribution to the theory of longwave instabilities and patterns in fluids. The hypotheses are clearly stated and the governing parameters are correctly selected, and the governing equations are solved both analytically and numerically. Every chapter of the book ends with a very careful discussion of the obtained results; the obtained results are shown to be physically realizable and can be applied with great confidence to problems of practical interest. Large lists of references are given at the end of every chapter, and represent altogether a very useful collection of papers. The book will be of interest for researchers and graduate students in applied mathematics, physics, and engineering. The authors are to be lauded for presenting an excellent book.
scientific article; zbMATH DE number 6813553