Propagation des ondes acoustiques à travers un milieu turbulent : études théorique et expérimentale des effets de diffraction et des effets non linéaires
Nonlinear-diffraction effects in propagation of sound waves through turbulent atmosphere: experimental and theoretical studies
Soutenue le 9 octobre 2008 devant la Commission d’Examen
JURY
Président : M. Daniel JUVÉ Examinateurs : M . Philippe BLANC-BENON (Co-Directeur de Thèse) Mme. Vera KHOKHLOVA (Co-Directeur de Thèse) M. Robin CLEVELAND (Rapporteur) M. Vladimir PREOBRAZHENSKY (Rapporteur) M. Oleg SAPOZHNIKOV
Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509 Ecole Centrale de Lyon et Département d’Acoustique, Faculté de Physique, Université d’État de Moscou TABLE OF CONTENTS
Nomenclature of main used notations ................................................................................................5 Introduction ..............................................................................................................................11 Chapter 1 NONLINEAR SOUND WAVES IN INHOMOGENEOUS MOVING MEDIA (REVIEW) ........................................................................................................................ ...
№ d'ordre : 2008-18 ANNÉE 2008
THÈSE
Présentée devant
L’ÉCOLE CENTRALE DE LYON
Pour obtenir
Le titre de DOCTEUR
SPECIALITÉ ACOUSTIQUE
Par
Mikhail AVERIYANOV
Propagation des ondes acoustiques à travers un milieu turbulent : études
théorique et expérimentale des effets de diffraction et des effets non linéaires
Nonlinear-diffraction effects in propagation of sound waves through turbulent
atmosphere: experimental and theoretical studies
Soutenue le 9 octobre 2008 devant la Commission d’Examen
JURY
Président : M. Daniel JUVÉ
Examinateurs : M . Philippe BLANC-BENON (Co-Directeur de Thèse)
Mme. Vera KHOKHLOVA (Co-Directeur de Thèse)
M. Robin CLEVELAND (Rapporteur)
M. Vladimir PREOBRAZHENSKY (Rapporteur)
M. Oleg SAPOZHNIKOV
Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509
Ecole Centrale de Lyon
et
Département d’Acoustique, Faculté de Physique, Université d’État de Moscou
TABLE OF CONTENTS
Nomenclature of main used notations ................................................................................................5
Introduction ..............................................................................................................................11
Chapter 1 NONLINEAR SOUND WAVES IN INHOMOGENEOUS MOVING MEDIA
(REVIEW) ........................................................................................................................... 19
§ 1.1 Sonic boom in turbulent atmosphere .......................................................................................19
1.1.1 Ecological aspects of the problem .........................................................................................19
1.1.2 Outdoor and laboratory experiments .....................................................................................21
§ 1.2 Mathematical models for nonlinear sound waves propagating in inhomogeneous
moving media ............................................................................................................................24
1.2.1 Wave equations in acoustics of inhomogeneous moving media ...........................................24
1.2.2 Parabolic approximation for nonlinear sound waves in media with scalar
inhomogeneities....................................................................................................................28
1.2.3 Equations of nonlinear geometrical acoustics .......................................................................33
§ 1.3 Theoretical modelling of turbulent media................................................................................36
§ 1.4 Conclusion.................................................................................................................................41
Chapter 2 PROPAGATION OF NONLINEAR N-WAVES IN A TURBULENT
VELOCITY FIELD (laboratory-scaled experiment)........................................................... 43
§ 2.1 Generation and measurement of fully developed turbulent field............................................45
2.1.1 Experimental setup ................................................................................................................45
2.1.2 Measurement of the turbulent field parameters .....................................................................46
§ 2.2 Acoustic measurements.............................................................................................................53
2.2.1 ...53
2.2.2 Characteristics of N-waves measured without turbulence.....................................................55
§ 2.3 Analysis of the effects of turbulence on N-waves ....................................................................58
2.3.1 Typical measured waveforms. Estimation of the focusing zone width .................................58
2.3.2 Effect of the turbulence intensity on the N-wave statistics, average and
peak characteristics...............................................................................................................60
2.3.3 Effect of propagation distance through turbulent medium on the statistics, average
and peak characteristics of the acoustic N-wave ..................................................................64
