In this work, the evolution of contrails in the vortex and dissipation regimes is studied by means of fully three-dimensional large-eddy simulation (LES) coupled to a Lagrangian particle tracking method to treat the ice phase. In this paper, fine-scale atmospheric turbulence is generated and sustained by means of a stochastic forcing that mimics the properties of stably stratified turbulent flows as those occurring in the upper troposphere and lower stratosphere. The initial flow field is composed of the turbulent background flow and a wake flow obtained from separate LES of the jet regime. Atmospheric turbulence is the main driver of the wake instability and the structure of the resulting wake is sensitive to the intensity of the perturbations, primarily in the vertical direction. A stronger turbulence accelerates the onset of the instability, which results in shorter contrail descent and more effective mixing in the interior of the plume. However, the self-induced turbulence that is produced in the wake after the vortex breakup dominates over background turbulence until the end of the vortex regime and controls the mixing with ambient air. This results in mean microphysical characteristics such as ice mass and optical depth that are slightly affected by the intensity of atmospheric turbulence. However, the background humidity and temperature have a first-order effect on the survival of ice crystals and particle size distribution, which is in line with recent studies.

Aircraft-induced cloudiness in the form of condensation trails
(contrails) and contrail cirrus is among the most uncertain
contributors to the Earth radiative forcing from aviation

According to the classification given by

From a computational perspective, the vortex regime is particularly
challenging because of the intricate transformations that occur
in the wake and changes in the flow topology, which manifest as abrupt
expansions of the contrail in both horizontal and vertical directions

The dynamics of aircraft wake vortices have been studied traditionally in the
wake vortex community for wake hazard applications. (The reader is invited to
consult the reviews by

An aspect that has not been fully investigated so far is the role of
atmospheric turbulence in determining the three-dimensional structure of
contrails and the ice microphysical properties. For example, it is likely
that turbulence enhances the mixing of ice crystals with atmospheric water
vapor, especially in the secondary wake, and it influences the detrainment of
exhausts at the vortex boundaries. In addition, vortex instabilities such as
Crow instability

This work is part of a larger project that aims at evaluating the
atmospheric impact of contrail cirrus using a systematic chain of
models and LES computations that cover the contrail lifetime from the
formation to its demise in the atmosphere. While this strategy is
similar to that employed recently by other authors who explored a
large set of parameter space

Although full unsteady spatial simulations of wake formation including the
exhaust jets would help understanding the details of ice nucleation in
rapidly changing thermodynamic conditions, they have not been performed so
far as they would require far higher resolution and computational resources
that are hardly available on present supercomputers. Hence, for the present
study, the initial wake-flow field was reconstructed using data from temporal
LES of the jet regime at a wake age of

The paper is organized as follows: Sect.

The computational model used in this work is based on an Eulerian–Lagrangian
approach: the large-scale eddies of the gaseous atmosphere are solved with
compressible Navier–Stokes equations, while ice crystals are treated by a
Lagrangian tracking method and mass transfer between the two phases. As this
model has already been presented elsewhere

Equation (

The model uses a Lagrangian approach to track the trajectories of
particles: ice crystals and nucleation sites (soot particles emitted
by engines in the present study) onto which ice forms by deposition of
water vapor. Given the large soot emission index EI

The mass of vapor removed through deposition is

To close the problem, a model for the deposition rate

Vertical cross sections of the computational domain and
along the contrail longitudinal axis (left panel) and transverse axis (right panel).
The mesh is regular in the subdomain

Vertical (left) and horizontal (right) cross sections of
potential temperature difference

Reference values common to all cases. Aircraft data refer to a B747 (4-engines) aircraft. Exhaust jet values are expressed in meter of flight.

We included the Kelvin effect in Eq. (

The numerical simulations are based on a temporal approach, which is commonly
used in the large-eddy simulation (LES) of wake vortex systems. The
computational domain is a box of lengths

The background atmosphere is representative of an upper troposphere
lower stratosphere region, i.e., stably stratified. The background
thermodynamic variables

Table of simulations. The parameter

The initial turbulent fields for the present simulations were
extracted from the larger computational domain as shown by the black
box in Fig.

