Influence of tail plan vortices on contrail vortex and dissipation phase

Contrails are ice clouds formed by both the aircraft emissions and the water content of the atmosphere. Under specific atmospheric conditions, contrails can persist for several hours. During this time, these human made clouds perturb the energy balance of the atmosphere. It has been shown in [1] that contrails are the main contribution of non CO₂ radiative forcing due to aviation. There effective radiative forcing is estimated to be about twice the one from the CO₂ emitted by the aircrafts; however, this value remains uncertain.

Contrails climatic impact is usually studied either by a dedicated parametrization in global climate model [2] or using a Gaussian model [3]. In both kinds of model, contrails are initialized once the dynamic of the aircraft can be neglected (about 7.5 min after the aircraft). Therefore, it is important to have the best parametrization of contrails at this stage of contrail’s life. To study contrails up to 7.5 minutes usually two different kinds of simulations are made. The first one covering the contrail formation (known as jet phase), and another one looking at the dissipation of the wing tip vortices (vortex and dissipation phases). Their formation is studied using RANS simulation [4] or with 0D models run on streamlines of a previous LES simulation of a single jet [5]. Then the results are injected in the vortex phase simulation ([6],[7]). When only a jet simulation is used, the wing tip vortices are initialized with two Lamb-Oseen vortices scaled based on the lift of the aircraft. However, a recent study [8] has shown some differences in terms of dilution between a simulation initialized based on a RANS solution and the analytical solution. This has be explained by 4 vortex instabilities which triggers shorter waves than the so called crow instabilities [9] as shown in [10].

In this study, we test the influence of the tail plan vortices on contrails characteristics assuming different tail plan vortices strength in order to see the dependency of the aircraft equilibrium on contrail.

[1] Lee et al. (2021). The contribution of global aviation to anthropogenic climate forcing for 2000 to 2018. Atmospheric environment

[2] Burkhardt et al. (2010). Global modeling of the contrail and contrail cirrus climate impact. Bulletin of the American Meteorological Society

[3] Schumann  (2012). A contrail cirrus prediction model. Geoscientific Model Development

[4] Khou et al. (2015). Spatial simulation of contrail formation in near-field of commercial aircraft. Journal of Aircraft

[5] Bier et al. (2022). Box model trajectory studies of contrail formation using a particle-based cloud microphysics scheme. Atmospheric Chemistry and Physics

[6] Paoli et al. (2013). Effects of jet/vortex interaction on contrail formation in supersaturated conditions. Physics of Fluids

[7] Unterstrasser et al. (2014). Dimension of aircraft exhaust plumes at cruise conditions: effect of wake vortices. Atmospheric Chemistry and Physics

[8] Bouhafid et al. (2024). Combined Reynolds-averaged Navier-Stokes/Large-Eddy Simulations for an aircraft wake until dissipation regime. Aerospace Science and Technology

[9] Crow (1970). Stability theory for a pair of trailing vortices. AIAA journal

[10] Fabre et al. (2000). Stability of a four-vortex aircraft wake model. Physics of Fluids,