§ 2.4 Characteristic scales: atmosphere and laboratory experiment................................................67
§ 2.5 Conclusion.................................................................................................................................68
Chapter 3 MEASUREMENT AND MODELLING OF SPHERICALLY DIVERGING SHOCK
PULSES IN RELAXING AIR. CALIBRATION OF THE MICROPHONE. ................... 71
§ 3.1 Acoustic measurements. Mean and peak characteristics of the N-wave parameters .............73
§ 3.2 Theoretical model......................................................................................................................74
3.2.1 Modified Burgers equation for divergent waves in relaxing medium ...................................74
3.2.2 Numerical algorithm..............................................................................................................76
3.2.3 Effects of nonlinearity, thermoviscous absorption and relaxation on the acoustic
wave propagation..................................................................................................................78
§ 3.3 Calibration of measuring system based on nonlinear effects..................................................81
§ 3.4 Amplitude and phase frequency characteristics of measuring system....................................82
§ 3.5 N-wave characteristic parameters. Comparison of experimental data with the results of
numerical modelling.....85
§ 3.6 Conclusion.................................................................................................................................86 Chapter 4 NONLINEAR EVOLUTION EQUATION OF KHOKHLOV- ZABOLOTSKAYA
TYPE FOR THE DESCRIPTION OF ACOUSTIC WAVE PROPAGATION IN
INHOMOGENEOUS MOVING MEDIA ........................................................................... 89
§ 4.1 Theoretical model. Parabolic equation for nonlinear sound waves in inhomogeneous
moving media. .......................................................................................................................... 90
§ 4.2 Self similarity property of the KZK type equation................................................................... 95
§ 4.3 Numerical algorithms .............................................................................................................. 96
4.3.1 Frequency domain approach to model periodic waves with shocks..................................... 96
4.3.2 Time domain approach to model propagation of single shock pulses .................................. 98
§ 4.4 Benchmark solutions and validation of the model................................................................ 106
§ 4.5 Conclusion.............................................................................................................................. 108
Chapter 5 NONLINEAR AND DIFFRACTION EFFECTS DURING THE PROPAGATION OF
ACOUSTIC SIGNALS IN RANDOMLY INHOMOGENEOUS MOVING MEDIUM
(Numerical modelling)....................................................................................................... 111
§ 5.1 Periodic waves ........................................................................................................................ 111
5.1.1 Nonlinear versus linear effects of random focusing in an inhomogeneous
moving medium 111
5.1.2 Effect of the transverse component of turbulent velocity field: vector versus scalar
contributions of inhomogeneities ...................................................................................... 115
5.1.3 Diffraction effects: ray tracing and acoustic field patterns obtained with the
KZK equation .................................................................................................................... 116
5.1.4 Effect of spatial correlation lengths and intensity of the turbulence on acoustic field
characteristics .................................................................................................................... 117
§ 5.2 Acoustic pulses. N-waves ....................................................................................................... 120
5.2.1 Parameters of simulations, 2D patterns of randomly inhomogeneous velocity field ......... 120
5.2.2 Diffraction effects: ray tracing and acoustic field patterns obtained with the
KZK equation. 121
5.2.3 Nonlinear versus linear effects on random focusing in an inhomogeneous medium ......... 124
5.2.4 Influence of randomly inhomogeneous medium on statistics, average and peak
characteristics of the acoustic N-wave............................................................................... 127
5.2.5 Effect of the transverse component of turbulent velocity: vector versus scalar
contributions of inhomogeneities ...................................................................................... 132
5.2.6 Effect of spatial correlation lengths and turbulent kinetic energy distribution law
on acoustic field characteristics ......................................................................................... 134
§ 5.3 Comparison of numerical model results with experimental data......................................... 136
§ 5.4 Conclusion.............................................................................................................................. 146
CONCLUSION ........................................................................................................................... 149
Appendix A : GEOMETRICAL ACOUSTICS APPROACH