(Downloads - 0)
For more info about our services contact : help@bestpfe.com
Table of contents
Acknowledgement
Publications and conferences
Abbreviations
Symbols
Introduction
I Passive Scalar in Isotropic Turbulence & Velocity Field in Anisotropic Turbulence
1 Passive Scalar Mixing in Homogeneous Isotropic Turbulence
1.1 The equations of homogeneous isotropic turbulence
1.2 The inertial scaling of ET for Pr 1
1.3 Mixed-derivative skewness ST for Pr 1
1.4 Time evolution of scalar integrated quantities
1.4.1 The basics of the CBC dimensional analysis
1.4.2 Validation at large Reynolds numbers for Pr 6= 1
1.4.3 Transition to low Reynolds and Peclet numbers
1.4.4 Transition for Pr 6= 1
1.4.5 Study of the integral scales L and LT
1.5 Conclusions for a passive scalar eld in HIT
2 Spectral Modelling of the Velocity Field in Homogeneous Turbulence
2.1 Equations in physical space
2.2 Spectral equations and transfers
2.2.1 Craya equation for ^Rij
2.2.2 Craya-Herring frame – E Z decomposition
2.2.3 Generalized Lin equations
2.3 The closure problem
2.3.1 The EDQNM approximation
2.3.2 Directional and Polarization transfers TE and TZ
2.4 Spherically-averaged equations
2.4.1 Spherically-averaged descriptors
2.4.2 Spherically-averaged nal Lin equations
2.4.3 Return to isotropy – Spectral tensor
3 Dynamics of the Velocity Field in Shear-driven Turbulence
3.1 Homogeneous Shear-Released Turbulence (HSRT)
3.1.1 Validation of HSRT with Rapid Distortion Theory
3.1.2 Kinetic energy spectrum E(k; t) and spectral tensor ij(k; t)
3.1.3 Anisotropy descriptors bij(t) and H() ij (k; t)
3.1.4 Modelling of the pressure-strain tensor (s)
3.1.5 Additional remarks on HSRT
3.2 Decay of K(t) and R13(t) in Saman and Batchelor HSRT
3.3 Homogeneous Shear Turbulence
3.3.1 Exponential growth of the kinetic energy K(t)
3.3.2 Non-linear transfers and the shear wavenumber
3.3.3 Discussion on the scattering of integrated quantities in HST
3.4 Conclusion and perspectives
3.4.1 Conclusions on HST and HSRT
3.4.2 Exponential growth rate
3.4.3 Perspectives
II Transport and Mixing in Homogeneous Anisotropic Turbulence
4 Spectral Modelling of a Passive Scalar in Homogeneous Turbulence
4.1 Scalar and scalar ux generalized Lin equations
4.2 EDQNM closure for ET and Fi
4.3 Final spherically-averaged scalar Lin equations
4.3.1 Modelling of ET and Fi
4.3.2 Spherical average of the passive scalar and scalar ux
4.4 Cospectrum for an uniform mean scalar gradient
5 Dynamics of a Passive Scalar in Homogeneous Turbulence
5.1 Homogeneous shear-driven turbulence
5.1.1 Scalar spectrum ET (k; t) and non-linear transfers
5.1.2 Scalar decay laws and RTI in HSRT
5.1.3 Sustained shear (HST)
5.1.4 Decay and growth laws for the passive scalar in HSRT and HST
5.2 Isotropic Turbulence with a mean Scalar Gradient
5.2.1 Spectra and transfers
5.2.2 Comparisons with experimental and numerical results
5.2.3 Decay and growth laws for the cospectrum and passive scalar
5.2.4 Return to isotropy in HITSG
5.3 Homogeneous Shear Turbulence with Scalar Gradient
5.3.1 Denitions and transfers
5.3.2 Comparisons with experimental and numerical results
5.3.3 Growth of K, KT , KF and KSF
5.3.4 Streamwise ux spectrum FS(k; t)
5.3.5 Return to isotropy in HSTSG
5.4 Conclusions for the passive scalar at Pr = 1
6 Prandtl Number Eects on Passive Scalar Dynamics
6.1 Prandtl number eects in HITSG
6.1.1 Inertial scalings for ET (k; t) and F(k; t) – Comparisons
6.1.1.1 Highly diusive passive scalar Pr 1
6.1.1.2 Weakly diusive passive scalar Pr 1
6.1.1.3 Spectral transfers and conclusions for the inertial scalings
6.1.2 Numerical results – Time evolution and anisotropy
6.1.2.1 Prandtl eects on the decay and growth of < u3 > and < 2 >
6.1.2.2 Cospectrum correlation w, pressure-scalar correlation F, and Nusselt number Nu
6.1.2.3 Return to isotropy of small scales
6.1.3 Conclusions for Pr 6= 1 in HITSG
6.2 Prandtl number eects in shear-driven turbulence
6.2.1 Homogeneous shear-released turbulence
6.2.2 Sustained shear ow
6.2.3 Homogeneous Shear Turbulence with a mean Scalar Gradient
6.2.4 Conclusions about shear-driven turbulence for Pr 6= 1
7 Spectral Modelling for Unstably Stratied Homogeneous Turbulence
7.1 Evolution equations in USHT
7.1.1 Additional coupling terms
7.1.2 Spherically-averaged Lin equations for USHT
7.2 Spectral scaling and infrared dynamics