Summary of main contrail characteristics: lifespan

Top views of iso-contours

The initial wake of the aircraft is reconstructed using data from simulations
of the jet regime at a wake age of

At this wake age all particles are already activated.
In order to characterize the interaction between background turbulence
and vortex dynamics, it is useful to introduce the relative turbulence
intensity

The effective Reynolds number based on circulation

The simulations have been organized as follows: the reference simulation,
labeled case 2, is based on a supersaturated atmosphere at

Wake vortices are detected using the

Iso-contours

Time histories of vortex length ratios

In order to measure the lifespan of wake vortices, their intensities are
evaluated as a function of time: the minimum value of

Lifespans of wake vortices as a function of relative turbulence
intensity. The solid line is the analytical estimation by

Non-dimensional maximum descent

In order to evaluate the vertical displacement of the wake vortices, vertical
profiles

Vertical profiles of

Snapshots of ice crystals spatial distribution for cases 1,
2, and 3. Crystals are colored with diameters. The figure shows
the development of the secondary wake at

Vertical profiles of normalized number

As explained in Sect.

Normalized contrail volume per unit flight distance. Note the increased mixing following the vortex breakup where the exhaust material is released into the atmosphere.

Contrail diffusion is analyzed in Fig.

Ice mass per unit flight distance normalized by the mass of
emitted water vapor.
Adiabatic compression reduces

Vertical profiles of normalized mass

Figure

At the beginning of the vortex regime, the emitted water vapor

The vertical structure of the contrail is further analyzed in
Fig.

Normalized number of activated particles (fraction of surviving
crystals). Adiabatic compression is
strong enough in weakly supersaturated atmosphere (case 4) to
completely sublimate

The number of particles surviving the adiabatic compression is
an important parameter to consider when evaluating the global and climate impact
of contrail

Figure

Ratio of deposed mass. In the vortex regime, the contrail
is close to equilibrium (

It is interesting to evaluate the mass of ice that would be formed by
a model that would enforce equilibrium between ice and vapor phase at
each time step. This kind of models may be attractive as they are less
computationally expensive. The equilibrium ice mass

Mean saturation ratio computed as an ensemble average over all ice particles. The contrails is slightly subsaturated during the initial vortex descent between 1 and 2 min and supersaturated in the dissipation phase after 2 min.

Mean optical thickness. The horizontal black line
represent the visibility criterion

The optical thickness of the contrail

In Fig.

Crystal diameter distributions at 5

Figure

Top panel: normalized number of activated particles (fraction of surviving crystals). Bottom panel: mean optical thickness. Plain lines indicates simulations with the Kelvin effect activated.

For the high supersaturated cases,

This study presented the results of three-dimensional large-eddy simulations of contrail evolution in the vortex and dissipation regimes of an aircraft wake immersed in a turbulent atmospheric flow field. The computational model is based on an Eulerian–Lagrangian two-phase flow formulation where clusters of ice crystals are tracked as they move in the wake. The background turbulence and the initial condition for the contrail at the end of the jet regime were both generated from appropriate simulations. The focus of the study is to evaluate the effects of atmospheric turbulence on the wake dynamics and the contrail properties and to compare with the effects of ambient humidity and temperature. The results showed a good agreement with numerical and experimental literature work, in terms of descent and lifespan of wake vortices, overall mass of ice produced, and optical depth. Visual patterns of the primary and secondary wakes, Crow instability, and the formation of “puffs” also resembled qualitatively those found in observational analysis. The agreement of particle diameter distribution was also acceptable given the large data scatter and uncertainty of both ambient conditions and soot particle emissions in the experimental campaigns compared to those considered in the present study.

The main effect of atmospheric turbulence in the vortex regime is to trigger
instabilities in the wake vortices and to accelerate their descent. Stronger
turbulence accelerates the onset of the instability, leading to shorter
contrail descent and more effective mixing in the interior of the plume.
These results are in line with those published in recent wake vortex
literature

The mean contrail properties are in line with recent results obtained by
numerical simulations that explored a larger set of parameter space

Future work includes a sensitivity analysis of contrail characteristics to
the initial number of nucleation sites

In the large domain used to generate the ambient turbulence
(

The subgrid-scale model in this study is based on filtered structure function
by

Horizontal and vertical rms velocities measured in the regular subdomain.

Top panel: evolution of the turbulent-to-molecular viscosity ratio.
The three curves correspond to the minimum (

Financial support from the Direction Général de l'Aviation Civile through the project TC2 (Traînés de Condensation et Climat) is gratefully acknowledged. Computational resources were provided by CINES supercomputing center. The authors wish to thank the two referees for their constructive comments that helped to improve the paper.Edited by: C. Voigt