The purpose of this study is
to investigate the interaction between small-scale turbulence and aerosol and
cloud microphysical properties using direct numerical simulations (DNS). We
consider the domain located at the height of about 2000 m from the sea
level, experiencing transient high supersaturation due to atmospheric
fluctuations of temperature and humidity. To study the effect of total number
of particles (

Interaction of atmospheric turbulence with aerosol and cloud formation
processes has been studied extensively. Due to non-linearity of particle
formation and other aerosol dynamical processes, the fluctuations of
temperature and relative humidity can have strong effect on aerosol
formation. Large-scale fluctuations of atmospheric properties, which occur
for example in the atmospheric boundary layer, can drive the
initiation of particle formation

In-cloud turbulence has been shown to intensify cloud-microphysical
processes, determining cloud properties

The large-scale atmospheric turbulence is well known to affect aerosol processes significantly. In turn, aerosol properties may influence the buoyancy and turbulence. A motivation for a potential aerosol–turbulence interaction is that the most advanced cloud-microphysical models can now resolve the cloud edges where mixing occurs and where spatial gradients are great in turbulence and concentrations of hydrometeors, including aerosols. Consequently, by including a more complete set of such interactions in the models, the simulation of aerosols, turbulence and microphysics may be improved.

The main goal of this direct numerical simulation (DNS) study is to investigate
the interaction between small-scale turbulence and aerosol and cloud microphysical properties.
The chosen DNS domain is realistic for a small volume at the cloud edge, where turbulent mixing
is a dominate feature

We use a high-order public-domain
finite-difference code, Pencil Code, for compressible hydrodynamic flows.
The code is highly modular and comes with a large selection of physics modules.
It is widely documented in the literature

As a starting point for our simulations, we consider values typical for
observations made in trade wind cumuli. During the
CARRIBA (Cloud, Aerosol, Radiation and tuRbulence in the trade wInd regime over Barbados) project (

We assume a soluble aerosol (NaCl), which will dilute inside the droplet. We take
50 size bins, logarithmically distributed in the range [10 nm,
1000

We assume the following air composition O

The summary of key parameters for studying the effect of total
number of particles on air temperature, supersaturation and activation.

This model represents the 3-D fluid flow on the microscale inside a volume of
10 cm

Relative distribution of particles averaged over the domain at

Observed temperature and absolute humidity result in peak value of
supersaturation (

On the other hand, the supersaturation excess would be eliminated by condensation
onto droplets, and quasi-steady-state supersaturation
would be restored

Let us now assume a small eddy of size

Pressure,

To generate the initial turbulent field, we make the first 100 iterations without
evaporation/activation of aerosol particles (further “aerosol dynamics”),
including randomly directed external forces (see next section). After that
the external forces are set to zero, whereas the particles start to evolve.
Thus, the turbulence decays over the analysed time. The maximal time step
allowed by the Courant condition for convergence is

In all three directions we set periodic boundary conditions for all
variables, including the number density function. It means that at every
time step,

The summary of key parameters for studying the effect of aerosol on turbulence.

A detailed description of the main equations is presented by

We consider the evolution of aerosol number density function
because of evaporation/condensation of aerosol particles.
There is energy exchange between particles and ambient gas due to the release/absorption of latent heat caused by
condensation/evaporation on the droplet surface. The motion of the particles is determined exclusively
by their involvement in the motion of surroundings.
In the present study we modify
water vapour pressure over a droplet of radius

For generating the initial turbulence, the external forcing

To study the effect of aerosol on the turbulence we consider two initial
turbulent fields, taking different non-dimensional forcing amplitudes as

Temperature distribution at

Distribution of supersaturation at

In Fig.

Changing temperature distribution with time is mostly attributable to the
periodic boundary conditions: the coldest layers are moving from the bottom
to the middle of the domain. However, comparing panels a, b and c in
Figs.

Additionally, we investigate how fast the system with an initially high value of
supersaturation (

In this study we consider that all particles with radii larger than

Amount of liquid water accumulated in particles with corresponding
radius

Relative number of activated particles as a function of time

Averaged vertical velocity as a function of time with aerosol for

The dependence of the average turbulent kinetic energy on time with
aerosol for

The difference between turbulent kinetic energy averaged over time
period

Initial value of supersaturation averaged over the domain

In addition, in Fig.

The dependence of the

We find that while the total number in case 2 is 10 times smaller than in
case 3, liquid water content is similar in these two cases. On the other
hand, LWC appears to be smaller in case 1 than in cases 2, 3 (see
Table

We analyse the effect of aerosol on the turbulent motion, taking

We find that the vertical motion of air is accelerated because of aerosol
dynamics. Also, in Fig.

Also, we find that acceleration does not depend on intensity of turbulent
fluctuations; i.e. acceleration in vertical direction is the same in
low intensive turbulence and in high intensive turbulence
cases. Moreover, turbulent fluctuations grow because of presence of aerosol
particles in all four considered cases. The dependences of vertical velocity
and turbulent kinetic energy (TKE) averaged over the domain as a function of
time for non-equilibrium case with low intensive turbulence
are presented in Figs.

Finally, we find that there is a strong variation of TKE with time (see
Fig.

The dependence of count mean diameter (CMD) on time for case 1 (green solid curve), case 2 (red solid curve), case 3 (black solid curve), case 4 (black dashed curve).

The dependence of supersaturation averaged over the calculation
domain on time for case 1 (green solid curve), case 2 (red solid curve), case 3 (black solid curve), case 4 (black dashed curve). Horizontal lines show the corresponding values of

To illustrate the effect of initial supersaturation on activation of aerosol
particles we modify the initial distribution of absolute humidity in case 3,
decreasing it by 10 %. In that case the initial supersaturation averaged
over the domain becomes 0.6 %. To study the effect of initial supersaturation
on the activation of aerosol particles in Fig.

Additionally, in Fig.

Turbulence, aerosol growth and microphysics of hydrometeors in clouds are intimately coupled. In the present study a new modelling approach was applied so as to quantify this link. We study the interaction in the cloud area under transient, high supersaturation conditions, using direct numerical simulations. As the initial conditions, we take observational data. To analyse the effect of aerosol and droplets on turbulence, a small volume with supersaturation of 10 % was considered. Under such extreme conditions, condensation is the dominant process. The results cannot be linearly extended to bigger cloud volumes but should be considered relevant for a small cloud parcel with extreme supersaturation due to turbulent mixing of the water vapour and temperature field. As an initial distribution of particles, we take the data of measurements at the sea level and analyse the droplets activated by aerosols in the simulations.

To study the effect of total number of particles on activation, air
temperature and supersaturation, we vary the total number of particles and
take the other parameters which correspond to low intensive turbulence
and non-equilibrium case, i.e. when the vertical motion is generated
within domain because of buoyancy. We compare the results of simulations with
particles and without them. We find that the total number of particles in the
domain is crucial for the distribution of temperature and for developing
turbulence. Even small amounts of aerosol particles (55.5 cm

To analyse the effect of aerosol dynamics on the turbulent kinetic energy and
on vertical velocity, we take the maximal value of

The description of data from CARRIBA project has been published in

We thank the Helsinki University Centre for Environment (HENVI) and computational resources from CSC – IT Center for Science Ltd are all gratefully acknowledged. This research is supported by the Academy of Finland Center of Excellence program (project number 272041). Anthropogenic emissions on Clouds and Climate: towards a Holistic UnderStanding (BACCHUS), project no. 603445. Edited by: S. M. Noe