Routes to Absolute Instability in Porous Media
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 parad
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Routes to Absolute Instability in Porous Media
Routes to Absolute Instability in Porous Media
Antonio Barletta
Routes to Absolute Instability in Porous Media
123
Antonio Barletta Department of Industrial Engineering Alma Mater Studiorum Università di Bologna Bologna, Italy
ISBN 978-3-030-06193-7 ISBN 978-3-030-06194-4 https://doi.org/10.1007/978-3-030-06194-4
(eBook)
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What we cannot speak about we must pass over in silence. Ludwig Wittgenstein
Foreword
Stability theory has an old and venerable history in the context of fluid mechanics: much is known and much remains to be discovered. In our desire to model accurately our highly nonlinear world, it is quite natural to begin slowly by determining first the flow field for small values of a parameter such as the Reynolds, Rayleigh, Taylor or Görtler numbers. In such cases, the flow is slow and nonlinear effects are barely felt. Perhaps it is unsurprising then that such flows are stable, not that we have yet defined this word. One potential definition of stability might be that the flow is unique, but this idea is unsatisfactory because it mentions neither the presence of nor the rôle played by disturbances of any kind. Consideration of these matters is central to stability theory and is essential before pressing on to fully numerical simulations and the transition to turbulence. We all have an intuitive idea of what the words stable and unstable mean because they may be related to many aspects of human life and experience: nitroglycerine is unstable; a cyclist in motion is stable; a poorly constructed building
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