Statistics of temperature fluctuations

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Table of contents

I General Introduction 
II Temperature fluctuations in turbulent flows 
II.1 Theoretical background
II.1.1 The governing equations
II.1.2 Limit I: Incompressible flow
II.1.3 Limit II: Acoustic wave
II.1.4 Limit III: Perfect fluid
II.1.5 Temperature fluctuations in incompressible, homogeneous and isotropic turbulent flows: Theory
II.1.6 Temperature fluctuations in incompressible, homogeneous and isotropic turbulent flows: Energy spectrum and RMS
II.2 Temperature fluctuations due to viscous dissipation
II.2.1 The von Kármán swirling flow
II.2.2 Experimental setup
II.2.3 Characterization of the flow
II.3 Experimental Results
II.3.1 Statistics of temperature fluctuations
II.3.2 Pressure fluctuations and their similarity to temperature fluctuations 
II.3.3 Joint PDFs of pressure and temperature fluctuations
II.3.4 Structure of negative peaks in pressure and temperature fluctuations
II.3.5 A steady solution for single weakly compressible adiabatic vortex
II.3.6 The energy spectra of temperature fluctuations
II.4 Conclusion
II.A Estimation of RMS of velocity fluctuations from 1D hot-wire probe
II.B Method of coherent averaging
II.B.1 Demonstration
IIICoherence of velocity fluctuations in turbulent flows 
III.1 Theoretical background
III.1.1 The sweeping effect and the energy spectrum
III.1.2 The sweeping effect and coherence
III.2 Experimental setup I
III.2.1 Characterization of the flow
III.3 Experimental results of setup I
III.4 Experimental setup II
III.4.1 Forcing mechanism: Helices and motors
III.4.2 Working fluid and its properties
III.4.3 The setup of the PIV technique
III.4.4 Characterization of the flow
III.5 Experimental results of setup II
III.6 Conclusion
IVAcoustic scattering by turbulent flows 
IV.1 Theoretical background
IV.1.1 Vortex sound
IV.1.2 Acoustic scattering
IV.1.3 The geometrical acoustic limit
IV.2 Acoustic scattering in Line Of Sight (LOS) propagation
IV.2.1 Parameter fluctuations of incident wave in LOS propagation
IV.2.2 Statistical properties of phase fluctuations of the incident wave .
IV.2.3 Statistical properties of log-amplitude fluctuations of the incident wave
IV.2.4 Coherent wave propagation and change in speed of sound
IV.3 Experimental setup
IV.4 Experimental results
IV.4.1 Parameter fluctuations of incident wave in LOS propagation
IV.4.2 Change in speed of sound due to turbulent flow
IV.5 Conclusion
IV.A The governing equation of vortex sound
IV.B The governing equation of acoustic scattering
IV.C The governing equation for the geometrical acoustic limit
IV.D The governing equations for log-amplitude and phase fluctuations
V General conclusion and perspectives 
V.1 Perspectives
A Calibration of hot-wire probes 
A.1 King’s law
A.2 Setup
A.3 Results
Bibliography