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A century ago, Lewis Fry Richardson introduced the concept of energy cascades in turbulence. Since this conceptual breakthrough, turbulence has been studied in diverse systems and our knowledge has increased considerably through theoretical, numerical, experimental and observational advances. Eddy turbulence and wave turbulence are the two regimes we can find in nature. So far, most attention has been devoted to the former regime, eddy turbulence, which is often observed in water. However, physicists are often interested in systems for which wave turbulence is relevant. This textbook deals with wave turbulence and systems composed of a sea of weak waves interacting non-linearly. After a general introduction which includes a brief history of the field, the theory of wave turbulence is introduced rigorously for surface waves. The theory is then applied to examples in hydrodynamics, plasma physics, astrophysics and cosmology, giving the reader a modern and interdisciplinary view of the subject.
Modelling transport and mixing by turbulence in complex flows are huge challenges for computational fluid dynamics (CFD). This highly readable book introduces readers to modelling levels that respect the physical complexity of turbulent flows. It examines the hierarchy of Reynolds-averaged Navier-Stokes (RANS) closures in various situations ranging from fundamental flows to three-dimensional industrial and environmental applications. The general second-moment closure is simplified to linear eddy-viscosity models, demonstrating how to assess the applicability of simpler schemes and the conditions under which they give satisfactory predictions. The principal changes for the second edition reflect the impact of computing power: a new chapter devoted to unsteady RANS and another on how large-eddy simulation, LES, and RANS strategies can be effectively combined for particular applications. This book will remain the standard for those in industry and academia seeking expert guidance on the modelling options available, and for graduate students in physics, applied mathematics and engineering entering the world of turbulent flow CFD.