Kapitel 5.1 Wake Vortex Behaviour Modelling

Abstract

Wake vortex behaviour modelling is the technology relating to the operational (thus necessarily simplified) modelling of aircraft wake vortex behaviour: the transport and the decay of the port and starboard vortices of the two-vortex system formed after complete rollup of the wake behind an aircraft. Those vortices are influenced by various parameters: the characteristics (weight, span, flight speed, attitude, span loading) of the aircraft that generates them, the local meteorological conditions (cross wind and head wind, wind shear, turbulence, stratification) in which they then evolve, and the ground proximity conditions which also affects their transport and decay. Depending on application, operational refers to such software tools being useable for off-line studies or for real-time systems. The operational models developed are physics-based (hence they are also called “physical models”) and aim at predicting the behaviour of the wake vortices in one plane crossing the flight path. The models are expressed, typically, as ordinary differential equations (ODE; with added stochastic components in some cases), and that are integrated in time. Some models also take into account the uncertainty/variability of the impact parameters: they are then denoted probabilistic. Operational wake vortex models are still being further developed and used essentially in Europe and in the USA. Two platforms have also been developed that use the European models in several gates to rebuild the 3-D wake generated by an aircraft evolving in given meteorological conditions, also enabling analyses relating to potential wake vortex encounter. For some applications, wake vortex behaviour modelling also refers to modelling the expected topology of the wake vortices (e.g., amplitude of the Crow instability development, topology of the vortex rings formed after reconnection and their decay). Also the use of velocity field databases in flight simulators, obtained from very detailed large-eddy simulations (LES) of wake vortices in specific conditions, can be considered as some kind of “operational modelling”. As such databases can be very large (e.g., 1 GB for one 3-D velocity field at one time), they must be reduced to a smaller set for real-time access in the flight simulator. In some cases (e.g., Crow instability in weak atmospheric turbulence and without or weak stratification), the database itself can be reduced to a simplified mathematical model which fits properly the main vortex 3-D topology; the model can then, in turn, be used to feed the flight simulator with velocity fields computed using an efficient Biot-Savart evaluation. Finally, this section also describes recent developments achieved with LES and the analysis of field measurement data.