Mathematical modeling and simulation in hydrodynamic stability

Hydrodynamic stability is of fundamental importance in the mechanics of fluids and is mainly concerned with the problem of the transition to turbulence. This book is devoted to publication of original research papers, research-expository and survey articles with an emphasis on unsolved problems and open questions in the mathematical modeling and computational aspects of hydrodynamic stability. Review chapters on the mathematical modeling and numerical simulation aspects of hydrodynamic stability, the physical background, and the limitations of the modeling and simulation procedures, due to particular mathematical or computational methods used, are included. This book will be appropriate for use in research and in research-related courses on the subject. It includes chapters on bifurcations in fluid systems, flow patterns, channel flows, non-parallel shear flows, thin-film flows, strong viscous shear flows, Gortler vortices, bifurcations in convection, wavy film flows and boundary layers.

The Linear Stability of Gortler Vortices Revisited / A. Bottaro and P. Luchini -- The Sequence-of-Bifurcations Approach Towards an Understanding of Complex Flows / F.H. Busse and R.M. Clever -- Derivation and Simulations of Evolution Equations of Wavy Film Flows / A.L. Frenkel and K. Indireshkumar -- Instabilities due to Soret Diffusion Coupled to the Morphology of a Solid-Liquid Interface / L. Hadji -- The Instability of Finite Amplitude Waves in Strong Viscid and Inviscid Shear / W.R.C. Phillips -- Nonlinear Stability Analysis and Modeling for Convective Flows / D.N. Riahi -- Modeling and Simulation for Primary Instabilities in Shear Flows / D.N. Riahi -- Gortler Vortices with System Rotation / A. Zebib, A. Bottaro and B.G.B. Klingmann.