Dunes are beautiful and also a technological problem.
They appear in deserts, along coasts on the ocean floor
and even on mars
The figure shows Barchan dunes close to Laayounne in
Southern Marocco. You can find more details about our measurements of the form
and the scaling with size in our
published in Geomorphology Vol 36, p.47-62 (2000).
We did some studies of a huge Barchan
close to the beach of Jericoacoara in Brazil measuring
air velocity and sand flux as described in the following
that was published in Geomorphology Vol.1325, p.1-11 (2003).
There the transport mechanism by saltation can be very
violent as seen in the following
With Murilo de Almeida
and Jose Soares Andrade
we simulated the saltation process in a virtual wind channel as
published in Physical Review Letters
Vol.96, 018001 (2006). There we show that only above a certain
wind strength one finds granular transport and that the saturated
sand flux increases quadratically with the extra wind strength.
Using the same technique we also studied what happens under Mars
conditions as published in PNAS Vol.105, 6222 (2008)
finding giant saltation trajectories and a rather low threshold
wind strength to sustain the saturated flux. This paper
found large resonance in the media with a
list of 60 sites
that include journals like
Der Spiegel , National Geographic ,
Science News ,
Ciencia Hoje ,
New Scientist ,
O Povo ,
Folha de Sao Paulo ,
and even a blog was created.
With Marcus Vinicius Carneiro we did a full three dimensional simulation of
the particle trajectories in saltation published in
Physical Review Letters Vol. 107, 098001 (2011) finding that the onset
of saltation exhibits a jump in the sand flux. With the same technique we
discovered that mid-air collisions enhance the flux substantially as
shown in the paper
in Physical Review Letters Vol. 111, 058001 (2013), which was
commented among others in Research Highlights of
Nature, Physics World ,
A striking phenomenon observed during saltation is that the sand
can charge up electrically. This is not easy to understand because all
grains are made of the same material and have about the same size. With
Troy Shinbrot we studied this phenomenon numerically and experimentally
with glass beads and found that polarization at collisions where charge
annihilation only occurs locally at the contact point can explain the
phenomenon as described in a recent paper
which has been commented in
Science News ,
News and Views ,
Online FAPESP and
Wired Science .
With Gerd Sauermann and
Klaus Kroy we developped a model
consisting of three coupled equations for the motion of the
free sand surface under the action of the wind. The model
is described in a
paper in Phys. Rev. Lett. Vol. 88, p. 54301 (2002) and
derived in a
paper published in Phys.Rev. E Vol.64, p.31305 (2001)
and a later
paper published in Phys. Rev. E Vol.66, p.31302 (2002).
At the meeting on dunes in Nouakchott in february of 2001 we
presented the following
contribution that gives a brief review of the model and an
even simpler version of the model is described in an older
paper published in Physica A, Vol 283, p. 24-30 (2000).
The most recent version of our full computer program can be downloaded
One particularly subtle problem is the correct
modelization of the "separation bubble" behind the crest of a dune
inside which the wind is so strongly screened that aeolian
grain transport is virtually suppressed. The shape of this
separation bubble can be obtained on given topographies using
the commercial code FLUENT and in a
paper published in Physica A,
Vol.357, p.44-49 (2005) we present with Soares Andrade,
Eric Parteli and Volker Schatz some results. In a
to the proceedings of Powders and Grains we propose
a closed expression for the size of the separation bubble as
function of the distance between crest and brink.
I also wrote with Pierre Rognon a small
article for the Bulletin of the SFP in french
destined to a broader public. An overview over the mechanisms
of wind-blown sand and derivations of the equations are
also given in my
review which was published in a
book edited by H. Hinrichsen and D. Wolf. I also wrote
chapter on dunes in the Encyclopedia of Nonlinear Science.
You can also download a talk
that I gave in several occasions on the subject.
In the figure to the left we see the result of the
numerical solution of these
equations for a given initial configuration consisting of several
Gaussian heaps resulting after the wind has blown from the same direction
during some time. More detailed numerical studies on Barchans were performed
Veit Schwämmle and are written up in the following
paper published in EPJE Vol.16, p.57-65 (2005).
There exists a minimal size for Barchans below which they are not
stable anymore. This was systematically investigated in a
paper with Eric Parteli and Orencio Duran
published in Phys. Rev. E, Vol.75, 011301 (2007).
Veit Schwämmle we also simulated
transverse dunes as
published in Earth Surface Processes and Landforms, Vol.29, p.769-784
(2004) and found that their evolution from a flat
surface is like a dilatation, i.e. that with time they
increase and separate from each other.
A particularly beautiful realization of transverse dunes are the
in the northeast of Brazil. As seen on the photo
below the dunes in this natural park are separated by lagoons.
Eric Parteli , Veit Schwämmle and Luis Parente Maia
we studied in a field trip during september 2003
these dunes and reproduced the measured profiles with our model
as can be read about in our
paper published in Geomorphology Vol.81, p. 29-42 (2006).
There the transport mechanism by saltation can even
occur on wet sand as seen in the following
movie . The velocity of the dunes can
monitored there also by studying the residual ridges they leave behind
as we did with Noam Levin and Haim Tsoar as
published in Sedimentology Vol.56, p.1623 (2009) where is even became the
cover . In 2006 we went there
again to study quicksand .
When the wind is not constant but periodically switches directions
other shapes of duenes appear like longitudinal or seif dunes. With
Eric Parteli, Orencio Durán and Haim Tsoar we studied this case
as presented in our recent PNAS Vol. 106, 22085
paper in Nature Vol.426, p.619-620 (2003) we
showed with Veit Schwämmle that when a smaller Barchan dune hits
a larger one from the back it can either coalesce completely,
join and eject two babies from the horns (see this
movie ) or exchange so much mass
that finally the one in front escapes and in such a way they behave
like solitary waves as seen in the following
movie . An
article with more details was published with
Orencio Duran in Phys.Rev.E. Vol.72, 021308 (2005).
An entire field of barchan dunes was modelled in a
paper printed in Physica A, Vol.310, 487-500 (2002)
and shown that the field stays confined within
a stripe. With
Eric Parteli we developped a simple one-dimensional model
for a field of transverse dunes with flux between the dunes
which reproduced the selection of a characteristic dune height.
as shown in the
paper printed in Physica A, Vol.327, p.554-562 (2003).
This model has been made more realistic and compared to
the fields in Lençóis Maranhenses
with Jae Hwan Lee in a paper
Int.J.Mod.Phys.C Vol.16, p.1879-1892 (2005).
A beautiful simulation of the genesis
of a dune field using our equations of motion can be seen in a
movie made by
Orencio Duran .
Orencio Duran we extended the model to also include the growth of
vegetation by including a further equation. Vegetation can stop sand motion
but sand motion can also kill vegetation. The two effects therefore
compete against each other. In a paper
published in Physical Review Letters Vol. 97, 188001 (2006) we showed
that vegetation can tranform Barchans into parabolic dunes. In the image on the
left side we see different such parabolic dunes depending on the ratio between
dune velocity and vegetation growth velocity. These shapes compare
very well with aeral photos from
real dunes. We also did a field study of parabolic dunes along the
Northeastern coast of Brazil and compared them to our calculations
as discussed in a paper published in
Geomorphology Vol.102, p.460 (2008).
Our work on vegetation was commented in the
Physics Web and
Plus magazine .
On Mars there are also dunes as the "cockroach" Barchans seen in the image
at right. Some Mars dunes have shapes never seen on Earth. With
Eric Parteli we applied our equations using Mars parameters to
reproduce some of these shapes as described in a
paper published in Physical Review Letters Vol.98, 198001 (2007) and
in more detail in a paper published in Phys.
Rev.E, Vol.76, 041307 (2007). This work was
Physics Web ,
Physics Update ,
and in over 100 other journals and sites like,
in softpedia , in the Dutch
Kennislink , in the
Mars Society , in the Russian magazines
our Texas and
podrobnosti , in
sci.astro.amateur , in
and in the Brazilian
Pesquisa Fapesp and
Funcap Ciencia . See a list
of all the sites which comment this paper. A longer article also appeared in
SIAM News .
We see a "cockroach" Barchan calculated in this way below.
We also studied with
Eric Parteli and
Haim Tsoar dunes under periodically varying wind directions
as for instance linear or seif dunes on Earth and on Mars conditions
as described in an article published in PNAS,
Vol.106, p.22085 (2009) and discussed in
Ciencia Hoje .
My fascination with dunes in fact is quite old. In the picture left
you see me 30 years ago on the highest dune of South America
which is called "El Purpur" and lies in Peru according to the
legend stuck on an ancient Chan-Chan ruin.