XIII E: Role of Mathematics behind surprising dunes and ripples.

XIII E:Role of Mathematics behind surprising dunes and ripples.
           [Contd. A Journey to the Wonderland of Math.by Ajay Kumar Chaudhuri.]
                            
          "There is something of the marvelous in all things of nature."-------Aristotle
  

We have already seen many patterns in nature. They are amazing, beautiful and attract us. 

Dunes and ripples are two such patterns, generally found on vast expanse of sand, particularly in deserts.

When you picture a sand dune in your mind, you may think of grass–tufted mounds at the back or enormous hills of sand found in extremely dry places like Saharan deserts. When you hear the word ‘ripple’, might think of much smaller things, like regularly–spaced mounds of dirt only a few cm apart, like that form street gutters after it rains. Both dunes and ripples are combinedly termed as ‘bedforms’ which is a fancy word for piles of stuff that form as the wind blows the stuff along the ground. [Pic. No.-19a: Great sand dunes on Colorado Desert]

                      Pic.No19a  

[Great sand dunes on Colorado desert]

Bedforms don’t have to be made by wind only, any fluid will do. For example, there are plenty of lovely dunes at the bottoms of rivers, lakes and oceans, all formed by moving water. The stuffs in the bedforms can be sand or ice pellets, or anything like gravels that can be moved by a fluid, for instance, Altiplano, a region of southeastern Peru and Western Bolivia of South-America. The Altiplano originates northwest of Lake Titicaca in Southern Peru and extends about 600 miles. It is a series of mountain (a wide valley between mountain ranges) basins lying at about 1200 ft above sea levels.

As waves in water or wind past over sand, they create patterns of ripples. When wind blows over large bodies of sand, they create dunes, sometimes in extensive dune fields as in the Taklamakan Desert, lying between Tien Shan and Kunlun mountain ranges in northeast China. It is the largest desert in China at over 620 miles long and 250 miles wide. There is a horrifying story about this desert, which runs thus: The Takla makan Desert is known as “Place of Ruins” or “Sea of Death”, since it is a waterless death trap, experiencing an average annual rainfall of just 0.4inch (1 cm). Legend states that you can get into the Taklamakan, but you will never get out.

Sand dunes are classic desert structure. Picture a herd of camels and you’ll probably also imagine a dune in the back ground.  You will find them anywhere there’s enough sand around that isn’t trapped by vegetation or moisture and when the wind is strong enough to move the sand.

Bedforms occur all over the world, even outside, such as on Titan, a moon of Saturn or on our nearest planet- the Mars, under many different conditions and produce a magnificent variety of shapes and patterns.

On Earth dunes ranges in heights about 1 to 500 meters. That’s a plenty wide range! Dunes may form a range of patterns including crescents, very long straight lines, stars (pyramidal sand dunes) domes, parabolas, or sword shapes. Some of them remain stationary, such as diamond – shaped patterns sometimes seen as a dry beach. Others such as dunes in the desert, move in a direction of the prevailing wind or current. Sometimes moving dunes may pose environmental hazards. In some places of Africa and Asia, city - sized dunes are moving over buildings, roads and pipes creating air pollution problems for people and machines. Knowing how dunes form and move can help engineers divert or stop this sand motion.

Titan is the Earth –like and largest moon of Saturn. It is the only moon known to have a dense atmosphere of Nitrogen and methane and the only object in space other than Earth where clear evidence of stable bodies of surface liquid has been found, ice particles are drifted into stripes 330 ft high and 60 miles long, called a longitudinal dune. Large areas of Titan’s surfaces are covered with sand dunes. Dunes on Titan may resemble the Namibian desert in Africa. [Pic. No. 19b: Ripple on the surface of Titan, the largest moon of the planet Saturn.] The famous space Research organisation America’s NASA launched a car sized robotic rover “Curiosity” on November 26, 2011, for exploring Gale Crater on Mars. Rover’s Sand dune studies yield surprise. Some of the wind – sculptured sand ripples are a type not seen on Earth and their relationship to the thin Martian atmosphere today provides new clues about atmospheric history. It is remarkable that Earth and Mars both have big sand dunes and small sand ripples, but on Mars, there’s something in between that we don’t have on Earth. [Pic. No. – 19c: Puzzling sand dunes on Mars]

       pic.No19b.

 

                                Sand dunes on Saturn`s giant moon Titan (upper photo) compared  
                      to Namibian sand dunes on Earth (lower photo).
                  
                                                           

 Pic.No19c.

[Puzzling sand dunes on Mars]

The ripples and dunes, almost of similar features, are found on Earth as well as on Titan and Mars but in a very different environment, yet the physics is similar enough to generate similar shapes.

Since the characteristics of ripples and dunes are guided by the rules of physics, so   it is evident that there is math behind it. But the discussions on the role of math in this aspect will be a bit cumbersome, so it will be better to skip it off.                                             [To continue.]
Reference: Internet.
                  Pic.No19a.--Great sand dunes on Colorado desert.
                                       Downloaded from Public Domain.
                  Image credit:
                   Pic.No19b.---Sand dunes on Titan:NASA image.
                  Pic.No19c----Sand dunes on Mars:NASA/JPL--CALTECH/MSSS