Starting with a look at the historical and scientific context of multifractals and turbulence, this book goes on to examine hydrodynamic turbulence, intermittency, multifractal processes and generalized scale invariance. The book is aimed at physicists and students of fluid dynamics.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
Maße
ISBN-13
978-981-02-0886-8 (9789810208868)
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Schweitzer Klassifikation
Part 1 Historical background and scientific context: from speculative turbulance to phenomenological cascades models; scientific crisis; symmetries and complexity; scale symmetry; fields and geometry. Part 2 Hydrodynamic turbulence: equations of evolution; basic physics of three-dimensional turbulence; symmetries and conservation laws; statistical descriptors and singular behaviours; the very special case of 2-D turbulence; some mathematical exact results and conjectures; unpredictability and the caricature of deterministic chaos; renormalization techniques. Part 3 Intermittency: failures of homogeneous turbulence; phenomenological cascades; discrete multiplicative processes; dual representations - singularities/statistical moments; continuous multiplicative processes. Part 4 Multifractal processes: general considerations; classification of the multifractal singularities and processes; bare and dressed properties; universality; miscellaneous properties; fluxdynamics and thermodynamics formalisms; renormalization revisited; data analysis methods; numerical simulations. Part 5 Generalized scale invariance: scaling anisotropy in space and in space-time; global scale transformations; local scale transformation; stochastic scale transformation; data analysis methods; numerical simulations.