7.2.1 Spectral scaling of E, ET and F
7.2.2 Infrared dynamics
7.3 One-point statistics
7.3.1 The Froude number Fr
7.3.2 The mixing intensity
7.3.3 Growth of the kinetic energy K(t)
7.3.4 Global anisotropy
7.3.5 Comparison with Burlot et al. (2015b)
7.3.6 Conclusions on one-point statistics
7.3.7 Eddy-damping constants
7.4 Scale by scale anisotropy and structure of the ow
7.5 Pressure spectra and high Schmidt numbers
7.5.1 Pressure spectra
7.5.2 Cospectrum at high Schmidt numbers
7.6 Conclusion on USHT
7.7 Perspective – Variable stratication N(t)
7.7.1 Evolution equations with variable stratication
7.7.2 Prediction of the growth rate RT
7.7.3 Numerical results
8 Dynamics of Helicity in Skew-Isotropic Turbulence
8.1 Spectral modelling of helicity
8.1.1 The E-H decomposition
8.1.2 Spherically-averaged helical Lin equations for E(k; t) and H(k; t)
8.2 Numerical results on the helical and kinetic elds
8.2.1 The importance of initial conditions H(k; t = 0)
8.2.2 Helical spectrum H(k; t) and non-linear transfers
8.2.3 Infrared dynamics and non-local transfers
8.2.4 Decay laws in helical ows
8.2.5 Robustness of the decay exponents – Altered infrared dynamics
8.3 Structure functions in helical turbulence
8.3.1 Inertial scaling for S(r) and D(uu!)(r)
8.3.2 Evolution equation of H
8.4 Eect of helicity on the scalar ux
8.4.1 Modelling of the quadrature spectrum
8.4.2 Decay of < !3 > and inertial scaling of Q(k; t)
8.5 Conclusion on homogeneous skew-isotropic turbulence
9 General Conclusions and Perspectives
A Statistics and Structure Functions
A.1 Evolution equations and denitions
A.2 Tensorial relations for homogeneous turbulence
A.2.1 Dissipation and enstrophy < !2 >
A.2.2 Identities for the velocity eld
A.2.3 Evolution equations of Wij and < !2 >
A.2.4 Evolution equation of ij
A.2.5 Evolution equations of < ij > and < 2 >
A.2.6 Cospectrum in isotropic turbulence with mean scalar gradient
A.3 Homogeneous isotropic turbulence
A.3.1 Spectral formalism
A.3.2 Second and third-order statistics
A.3.3 Results for the velocity eld
A.3.4 Results for the passive scalar eld
A.4 Structure functions and auto-correlations
A.4.1 Second-order longitudinal correlation and structure function
A.4.2 Third-order longitudinal correlation and structure function
A.4.3 Towards the Karman-Howarth equation
A.4.4 Yaglom and Corrsin equations
B Non-local Expansions of the Non-Linear Transfers
B.1 Non-local uxes
B.2 Expansions for q k p
B.3 Expansions for k p q
B.4 Applications of the isotropic non-local transfers
C Details on the Spherically-Averaged Lin Equations
C.1 Spectral evolution equations
C.1.1 Craya equation
C.1.2 Generalized Lin equations for E and Z
C.1.3 Evolution equation of Sijk(k; p; t)
C.2 Calculations of TE and TZ
C.2.1 Relations between frameworks
C.2.2 Computation of TQN
C.3 Spherically-averaged non-linear transfers
C.3.1 -integration
C.3.2 Spherical integration
C.4 Spherically-averaged linear transfers
C.4.1 Spherical integration
C.4.2 Computation of TL
C.4.3 Return to isotropy
C.4.4 Rotation
C.5 Kinetic quadratic anisotropic contributions
C.6 Fourth-order expansion for E and Z
C.6.1 Fourth order linear transfers
C.6.2 Fourth order non-linear transfers
C.6.3 Fourth-order nal spherically-averaged equations
D Additional Results for the Velocity Field in Homogeneous Turbulence
D.1 Rapid Distortion Theory
D.2 Homogeneous Axisymmetric Turbulence
D.3 Homogeneous Plane Distortion
D.4 Pressure uctuations in HAT
D.4.1 Evolution equation of the pressure correlation EP
D.4.2 Spectrum and pressure variance
D.5 Details on helical turbulence
D.5.1 Non-linear helical transfer TH
D.5.2 Non-linear purely helical transfer
D.5.3 Details on the evolution equation of H
D.5.4 Re-interpretation of the helical viscous cuto kH
E Details on Spherically-Averaged Scalar Lin Equations
E.1 Scalar-scalar correlation
E.1.1 Scalar Craya equation
E.1.2 EDQNM closure for ET
E.1.3 Spherically-averaged scalar Lin equations
E.1.4 Scalar quadratic anisotropic contributions
E.2 Scalar-velocity correlation F
E.2.1 Craya equation for the cospectrum
E.2.2 Quasi-normal approximation for Fi
E.2.3 Computation of the non-linear transfers of Fi
E.2.4 Spherically-averaged cospectrum Lin equations
E.2.5 Alternative modelling for F
E.2.6 Scalarux quadratic anisotropic contributions
E.2.7 Scalarux in HHTSG
Bibliography
