I didn't know what a Hadley cell was until now. For what the Hadley cell is, you might go to Wikipedia.
Hadley cells are atmospheric circulation patterns observed between the tropics.
The air rises at the equator, moves towards the poles and then descends in the subtropics.
How Hadley Cells work
First the air rises at the solar equator, then moves towards the poles, and as at the equator, air is stationary relative to the ground below, it carries the linear speed at the equator to the subtropics, thus sliding pole+eastwards relative to the slower ground.
At the subtropics it reaches a point where it's no longer so hot and it descends.
After descending, it will move along the ground either towards the poles (and forming part of the Ferrel cell) or back towards the equator. As it moves towards the equator, the ground's linear speed will increase (because at the poles you have angular speed but no linear speed, you only rotate around yourself and move 0 km every day; while at the equator you have the maximum linear speed, you move 2piEarth's_Radius (km) every day) and thus, the wind moves equator+westwards relative to the ground.
Climatic consequences of the Hadley Cell
As the air at the equator usually is full of humidity, because the Sun warms the seas, lakes and rivers, the vegetation also help keeping the air humid at night. When this humid air ascends at the equator towards higher places, it cools down very fast and also it generates a zone of low atmospheric pressure (at ground level).
When humid air cools down, the water in the air condenses a bit becoming visible as clouds. When clouds are cooled down even more you get rain. If it cools down further you get snow sometimes.
Now, when humid air cools down very fast you have your typical equatorial rains (at the equatorial climate zones).
When the hot, cooled air exits the equatorial zone, it has lost all of it's humidity, and now it will travel all the way to the subtropics, where it descends creating a zone of high atmospheric pressure (at ground level). Also, this air has lost its humidity at the equatorial rainfalls.
In school we learned (I did, at least) that when there was a high pressure zone, it meant a sunny day, and that when there was a low pressure zone it meant a rainy day.
When the air descends in the Hadley cells, you get a desertic climate, because they get constatly sunny days, with no rainy days.
The dry wind goes equatorwards again, dragging with it all the humidity it encounters towards the humid, hot and rainy equator.
Seasons and axial tilt consequences
Finally, as Earth's rotation axis is tilted 23.5 degrees, the solar equator (the parallel at which the Sun shines perpendicular to the ground) changes every day, oscilating from north to south on a yearly period. The northenmost parallel where this happens is called the Tropic of Cancer. The southernmost one is called the Tropic of Capricorn.
The axial tilt means that the solar equator is always moving, and thus the updraft air of the Hadley cell will move acordingly, bringing precious rain to places that would otherwise receive none. That is why the main subtropical climates have a dry season (when the Hadley cell's updraft isn't near their latitude) and a wet season (when the Hadley cell's updraft is just over them).
The equatorial climate are a special case because they always have the updraft of the Hadley cell over them.
The deserts are areas where there's never an updraft or there's never humidity in the updraft.
Desert Listing and comprobation
I've made a list of the main (hot) deserts/desert zones in the world and the latitudes between which they are:
- Sahara -> 12ºN - 36ºN
- African Rift -> 4ºS - 3ºN
- Arabian + Iranian + Thar -> 12ºN - 36ºN
- Turkestan -> 36ºN - 53ºN
- Takla-Makan + Gobi + Tibet -> 27ºN - 51ºN
- Australian -> 15ºS - 35ºS
- Atacama -> 4ºS or 8ºS - 32ºS
- North American -> 21ºN - 39ºN
From this list, we can enumerate the reasons why they are deserts:
- Most of them are placed between the paralells 12 to 36. These are the places more affected by the Hadley cells: Sahara, Namib, Kalahari, Arabian, Iranian, Thar, Australian, North American and part of the Atacama desert.
- Then we have the deserts originated because they are at the center of their continent, and if there was ever any humidity in the winds, it has already rained down somewhere else before reaching there. These are: the Turkestan Desert, the Gobi, the Takla-Makan and the Tibet deserts.
- Lastly we have the strangest kinds of desert, because they suposedly have no reason to be there, they are just next to the sea. The humidity should be there. Actually there isn't any humidity because the sea has a cold sea current that keeps the water cold, and it doesn't let it evaporate. These deserts are: the Namib and the Atacama deserts.
Why do they need to go in odd numbers per hemisphere?
The reason they go in odd numbers is because at the solar equator you will always have an updraft, and if your planet's axis is tilted less than 30 degrees, you will always have a downdraft at the poles. to maintain these two conditions you must have 1, 3 or 5 cells.
About the possibility of more than 3 cells (speculation)
I think that you could get more cells if you tilted your planet's axis to 36 degrees.
With this configuration, you will have the tropics at 36ºN and 36ºS and the polar circles (nearest parallel towards the equator where the sunlight can shine parallel to the ground) will come down to 54ºN and 54ºS.
There will be enough space for a Hadley cell between parallels 0º to 18º, an equatorial Ferrel cell between parallels 18º and 36º, an exchange Amaram cell between parallels 36º to 56º, a polar Ferrel cell between parallels 54º and 72º and a Polar cell between latitudes 72º and 90º.
On the middle of summer and winter, the polar cell may merge with the polar Ferrel cell to originate a turbulent flow similar to the one we can see on Jupiter's poles, and in the middle of autumn and spring there may be a clear differentiation between the Polar cell and the polar Ferrel cell as the hexagon shaped cloud on the pole of Saturn.