# Airplane Vortices Evolution Near Ground
## 1 Introduction  
The study of the vortex wake evolution generated by an airplane in ground proximity is a very interesting field in airport management, as it could be used in order to optimize the time between two consecutive airplanes during take-off or landing, hence increasing the airport traffic and throughput. The time between two consecutive airplanes needs to be large enough to avoid wake interaction between the previous airplane and the following one; otherwise the risk of having a crash rises. It is particularly interesting to employ potential flow theory to evaluate vortices' evolution; then the computational time required to perform the calculations is very low and therefore the calculations could be done in situ, which may be convenient for safety requirements. For example, if the simulation is desired to be done using Computational Fluid Dynamics (CFD), the computational time would be extremely high due to the large mesh needed to cover the extensive domain. In any case it needs to be kept in mind that the main problem with the use of potential flow theory is that it does not take into account the effect of fluid viscosity, and thus there is no dissipation of the vortex and its temporary behavior may not be fully precise. In the present paper this problem is minimized thanks to the use of time-dependent circulation. Nowadays, the situation is the following. The regulation of the time between airplanes is established by the International Civil Aviation Organization (ICAO) and divides the different airplanes into four categories depending on their weight ([PERSON] et al. [1]). The time between two consecutive airplanes needs to be large enough to secure that thereis no possible effect of the previous airplane vortex wake on the following one. The calculation of this time is based on empirical data obtained from a wide range of historical measurements. This categorization has a big safety factor, so it appears that a better knowledge of the vortical structures and their evolution would lead to a time reduction. Another weakness of the method used nowadays is the uncertainties when a new airplane model is incorporated, since there are no empirical measurements available. For example, due to the appearance of big airplanes (such as the A380-800) the categorization rules had to be modified. However, to optimize the procedures a solid and fast method to calculate the characteristics of the vortices is needed, as they can vary either as a function of the atmospheric pressure or the crosswind, among other parameters. To better understand the actual situation of the research it is interesting to consider the work done by [2], which focuses on the dynamic behavior of the vortical structures produced by airplanes during touchdown, providing valuable information regarding the different instabilities and the vortex decay process. As will be seen later, the understanding of this process is used, in some studies ([PERSON] et al. [3] and [PERSON] et al. [4]), to reduce the mentioned instabilities and force a faster propagation of the vortices. The main method being used in several references [3; 5; 6; 7; 8] is the measurement of the vortex wake's characteristics through a Doppler LIDAR system, as explained in [PERSON] et al. [9]. There are some studies (see [PERSON] et al. [6]) where this method is used taking into account the ground effect, with the aim of increasing the precision of the results. Nevertheless, regardless of the method employed, the results are subjected to the intrinsic errors of the Doppler LIDAR radar measurements. The implementation of this experimentally-based methodology requires some simplifications to reduce the number of variables as well as the computational time. The different errors generated at each step of the process build up, providing a bigger final error, even though it is usually considered as acceptable.