# Routes to Absolute Instability in Porous Media

• Antonio Barletta
Book

1. Front Matter
Pages i-xix
2. Antonio Barletta
Pages 1-3
3. ### Mathematical Models of Flow Instability

1. Front Matter
Pages 5-5
2. Antonio Barletta
Pages 7-27
3. Antonio Barletta
Pages 29-63
4. Antonio Barletta
Pages 65-90
4. ### Flow and Convection in Porous Media

1. Front Matter
Pages 91-91
2. Antonio Barletta
Pages 93-119
3. Antonio Barletta
Pages 121-133
4. Antonio Barletta
Pages 135-175
5. ### From Convective to Absolute Instability in Porous Media

1. Front Matter
Pages 177-177
2. Antonio Barletta
Pages 179-216
3. Antonio Barletta
Pages 217-242
4. Antonio Barletta
Pages 243-259
6. Antonio Barletta
Pages C1-C1
7. Back Matter
Pages 261-283

### Introduction

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.

### Keywords

Porous Medium Flow Stability Convection Heat Transfer Wave Packet Dynamics Absolute Instability Eigenvalue Stability Problems

#### Authors and affiliations

• Antonio Barletta
• 1
1. 1.Department of Industrial EngineeringAlma Mater Studiorum Università di BolognaBolognaItaly