PRELIMINARY ANALYSIS OF SMALL-SCALE TURBULENCE AT THE INSIGHT LANDING SITE ON MARS.
M. Alfahim, School of Engineering and Materials Science, Queen Mary University of London, UK., National Space
Science and Technology Center, United Arab Emirates University, Al Ain, United Arab Emirates., M. Alhmoudi,
Department of Mathematics & National Space Science and Technology Center, United Arab Emirates University, Al
Ain, United Arab Emirates., M. Alawadhi, R. M. B. Young, Department of Physics & National Space Science and
Technology Center, United Arab Emirates University, Al Ain, United Arab Emirates (roland.young@uaeu.ac.ae).

Introduction
NASA’s InSight lander is the first seismology station sent
to Mars, where it has been studying the interior structure
of the planet since November 2018. To interpret possible
“marsquakes” and other observations correctly, it carries
a weather station that measures pressure (PS) and nearsurface winds (TWINS) at high frequency (Banfield et al.
2020). One aspect of Martian meteorology that is poorly
understood is small-scale turbulence. By observing at
such high frequency, Insight provides a unique dataset
that can be used to study Mars small-scale turbulence.
We have used InSight wind and surface pressure
measurements to study atmospheric turbulence around
the lander. In particular, the turbulent structure functions quantify correlations in wind speed and direction
between different locations. These can reveal information about the type of turbulence that occurs in the Martian atmosphere, such as the kinetic energy cascade rate,
the direction of energy transfer as a function of length
scale, and (under suitable assumptions) the kinetic energy spectrum.
This type of analysis ideally requires a network or
grid of weather stations but it turns out that, when the average wind speed is faster than typical turbulent motions,
we can estimate the structure functions from a single
measurement using the “frozen turbulence” hypothesis
(Taylor, 1938; Byrne & Zhang, 2013). Therefore it is
possible in principle to measure these structure functions
using the InSight wind and pressure observations.

Fig. 1. Wind speeds during sol 19. Blue dots are individ-

ual observations, red and purple are the running mean
and standard deviation over a 130s window, and orange
dots are individual deviations from the running mean.

Velocity structure functions
We focused on observations from sol 19 of the mission,
after Banfield et al. (2020). The sol 19 wind observations are well suited to this analysis, particularly during
the nighttime, when the ratio between the kinetic energy
of the mean flow and the kinetic energy of the eddies is
large, which is a requirement for the frozen turbulence
hypothesis to apply (Fig. 1).
We computed the second- and third- order structure
functions during sol 19 between 0200-0500 and 10001500 local mean solar time (Fig. 2).

Preliminary third order longitudinal structure
functions computed for InSight sol 19 for 2–5 AM
LMST (top) and 10 AM – 3 PM LMST (bottom). Note
the different values of  in the fitting function.
Fig. 2.

The third order structure functions showed a reasonable
fit to a linear fitting function hδu3L i ∝ r, but with a
sign for  indicative of upscale energy transfer, which
was quite surprising. Further work is required to ascertain whether this is real, in particular by averaging over
many different sols. The energy injection rate  was significantly larger during the daytime than the nighttime,
consistent with our understanding of Mars’ boundary
layer.

as systematically examining how they vary at different
times of day and year.

Pressure structure functions
Pressure structure functions focused on the later sol 186,
which falls within a long unbroken period of pressure
observations at 10 Hz. The 2nd order pressure structure
function is Π(r) ∝ ρ2 4/3 r4/3 for isotropic, homogeneous turbulence. Figure 3 shows the measured 2nd
order pressure structure function for a short period during sol 186. The pressure time series is sampled at 10
Hz, while the wind speeds are measured at 1 Hz, so
there is less noise in the pressure structure function than
in the wind structure function. There is a small range
where the slope is close to r4/3 , around 100m separation,
but the fit is not yet convincing, and further analysis of
other times of day and other sols is needed to build up
adequate statistics.
Conclusion
Preliminary analysis of Insight wind and pressure observations under the frozen turbulence hypothesis have
been presented. Further work is required to investigate
how these functions vary over different sols, as well

Fig. 3. Preliminary 2nd order pressure structure function

during sol 186. Blue shows the structure function and
black a line with slope r4/3 .
References
D. Banfield et al. (2020), Nat. Geosci., 13, 190–198.
D. Byrne & J. A. Zhang (2013), GRL, 40, 1439–1142.
G. I. Taylor (1938), PRSLA, 164, 476–490.

Acknowledgments
M. Alfahim’s contribution to this work was made possible by the Emirates Mars Mission Research Experience
for Undergraduates program.