Inertial Range Flow And Turbulent Cascades Classic Reprint PDF Download
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Author | : Alexandre Joël Chorin |
Publisher | : Forgotten Books |
Total Pages | : 50 |
Release | : 2018-02-06 |
Genre | : Science |
ISBN | : 9780267964321 |
Download Inertial Range Flow and Turbulent Cascades (Classic Reprint) Book in PDF, ePub and Kindle
Excerpt from Inertial Range Flow and Turbulent Cascades The study of the inertial and dissipation ranges is a sounder undertaking. Roughly speaking, energy reaches these ranges after a number of non-linear interactions; the influence of the boundary and initial conditions is no longer appreciable; over most of the flow the spectrum becomes independent of x and can be expected to embody an intrinsic property of turbulence. It is of course a task of a theory of turbulence to provide a more credible explanation of this lack of dependence between the several parts of the spectrum. When the Reynolds number is sufficiently large the inertial range is of considerable extent, and its influence on possible eddy coefficients is dominant. (see e.g. [11] and a forthcoming paper by the present author.) The present paper is devoted to the study of the inertial range. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author | : Alexandre Joel Chorin |
Publisher | : |
Total Pages | : 0 |
Release | : 1969 |
Genre | : Fluid dynamics |
ISBN | : |
Download Inertial Range Flow and Turbulent Cascades Book in PDF, ePub and Kindle
Author | : Mikhael Gorokhovski |
Publisher | : Springer |
Total Pages | : 294 |
Release | : 2019-05-21 |
Genre | : Technology & Engineering |
ISBN | : 3030125475 |
Download Turbulent Cascades II Book in PDF, ePub and Kindle
Gathering contributions by the most prominent researchers in a highly specialised field, this proceedings volume clarifies selected aspects of the physics of turbulent cascades and their statistical universalities under complex stationary and non-homogeneous conditions. Here, these conditions are induced by the presence of a gas/liquid interface, inertial particles, strong shear, rotation, MHD and stratification. By proposing different ways to model turbulence effects under these complex conditions, the book will be of considerable interest not only to academic researchers, but also to specialists and junior researchers in the domain of propulsion and power, as well as those whose work involves various applications related to atmospheric, oceanic and planetary physics.
Author | : Robert H. Kraichnan |
Publisher | : |
Total Pages | : 14 |
Release | : 1967 |
Genre | : |
ISBN | : |
Download Inertial Ranges in Two-dimensional Turbulence Book in PDF, ePub and Kindle
Two-dimensional turbulence has both kinetic energy and mean-square vorticity as inviscid constants of motion. Consequently it admits two formal inertial ranges, E(k) is approx. (epsilon to the 2/3 power) k to the -5/3 power and E(k) is approx. (eta to the 2/3 power) k to the -3rd power, where epsilon is the rate of cascade of kinetic energy per unit mass, eta is the rate of cascade of mean-square vorticity, and the kinetic energy per unit mass is the integral from 0 to infinity E(k)dk. The -5/3 range is found to entail backward energy cascade, from higher to lower wavenumbers k, together with zero vorticity flow. The -3 range gives an upward vorticity flow and zero energy flow. The paradox in these results is resolved by the irreducibly triangular nature of the elementary wavenumber-interactions. The formal -3 range gives a nonlocal cascade and consequently must be modified by logarithmic factors. If energy is fed in at a constant rate to a band of wavenumbers approx. k sub i and the Reynolds number is large, it is conjectured that a quasisteady state results with a -5/3 range for k “k sub i and a -3 range for k” k sub i, up to the viscous cut-off. The total kinetic energy increases steadily with time as the - 5/3 range pushes to ever-lower k, until scales the size of the entire fluid are strongly excited. The rate of energy dissipation by viscosity decreases to zero if kinematic viscosity is decreased to zero with other parameters unchanged.
Author | : Uriel Frisch |
Publisher | : Cambridge University Press |
Total Pages | : 314 |
Release | : 1995-11-30 |
Genre | : Science |
ISBN | : 9780521457132 |
Download Turbulence Book in PDF, ePub and Kindle
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.
Author | : Marcel Lesieur |
Publisher | : Springer Science & Business Media |
Total Pages | : 593 |
Release | : 2008-03-26 |
Genre | : Technology & Engineering |
ISBN | : 1402064357 |
Download Turbulence in Fluids Book in PDF, ePub and Kindle
Now in its fully updated fourth edition, this leading text in its field is an exhaustive monograph on turbulence in fluids in its theoretical and applied aspects. The authors examine a number of advanced developments using mathematical spectral methods, direct-numerical simulations, and large-eddy simulations. The book remains a hugely important contribution to the literature on a topic of great importance for engineering and environmental applications, and presents a very detailed presentation of the field.
