Abstract ...................................................... vii
Kurzfassung .................................................... ix
Nomenclature ................................................... xv
1 Introduction ............................................... 1
1.1 Motivation ................................................. 1
1.2 State of the Art ........................................... 3
1.2.1 Separation Standards ................................ 3
1.2.2 Wake vortex alleviation ............................. 4
1.2.3 Wake vortex prediction .............................. 5
1.2.4 Wake vortex detection ............................... 7
1.2.5 Encounter severity analysis ......................... 8
1.2.6 Ensemble forecasts .................................. 9
1.3 Context and Goals of this Thesis .......................... 10
1.4 Overview .................................................. 11
2 Wake Vortex Principles .................................... 13
2.1 Helmholtz Theorems ........................................ 13
2.2 Vortex System of a Wing ................................... 13
2.3 Wake Vortex Properties .................................... 15
2.3.1 Basic quantities ................................... 15
2.3.2 Non-dimensional quantities ......................... 16
2.4 Idealized Two-Dimensional Vortices ........................ 17
2.4.1 Decaying potential vortex .......................... 17
2.4.2 Lamb-Oseen model ................................... 18
2.4.3 Rosenhead-Burnham-Hallock vortex model ............. 18
2.5 Wake Vortex Evolution Stages .............................. 18
2.6 Wake Vortex Formation ..................................... 20
2.6.1 Vortex roll-up ..................................... 20
2.6.2 Vortex merging ..................................... 20
2.7 Wake Vortex Descent ....................................... 21
2.7.1 Out-of-ground effect ............................... 21
2.7.2 In- and near-ground effect ......................... 22
2.8 Wake Vortex Decay ......................................... 23
2.8.1 Out-of-ground effect ............................... 23
2.8.2 In- and near-ground effect ......................... 24
3 Field Measurement Data .................................... 27
3.1 Measurement Equipment ..................................... 27
3.1.1 LiDAR .............................................. 27
3.1.2 Sonic Detection and Ranging (SoDAR), Radio
Acoustic Sounding (RASS) and Ultrasonic
Anemometer (USA) System ............................ 28
3.2 Campaigns ................................................. 28
3.2.1 WakeFRA ............................................ 28
3.2.2 WakeMUC ............................................ 29
3.2.3 WakeOP ............................................. 30
3.2.4 MEM95 .............................................. 30
3.2.5 DFW97 .............................................. 30
3.2.6 DEN03 .............................................. 30
3.3 Distribution of Aircraft and Meteorological Parameters .... 31
4 Wake Vortex Prediction .................................... 33
4.1 Skill Metrics ............................................. 33
4.2 The Fast-Time Models ...................................... 33
4.2.1 Common model features .............................. 33
4.2.2 D2P ................................................ 34
4.2.3 АРА ................................................ 37
4.2.4 TDP ................................................ 39
4.2.5 Necessary adaptions to the model output ............ 39
4.3 Model Evaluation .......................................... 40
4.3.1 Initial conditions ................................. 40
4.3.2 Sensitivity analysis ............................... 41
4.3.3 Performance ........................................ 47
5 Multi-Model Ensemble Methods .............................. 51
5.1 Principles ................................................ 51
5.1.1 Conditions for the MME success ..................... 53
5.1.2 Qualification of the available wake vortex models .. 53
5.1.3 Spread-error correlation ........................... 55
5.2 Best Member Selection ..................................... 56
5.2.1 WakeMUC, WakeFRA, WakeOP ........................... 56
5.2.2 MEM95, DFW97 ....................................... 58
5.2.3 Reasons for absence of expert models ............... 58
5.3 Direct Ensemble Average (DEA) ............................. 60
5.4 Reliability Ensemble Averaging (REA) ...................... 60
5.4.1 Natural variability ................................ 61
5.4.2 Weighting of RB and RD ............................. 65
5.4.3 Potential .......................................... 65
5.5 Bayesian Model Averaging (BMA) ............................ 66
5.5.1 Maximum-likelihood estimation of ensemble
parameters ......................................... 67
5.5.2 Distribution formulation ........................... 70
5.5.3 Temporal development of model uncertainty .......... 71
5.5.4 Potential .......................................... 73
5.6 Monte Carlo Simulation (MCS) .............................. 76
5.7 Lagged Average Forecasting (LAF) .......................... 76
6 Results ................................................... 77
6.1 Evaluation of the LiDAR Wake Vortex Measurements .......... 77
6.1.1 Impact of initial height on descent and decay ...... 77
6.1.2 Impact of wind speed and direction on descent and
decay .............................................. 79
6.1.3 Comparison of the WakeMUC measurements with D2P .... 81
6.2 Assessment of the Ensemble Performance .................... 85
6.2.1 Deterministic Performance .......................... 86
6.2.2 Probabilistic Performance .......................... 95
6.2.3 Spread-error correlation .......................... 100
7 Discussion ............................................... 105
7.1 LiDAR Measurement Evaluation ............................. 105
7.2 Multi-Model Ensemble Wake Vortex Prediction .............. 105
7.2.1 Deterministic benefit of the ensemble approach .... 105
7.2.2 Probabilistic benefit of the ensemble approach .... 107
7.2.3 Skill distribution ................................ 115
7.2.4 Effort and benefit ................................ 116
7.2.5 Concept of operations ............................. 116
8 Conclusion and Outlook ................................... 123
A Appendix ................................................. 127
A.l Model Correlation ........................................ 127
A.2 Model Performance ........................................ 128
A.3 LiDAR Measurement Evaluation ............................. 130
A.4 Rare But Dangerous ....................................... 132
A.5 Extraordinary Measured Landings .......................... 135
A.6 Combined Confidence Areas for Vortex Position ............ 140
Bibliography .................................................. 143
Acknowledgments ............................................... 155
|
