Turbulence Nature and the Inverse Problem

By: L. N. Pyatnitsky

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Hardcover | 20 March 2009

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216 Pages

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Hydrodynamic equations well describe averaged parameters of turbulent steady flows, at least in pipes where boundary conditions can be estimated. The equations might outline the parameters fluctuations as well, if entry conditions at current boundaries were known. This raises, in addition, the more comprehensive problem of the primary perturbation nature, noted by H.A. Lorentz, which still remains unsolved. Generally, any flow steadiness should be supported by pressure waves emitted by some external source, e.g. a piston or a receiver. The wave plane front in channels quickly takes convex configuration owing to Rayleigh's law of diffraction divergence. The Schlieren technique and pressure wave registration were employed to investigate the wave interaction with boundary layer, while reflecting from the channel wall. The reflection induces boundary-layer local separation and following pressure rapid increase within the perturbation zone. It propagates as an acoustic wave packet of spherical shape, bearing oscillations of hydrodynamic parameters. Superposition of such packets forms a spatio-temporal field of oscillations fading as 1/r. This implies a mechanism of the turbulence. Vorticity existing in the boundary layer does not penetrate in itself into potential main stream. But the wave leaving the boundary layer carries away some part of fluid along with frozen-in vorticity. The vorticity eddies form another field of oscillations fading as 1/r². This implies a second mechanism of turbulence. Thereupon the oscillation spatio-temporal field and its randomization development are easy computed. Also, normal burning transition into detonation is explained, and the turbulence inverse problem is set and solved as applied to plasma channels created by laser Besselian beams.

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"This is an interesting book, whose focus is on the nature of turbulent fluctuations. ... This book will be particularly intriguing to specialists in the field and also to scientists who are interested in the many aspects of scientific debate." (Barbara Vanda Villone, Mathematical Reviews, Issue 2012 e)

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Published: 28th October 2010

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The turbulence problem	p. 1
The first interpretation	p. 1
The next approaches	p. 5
A new approach	p. 11
Fluid motion	p. 17
Equations of fluid motion	p. 17
Vorticity	p. 20
Wave equation and incompressibility conditions	p. 23
Distribution of parameters in viscous flow	p. 29
Velocity profiles in a flow cross-section	p. 29
Hypothesis on pressure profile in a flow cross-section	p. 33
Correction of the pressure profile	p. 38
Perturbations in viscous flow	p. 43
Fluid motion from the start	p. 43
Simple wave and wave beam	p. 47
Origin of pressure perturbations	p. 51
Perturbation in channels	p. 55
Perturbations in semi-infinite space	p. 55
Perturbation waves in flow	p. 58
Distortion of the wave packet in channels	p. 61
The wave packet in the boundary layer	p. 66
Spatio-temporal field of perturbations in channels	p. 73
Computing technique of wave configuration in channels	p. 73
Wave front configuration appearance in channels	p. 76
Structure of flow perturbations in channels	p. 79
Evolution of velocity oscillation field	p. 85
Oscillations of flow parameters produced by a wave	p. 85
Spatio-temporal field of oscillations in a wave sequence	p. 93
Chaotization of a spatio-temporal field	p. 97
Experimental substantiation of turbulence wave model	p. 103
Structure of a simple wave	p. 103
Boundary layer separation and flow perturbations	p. 114
Distribution of oscillations in flow cross-section	p. 119
Transition from normal combustion to detonation	p. 125
Short history of the problem	p. 125
Exposition of flame propagation in a pipe	p. 127
Initial stage of the flame propagation	p. 131
Uniform flame propagation and second acceleration	p. 135
Formation of detonation wave	p. 143
An inverse problem of turbulence	p. 155
Object of the inverse problem application	p. 155
Wave beam at Rayleigh divergence compensated	p. 158
Structures of plasma channels in lengthy wave beams	p. 160
Breakdown structures in the short heating impulse	p. 166
Formation of complex structures of the plasma channel	p. 171
Conclusion	p. 181
References	p. 185
Index	p. 193
Table of Contents provided by Ingram. All Rights Reserved.

Turbulence Nature and the Inverse Problem

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