This book addresses the concepts of unstable flow solutions, convective instability and absolute instability, with reference to simple (or toy) mathematical models, which are mathematically simple despite their purely abstract character. Within this paradigm, the book introduces the basic mathematical tools, Fourier transform, normal modes, wavepackets and their dynamics, before reviewing the fundamental ideas behind the mathematical modelling of fluid flow and heat transfer in porous media. The author goes on to discuss the fundamentals of the Rayleigh-Bénard instability and other thermal instabilities of convective flows in porous media, and then analyses various examples of transition from convective to absolute instability in detail, with an emphasis on the formulation, deduction of the dispersion relation and study of the numerical data regarding the threshold of absolute instability. The clear descriptions of the analytical and numerical methods needed to obtain these parametric threshold data enable readers to apply them in different or more general cases. This book is of interest to postgraduates and researchers in mechanical and thermal engineering, civil engineering, geophysics, applied mathematics, fluid mechanics, and energy technology.

This book addresses the concepts of unstable flow solutions, convective instability and absolute instability, with reference to simple (or toy) mathematical models, which are mathematically simple despite their purely abstract character. Within this paradigm, the book introduces the basic mathematical tools, Fourier transform, normal modes, wavepackets and their dynamics, before reviewing the fundamental ideas behind the mathematical modelling of fluid flow and heat transfer in porous media. The author goes on to discuss the fundamentals of the Rayleigh-Bénard instability and other thermal instabilities of convective flows in porous media, and then analyses various examples of transition from convective to absolute instability in detail, with an emphasis on the formulation, deduction of the dispersion relation and study of the numerical data regarding the threshold of absolute instability. The clear descriptions of the analytical and numerical methods needed to obtain these parametric threshold data enable readers to apply them in different or more general cases. This book is of interest to postgraduates and researchers in mechanical and thermal engineering, civil engineering, geophysics, applied mathematics, fluid mechanics, and energy technology.

This monograph provides state-of-the-art theoretical and computational findings from investigations on physical and chemical dissolution front instability problems in porous media, based on the author’s own work. Although numerical results are provided to complement theoretical ones, the focus of this monograph is on the theoretical aspects of the topic and those presented in this book are applicable to a wide range of scientific and engineering problems involving the instability of nonlinear dynamic systems. To appeal to a wider readership, common mathematical notations are used to derive the theoretical solutions. The book can be used either as a useful textbook for postgraduate students or as a valuable reference book for computational scientists, mathematicians, engineers and geoscientists.

This carefully edited book offers a state-of-the-art overview on formulation, mathematical analysis and numerical solution procedures of contact problems. The contributions collected in this volume summarize the lectures presented by leading scientists in the area of contact mechanics, during the 4th Contact Mechanics International Symposium (CMIS) held in Hannover, Germany, 2005.

This thesis studies how rocks evolve due to the coupled effects of flow and chemical reaction. The study was motivated by various experimental observations, both in igneous and sedimentary rocks. In the first part of this thesis, growth of microscopic, pore-scale, features in sedimentary rocks is theoretically investigated. It is found, in agreement with experiments, that statistical properties of pore-grain interfaces mirror growth conditions. The shapes of pore-grain intrefaces both influence and are influenced by large-scale transport properties of the rock. The second part of this thesis employs analytical methods to study flow patterns in melt upwelling beneath mid-ocean ridges. It is shown that high permeability channels spontaneously form, allowing for efficient extraction of melt from the system. This result may aid in understanding existing geochemical and geological observations. In the third part of this thesis, I present a new 3D computer model that simulates flow and reaction through a porous matrix. The model is used to study and compare the different characteristics of dissolution and deposition, and to simulate different settings for melt upwelling in the mantle.

Natural Convection in Composite Fluid-Porous Domains provides a timely overview of the current state of understanding on the phenomenon of convection in composite fluid-porous layers. Natural convection in horizontal fluid-porous layers has received renewed attention because of engineering problems such as post-accident cooling of nuclear reactors, contaminant transport in groundwater, and convection in fibrous insulation systems. Because applications of the problem span many scientific domains, the book serves as a valuable resource for a wide audience.

A detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear and selected nonlinear stability methods. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It is equally of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Stability theory has seen a rapid development over the past decade, this book includes such new developments as direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem.