# AiS Challenge Team Interim

Team Number: 079

School Name: Santa Fe High School

Area of Science: Earth Sciences

Project Title: A Study of Fluvial Processes in Desert Geomorphology

Problem Definition:
Our project is to understand and create a model of sand dune formation showing their movement, the periodicity of their movement, and the forces acting on dunes that create and displace them. To start simply, the four major types of dunes are barchan, parabolic, transverse, and longitudinal. Barchans are crescent-shaped dunes that are created when there is only a small amount of sand in an area. The tips of the crescent point downwind. Parabolic dunes are also crescents, but their tips point upwind and are typically held in place by vegetation. Transverse dunes are straight and fairly long and formed perpendicular to the wind direction. Longitudinal dunes are similar but are formed parallel to the wind direction. The rest of the dunes on this planet are highly irregular and fit into more than one of these categories.

We are currently brainstorming forces that may act on a dune and affect its formation. We have started analyzing the most simple and obvious forces, gradually working our way into the more complex ones. Gravity holds a dune on the earth. Wind is the driving force that moves the dune. Saturation, the amount of water in the sand, moderates the effects of gravity and wind. The shape of the grains determines how it interacts with the wind.

Most dunes have a fairly solid, saturated core, and only the very topmost layers of sand are allowed full movement. As wind blows the top layers of sand up and away (to an area unknown at this point), the humidity within the adjacent layers is allowed to evaporate and we have a constantly renewed upper layer of sand that in turn gets blown away. Thus we need to know the humidity in the air and the amount of water in the sand to determine how fast the water in the dune will evaporate.

Within the dune, we need to know what the dune is made of and the dune density. How are the particles in the dune shaped? The shape of the particles affects friction between them and thus affects how the dune is formed. Vegetation also effects dune formation. In parabolic dunes, vegetation in the middle of a dune makes the problem of its creation more complex. The branches and leaves change the wind flow and roots hold parts of the dune down, altering its formation considerably.

Air is the fluid moving the sand. The velocity of the air, and its direction affects the dunes. So does the temperature. If the air gets hot enough to sufficiently reduce its density, the dune just sits. If we are really brave, we will look into not only how the wind affects the shape of the sand, but also how the shape of the sand affects the wind. There is probably a considerable amount of turbulence that occurs, depending on how and where the air hits.

Our purpose is to understand some of the phenomena of deserts. Through this, we hope to determine if a desert is conquerable. Can roads be made across deserts? How high would barriers around these roads have to be to protect them from sand? What special structures could such barriers have? What happens to civilizations built near dunes? Is there a way to limit dust storms and improve living conditions in sandy areas? A desert is an intimidating thing.

Problem Solution to date:
We have checked out a book by the man who seems to be the guru of all desert geomorphologists: R.A. Bagnold. Bagnold is indeed very useful, but understanding a mere chapter of his book requires much background reading. He has supplied us with equations that seem as though they could be very, very useful. We have decided to simplify. We are focusing on (1) grains of sand and how they interact with each other, (2) wind and how it interacts with one grain of sand (using equations from Bagnold's book), and (3) wind and how it acts by itself. We eventually hope to put all of these things together. We have begun to propose hypothetical situations, such as a wind perpendicular to a flat and uniform area covered in sand. All the grains have the same shape, size, and substance, while the wind has a constant velocity, temperature, and direction. We then research as many of the parts of this problem as we can and then piece together equations we need. Computer programs will be very useful in this process, because our results depend on so many different complex factors and equations.

Progress to Date:
At the moment, we have a functioning C++ program that calculates susceptibility, a ratio of air resistance to gravity, for a single grain of sand. Factors used to derive this are: the density of the air, the velocity of the wind, gravity, and the density and diameter of the grain. For our purposes, we assume that the grain is perfectly spherical. All of this helps us to determine what a sand grain will do in a certain situation. When a grain is falling, if the susceptibility is larger than one (the air resistance is greater than gravity), then the grain will be slowing down. If the susceptibility is equal to one, (the air resistance equals gravity) the grain will be moving at a constant velocity. If the susceptibility is less than one (air resistance is less than gravity) the grain will be accelerating. In addition to this, we have located a visual graphics program of sand dropping into piles. We hope to obtain permission to alter this program for our own purposes. We have also found several equations for grains in one-dimensional vertical paths, and grains in two-dimensional parabolic paths. Eventually we will write programs for both of these, and then compute paths for multiple grains moving simultaneously.

Expected Results:
Our final product will be a program that, given a certain set of variables, shows a three-dimensional sand dune in motion. This program will include the effects of humidity and saturation of the sand. Others could use our program to create another program that models more than one dune, perhaps an entire desert field. Such a program would prove to be useful in the future for planetary exploration. Many planets, such as Mars, have perplexing climates we are not familiar with. Being able to predict the motion of sand dunes in such climates under different conditions would allow us to more efficiently explore and develop them.

Bibliography:
Bagnold, R. A. The Physics of Blown Sand and Desert Dunes. London: Chapman and Hall, 1984 [reprint of 1941 edition].

Carrington, Dave. Updated Reply- Better punctuation and sentences. [Online] available e-mail; d.stupin@prodigy.net from dcarring@lanl.gov, 18 Oct, 2001

Carrington, Dave. Updated Reply-Sand dune group correspondence. [Online] available e-mail; maritere413@hotmail.com from dcarring@lanl.gov, 17 Dec, 2001

Leopold, Luna P. et al. Fluvial Processes in Geomorphology. San Francisco: W. H. Freeman and Company, 1964.

Losert, Wolfgang. "The Science of Flowing Sand." February 2001. October 13, 2001.

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