Modélisation des machines électriques en vue du contrôle des efforts radiaux

Sommaire

List of abbreviations vi
List of symbols vi
Chapter I General introduction . 1
1. Context . 1
2. Water and crop yield 2
3. Modelling soil-plant hydrodynamics and plant water stress 3
4. Property emergence and organisation level . 5
5. Elemental laws and properties of the modelled system . 7
6. General objectives and thesis outline . 11
Chapter II A simple three-dimensional macroscopic root water
uptake model based on the hydraulic architecture approach. 15
1. Abstract 15
2. Introduction 16
3. Theory 19
3.1 Shape of the simplified root hydraulics model 21
3.2 Expression for compensatory root water uptake 22
3.3 Water stress function . 24
3.4 Expression of the simple root system hydraulics model at the soil
element scale . 26
4. Methodology 29
4.1 Description of the complex maize root system and of the simulation
domain 30
4.2 Existence and properties of the macroscopic parameters for the complex
root system 32
4.3 Validation of the macroscopic model 34
5. Results 35
5.1 Existence and properties of macroscopic para-meters for the complex
hydraulic architecture 35
5.2 Validation of the macroscopic model 41
6. Discussion 44
6.1 Shape of the macroscopic root water uptake model 44
6.2 Shape of the macroscopic water stress function 45
6.3 Emerging macroscopic parameters 46
6.4 The soil equivalent water potential sensed by plants . 48
6.5 Accuracy of the macroscopic model 49
6.6 Mathematical evidence of plant strategies against water stress . 50
7. Conclusions and outlook 51
8. Appendices 53
Appendix A: Analytical solutions of the radial water flow rates, of the
compensatory uptake rates and of the water stress equation in the simple
hydraulic architecture . 53
Chapter III Horizontal soil water potential heterogeneity: Simplifying
approaches for crop water dynamics models . 57
1. Abstract 57
2. Introduction 58
3. Theory 61
3.1 Equations for three-dimensional explicit water flow simulation . 61
3.2 Upscaling of water flow parameters and state variables 64
3.3 Simplifying assumptions for horizontal soil water flow 68
4. Methodology 71
4.1 Scenarios description . 71
4.2 Testing the simplifying approaches . 76
5. Results and discussion . 81
5.1 First conjecture: homogeneous soil water potential in upscaled soil
elements 81
5.2 Second conjecture: solution for implicitly hete-rogeneous soil water
potential in 1-D soil layers 92
6. Conclusions and outlook 98
7. Appendices 100
Appendix A: Definition of soil water flow divergence necessary to keep
soil water potential homogeneous during root water uptake in upscaled
soil elements . 100
Appendix B: Theoretical equation for the geometrical parameter ρg for
regular root distribution in a soil layer . 102
Chapter IV Impact of dynamic root hydraulic properties on plant
water availability under water stress 103
1. Abstract 103
2. Introduction 104
3. Theory 107
3.1 The dynamics of plant water availability . 107
3.2 Empirical and mechanistic approaches to plant water stress . 108
4. Methodology 113
4.1 Root system properties 114
4.2 Scenario description 117
5. Results and discussion . 118
5.1 Dynamics of plant actual transpiration and water potential . 118
5.2 Dynamics of macroscopic hydraulic parameters . 123
5.3 Water use envelopes 128
6. Conclusions and outlook 129
Chapter V Exact macroscopic solutions of water flow equations in
root hydraulic architectures. 133
1. Abstract 133
2. Introduction 134
3. Existing approaches of water flow dyna-mics modelling in root
system hydraulic architectures . 136
3.1 Doussan hydraulic architecture approach 136
3.2 Macroscopic hydraulic architecture simplified approach 140
4. Development of an exact macroscopic solu-tion of water flow in
hydraulic architec-tures 143
4.1 Basic equations development 143
4.2 Macroscopic hydraulic parameters properties . 145
5. Transversal comparison of approaches based on the hydraulic
architecture . 147
5.1 Doussan and exact macroscopic parameters 147
5.2 Exact and simplified macroscopic solutions: an adjusted definition of
compensatory root water uptake . 151
5.3 Dynamic parameterisation of simplified macro-scopic parameters . 155
6. Conclusions and outlook 157
7. Appendices 160
Appendix A: Description of the IM matrix 160
Appendix B: Doussan compact expressions for local root water uptake
rates under both boundary condition types . 161
Appendix C: The system of water flow equations in a hydraulic
architecture accepts only one solution 162
Appendix D: Transversal comparison of macroscopic para-meters with
Doussan matrix, from flux-type boundary condition solutions 163
Appendix E: The scalar product of diag(Krs) and SUF is symmetric:
demonstration . 163
Appendix F: Compact exact macroscopic solution of water flow for fluxtype
boundary conditions, and relation with Doussan solution using the C
matrix 164
Chapter VI General conclusion 167
1. Understanding plant root water uptake 167
2. Computing plant root water uptake . 170
3. Perspectives . 172
Bibliography . 175