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Turbulence is ubiquitous in science, technology and daily life and yet, despite years of research, our understanding of its fundamental nature is still tentative and incomplete. More generally, the tools required for a deep understanding of strongly interacting many-body systems remain underdeveloped. Inspired by a research programme held at the Newton Institute in Cambridge, this book contains reviews by leading experts that summarize our current understanding of the nature of turbulence from theoretical, experimental, observational and computational points of view. The articles cover a wide range of topics, including the scaling and organized motion in wall turbulence, small scale structure, dynamics and statistics of homogeneous turbulence, turbulent transport and mixing, and effects of rotation, stratification and magnetohydrodynamics, as well as superfluidity. The book will be useful to researchers and graduate students interested in the fundamental nature of turbulence at high Reynolds numbers.

Turbulence. --- Flow, Turbulent --- Turbulent flow --- Fluid dynamics

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The problem of accurate and reliable simulation of turbulent flows is a central and intractable challenge that crosses disciplinary boundaries. As the needs for accuracy increase and the applications expand beyond flows where extensive data is available for calibration, the importance of a sound mathematical foundation that addresses the needs of practical computing increases. This Special Issue is directed at this crossroads of rigorous numerical analysis, the physics of turbulence and the practical needs of turbulent flow simulations. It seeks papers providing a broad understanding of the status of the problem considered and open problems that comprise further steps.

Turbulence. --- Flow, Turbulent --- Turbulent flow --- Fluid dynamics

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Turbulence. --- Flow, Turbulent --- Turbulent flow --- Fluid dynamics --- Turbulence --- Mathematical models.

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Applied Mathematics --- Engineering & Applied Sciences --- Turbulence. --- Flow, Turbulent --- Turbulent flow --- Fluid dynamics

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Turbulence is a huge subject of ongoing research. This book bridges the modern development in dynamical systems theory and the theory of fully developed turbulence. Many solved and unsolved problems in turbulence have equivalencies in simple dynamical models, which are much easier to handle analytically and numerically. This book gives a modern view of the subject by first giving the essentials of the theory of turbulence before moving on to shell models. These show much of the same complex behaviour as fluid turbulence, but are much easier to handle analytically and numerically. Any necessary maths is explained and self-contained, making this book ideal for advanced undergraduates and graduate students, as well as researchers and professionals, wanting to understand the basics of fully developed turbulence.

Turbulence. --- Fluid dynamics. --- Dynamics --- Fluid mechanics --- Flow, Turbulent --- Turbulent flow --- Fluid dynamics