Quantum Nature Of Turbulence

This book presents an integral formulation of hydrodynamics in order to derive the pressure tensor and expressions of non-divergent transport coefficients. At the same time, the impossibility of finding pathologic solutions of the Liouville equation that may be identified with turbulence are examined. This book collects the ideas and papers that build up to the conclusion that turbulence is a quantum phenomenon, thereby encouraging more experimental and theoretical work in quantum non-equilibrium statistical mechanics. The book opens up a modern approach to the "classical" theory of turbulence, of interest to both engineers and physicists.

This book critically reexamines what turbulence really is, from a fundamental point of view and based on observations from nature, laboratories, and direct numerical simulations. It includes critical assessments and a comparative analysis of the key developments, their evolution and failures, along with key misconceptions and outdated paradigms. The main emphasis is on conceptual and problematic aspects, physical phenomena, observations, misconceptions and unresolved issues rather than on conventional formalistic aspects, models, etc. Apart from the obvious fundamental importance of turbulent flows, this emphasis stems from the basic premise that without corresponding progress in fundamental aspects there is little chance for progress in applications such as drag reduction, mixing, control and modeling of turbulence. More generally, there is also a desperate need to grasp the physical fundamentals of the technological processes in which turbulence plays a central role.

This book provides state-of-the-art results and theories in homogeneous turbulence, including anisotropy and compressibility effects with extension to quantum turbulence, magneto-hydodynamic turbulence and turbulence in non-newtonian fluids. Each chapter is devoted to a given type of interaction (strain, rotation, shear, etc.), and presents and compares experimental data, numerical results, analysis of the Reynolds stress budget equations and advanced multipoint spectral theories. The role of both linear and non-linear mechanisms is emphasized. The link between the statistical properties and the dynamics of coherent structures is also addressed. Despite its restriction to homogeneous turbulence, the book is of interest to all people working in turbulence, since the basic physical mechanisms which are present in all turbulent flows are explained. The reader will find a unified presentation of the results and a clear presentation of existing controversies. Special attention is given to bridge the results obtained in different research communities. Mathematical tools and advanced physical models are detailed in dedicated chapters.

An Introduction to the Theory of Plasma Turbulence is a collection of lectures given by the author at Culham laboratory. The book deals with developments on the theory of plasma turbulence. The author describes plasma properties in the turbulent regions as mostly non-linear in nature, and notes that these properties can be regarded as a universal spectrum independent of any type of instability. The text then discusses the general problems of the theory of plasma turbulence. The author also shows that elementary excitation of ""dressed"" particles have a finite lifetime associated with non-linear interactions. The book then discusses the excitation of ion-sound turbulence using different processes, for example, shock waves; the text also analyzes the kind of non-linear interactions present in such energy transfer. The author also explains the Langmuir plasma oscillations — a typical collective plasma motion that can be excited using different types of mechanism such as an electron beam. The book then describes the electromagnetic properties of turbulent plasma and relates the state of turbulent plasma as a natural occurrence in the universe. The book notes the problem of cosmic rays, not as an energy transfer to faster particles, but as an energy distribution between particles. The text will prove valuable for nuclear physicists, scientists, and academicians in the field of quantum mechanics.

Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together ex

This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A.N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such "fully developed turbulence" is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. First, a qualitative introduction is given to bring out the need for a probabilistic description of what is in essence a deterministic system. Kolmogorov's 1941 theory is presented in a novel fashion with emphasis on symmetries (including scaling transformations) which are broken by the mechanisms producing the turbulence and restored by the chaotic character of the cascade to small scales. Considerable material is devoted to intermittency, the clumpiness of small-scale activity, which has led to the development of fractal and multifractal models. Such models, pioneered by B. Mandelbrot, have applications in numerous fields besides turbulence (diffusion limited aggregation, solid-earth geophysics, attractors of dynamical systems, etc). The final chapter contains an introduction to analytic theories of the sort pioneered by R. Kraichnan, to the modern theory of eddy transport and renormalization and to recent developments in the statistical theory of two-dimensional turbulence. The book concludes with a guide to further reading. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers.

Bringing together two previously distinct strands of physics, this text introduces the interdisciplinary field of quantum turbulence, the realm of quantum fluids and vortices in superfluid helium and atomic Bose–Einstein condensates. Covering state-of-the-art methods and results, it is an essential read for students and seasoned researchers alike.