Nonlinear dynamics of surface-tension-driven instabilities

Pierre Colinet, Jean Claude Legros, Manuel G. Velarde3527402918, 9783527402915

A century after Henri B?nard discovered cellular convective structures, thermal convection in fluid layers still remains a central subject in nonlinear physics. Within this framework, surface-tension-driven instabilities have increasingly been the subject of attention over the last few years, owing to the even greater variety of pattern and wave-forming phenomena observed in this situation. This book provides readers with a progressive and complete insight into this vast field, describing as it does a number of “first principle” analyses of realistic set-ups, including several physicochemical processes at interfaces. Nonetheless, much emphasis is placed on the generality of the results and methods used, by way of the detailed derivation and analysis of a number of generic nonlinear equations known to hold in many physical systems, even outside the realm of fluid mechanics. The first introductory chapter describes nonlinear dissipative structures at a general level, with several examples of hydrodynamic instabilities in systems with interfaces. Chapter 2 contains a summary of the derivation of thermo-hydrodynamic equations, including boundary conditions prevailing at interfaces, while the third chapter is devoted to linear stability analyzes and identification of basic instability modes. The following two chapters deal with weakly nonlinear theories, both monotonic and oscillatory. Chapter 6 presents experimental and theoretical results on solitonic and shock-like surface waves, while Chapter 7 explores examples of multiple bifurcations. Finally, Chapter 8 presents recent results on strongly nonlinear surface-tension-driven convection and chaotic interfacial dynamics.