Turbulence nature and the inverse problem / L.N. Pyatnitsky.

Format:

Book

Author/Creator:

Pyatnitsky, L. N. (Lev N.)

Contributor:

Alumni and Friends Memorial Book Fund.

Series:

Fluid mechanics and its applications ; v. 89.

Fluid mechanics and its applications ; v. 89

Language:

English

Subjects (All):

Turbulence.

Fluid dynamics.

Physical Description:

xvi, 197 pages : illustrations ; 25 cm.

Place of Publication:

[Place of publication not identified] : Springer, [2009]

Summary:

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.

Contents:

1 The turbulence problem 1

1.1 The first interpretation 1

1.2 The next approaches 5

1.3 A new approach 11

2 Fluid motion 17

2.1 Equations of fluid motion 17

2.2 Vorticity 20

2.3 Wave equation and incompressibility conditions 23

3 Distribution of parameters in viscous flow 29

3.1 Velocity profiles in a flow cross-section 29

3.2 Hypothesis on pressure profile in a flow cross-section 33

3.3 Correction of the pressure profile 38

4 Perturbations in viscous flow 43

4.1 Fluid motion from the start 43

4.2 Simple wave and wave beam 47

4.3 Origin of pressure perturbations 51

5 Perturbation in channels 55

5.1 Perturbations in semi-infinite space 55

5.2 Perturbation waves in flow 58

5.3 Distortion of the wave packet in channels 61

5.4 The wave packet in the boundary layer 66

6 Spatio-temporal field of perturbations in channels 73

6.1 Computing technique of wave configuration in channels 73

6.2 Wave front configuration appearance in channels 76

6.3 Structure of flow perturbations in channels 79

7 Evolution of velocity oscillation field 85

7.1 Oscillations of flow parameters produced by a wave 85

7.2 Spatio-temporal field of oscillations in a wave sequence 93

7.3 Chaotization of a spatio-temporal field 97

8 Experimental substantiation of turbulence wave model 103

8.1 Structure of a simple wave 103

8.2 Boundary layer separation and flow perturbations 114

8.3 Distribution of oscillations in flow cross-section 119

9 Transition from normal combustion to detonation 125

9.1 Short history of the problem 125

9.2 Exposition of flame propagation in a pipe 127

9.3 Initial stage of the flame propagation 131

9.4 Uniform flame propagation and second acceleration 135

9.5 Formation of detonation wave 143

10 An inverse problem of turbulence 155

10.1 Object of the inverse problem application 155

10.2 Wave beam at Rayleigh divergence compensated 158

10.3 Structures of plasma channels in lengthy wave beams 160

10.4 Breakdown structures in the short heating impulse 166

10.5 Formation of complex structures of the plasma channel 171.

Notes:

Includes bibliographical references (pages 185-191) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

9789048122509

9048122503

OCLC:

310400770

Publisher Number:

99935479836