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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Druckformat: 2152-5102
ISSN Online: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v23.i5-6.10
pages 321-488

Numerical Experiment in Turbulence: from Order to Chaos

O. M. Belotserkovskii
Institute for Computer Aided Design RAS, Russia

ABSTRAKT

The book is concerned with analysis of fundamental concepts and methods needed for investigating turbulence and the interaction between order and chaos. New numerical techniques (computational experiments) are employed for direct numerical modeling of free developed shear turbulence: coherent structures, laminar-turbulent flows and transition to chaos. The studies of various kinds of hydrodynamical instabilities (Rayleigh−Taylor, Richtmyer−Meshkov) are an unquestionable interest, especially by the two- and three-dimensional calculation extended to the large temporal intervals up to the turbulent stage.
Submitted paper is a version in English of the same book, published by the author in Russian in 1997 (Nauka Publishing house, Moscow). The author supplemented English version with the latest new results of the research of the spa-tially-nonstationary problems of the development of Rayleigh−Taylor and Richtmyer−Meshkov instabilities. These materials and additional references are inserted at the end of the paper (Section 20). New monograph entitled "Turbulence and Instabilities", Publisher Moscow Institute of Physics and Technology (MIPT), Moscow, 1999, contains more completed information.

CONTENTS

321 Foreword
322 I. Direct Numerical Modeling of Free, Developed Shear Turbulence. General Tenets
322 1. Introduction
328 2. "Rational" Averaging in Numerical Investigation of Turbulence
341 3. Certain Experimentally Established Facts
345 II. Coherent Structures at High Reynolds Numbers. The Turbulent "Background" and the Far Wake
345 4. General Formulation of the Problem
347 5. Modeling of Coherent Structures in Turbulence
351 6. Correctness of the Problem
353 7. Examples of Calculation of Coherent Structures in the Near Wake of a Body at Supercritical Velocities
370 8. Numerical Simulation of the Stochastic Component of Turbulence (the Turbulent Background)
385 9. Statistical Modeling of Free Turbulent Flow in the Far Wake
390 III. Unsteady-State Separated and Transition Viscous Flows
390 10. Classification of Flow Modes
394 11. Unsteady-State Separation - the von Karman Vortex Street
396 12. The Laminar-Turbulent Transition
400 IV. Chaos. The Rayleigh-Taylor and the Richtmyer-Meshkov Instabilities. Cumulation Effects
400 13. Scenario of Transition to Chaos
402 14. Subcritical and Supercritical "Kolmogorov Flows" of a Viscous Fluid. Transition to Chaos
419 15. Investigation of Large-Scale Turbulence in the Ocean
429 16. Numerical Modeling of Internal Waves in Stratified Fluids
437 17. Development of the Rayleigh-Taylor Instability in the Two- and Three-Dimensional Case upon Multimode Interactions and Transition to the Turbulent Stage
448 18. Mathematical Simulation of the Richtmyer-Meshkov Hydrodynamic Instability
462 19. Three-Dimensional Flow of Gas in a Breakdown in Several Points of a Circumference (Cumulation Effects)
466 20. New Results of the Computational Analysis of a Spatially-Nonstationary Development of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities
475 21. Conclusions
477 V. Closure
477 22. An Axiomatic Model of Fully-Developed Turbulence
478 23. Principal Tenets of the Suggested Concept of Turbulence
480 References


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