Author | : Alexander J. Smits |
Publisher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2003-12-31 |
Genre | : Technology & Engineering |
ISBN | : 9781402017759 |
Download IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow Book in PDF, ePub and Kindle
This volume presents selected papers from the IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow, convened in Princeton, NJ, USA, September I1-13, 2002. The behavior ofturbulence at high Reynolds number is interesting from a fundamental point of view, in that most theories of turbulence make very specific predictions in the limit of infinite Reynolds number. From a more practical point of view, there exist many applications that involve turbulent flow where the Reynolds numbers are extremely large. For example, large vehicles such as submarines and commercial transports operate at Reynolds 9 numbers based on length ofthe order oft0 , and industrial pipe flows cover a 7 very wide range of Reynolds numbers up to 10 • Many very important applications of high Reynolds number flow pertain to atmospheric and other geophysical flows where extremely high Reynolds numbers are the rule rather than the exception, and the understanding of climate changes and the prediction of destructive weather effects hinges to some extent on our appreciation ofhigh-Reynolds number turbulence behavior. The important effects of Reynolds number on turbulence has received a great deal of recent attention. The objective of the Symposium was to bring together many of the world's experts in this area to appraise the new experimental results, discuss new scaling laws and turbulence models, and to enhance our mutual understanding of turbulence.
Author | : Jean Mathieu |
Publisher | : Cambridge University Press |
Total Pages | : 388 |
Release | : 2000-06-26 |
Genre | : Science |
ISBN | : 9780521775380 |
Download An Introduction to Turbulent Flow Book in PDF, ePub and Kindle
Most natural and industrial flows are turbulent. The atmosphere and oceans, automobile and aircraft engines, all provide examples of this ubiquitous phenomenon. In recent years, turbulence has become a very lively area of scientific research and application, attracting many newcomers who need a basic introduction to the subject. An Introduction to Turbulent Flow, first published in 2000, offers a solid grounding in the subject of turbulence, developing both physical insight and the mathematical framework needed to express the theory. It begins with a review of the physical nature of turbulence, statistical tools, and space and time scales of turbulence. Basic theory is presented next, illustrated by examples of simple turbulent flows and developed through classical models of jets, wakes, and boundary layers. A deeper understanding of turbulence dynamics is provided by spectral analysis and its applications. The final chapter introduces the numerical simulation of turbulent flows. This well-balanced text will interest graduate students in engineering, applied mathematics, and the physical sciences.
Author | : Pierre Sagaut |
Publisher | : Springer |
Total Pages | : 912 |
Release | : 2018-03-23 |
Genre | : Science |
ISBN | : 3319731629 |
Download Homogeneous Turbulence Dynamics Book in PDF, ePub and Kindle
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.
Author | : Joseph James Gilles Ballouz |
Publisher | : |
Total Pages | : |
Release | : 2020 |
Genre | : |
ISBN | : |
Download On the Efficiency of the Turbulent Cascade Book in PDF, ePub and Kindle
Turbulent flows are chaotic and highly fluctuating, with a large number of interacting scales of motion, which makes them difficult to predict. One approach (known as Large Eddy Simulation) is to resolve all scales of motion down to a cutoff scale of interest and to capture the effect of all omitted smaller scales by modeling the unclosed unresolved turbulent deviatoric stress. This stress appears in the energy equation of the resolved scales of motion in the scale-to-scale energy flux term. The energy flux term is a dot product of two symmetric tensors: the unresolved turbulent stress tensor and the resolved strain rate tensor. Thus, we may interpret it as mechanical work done by the large resolved scales of motion on the smaller unresolved ones. This work is not only a function of the magnitudes of these two tensors but also of the relative alignment of their eigenframes. For no work can be done when the direction of force (stress) is orthogonal to the displacement (strain). A new quantity that characterizes this alignment is the cascade efficiency. Although one of the defining characteristics of the turbulent cascade is the scale-to-scale energy transfer, this transfer is found to be on average inefficient in the inertial range (around 25\%) due to a poor alignment between the stress and strain rate tensors. Another finding is that the embedding dimension of the flow plays a strong role in setting the direction of the scale-to-scale energy flux, for when geometric alignments between the stress and strain rate tensors encountered in three-dimensional turbulence are projected onto a two-dimensional configuration, the direct energy cascade towards smaller scales of motion reverses to a two-dimensional inverse energy cascade towards larger scales. The efficiency proves to be an effective metric in revealing the broken time-reversal symmetry of the turbulent cascade, for it is seen that the geometry of the turbulent stress lags that of the strain rate in three-dimensional turbulence, which is the opposite of what is observed in two dimensions. However, the time lags required for peak alignment do not properly scale with filter size when considering Eulerian quantities lagged in-place or along particle trajectories. It is only when expressing the scale-to-scale energy flux in a fully Lagrangian manner based on the right Cauchy-Green strain rate tensor and the second Piola--Kirchhoff stress tensor, that the times required for peak efficiency along fluid eddies follow the expected 2/3 Kolmogorov scaling.