The Hadley cell is a giant machine made of air. At the business end at the equator the solar zenith tracks by every day at supersonic speed, and heats the surface layer of the atmosphere while it races by. Here there is no issue of planetary rotation induced Coriolis force to contend with, so the heated and moisture rich air increases in volume and falls in density. Eventually it explodes upward in a giant set of daily convection thunderstorms that reach to the stratosphere. Violent storms that jet liner pilots sensibly avoid.
As the moist air rises in the convection cell, it cools by adiabatic conversion of KE to PE and the precipitation process kicks in (it rains a lot) so the rising air dries out. At the tropopause the air has a problem, it cannot easily go back down because on ascent as it dried out it gained Latent Heat (both of vapour condensation, and for good measure also that of ice crystal fusion). Furthermore, the water that gave it that Latent Heat is now back on the ground, so while the air cooled at the moist adiabat on ascent, it is forced to warm at the dry adiabat on descent. So, guess what? Descending dry air gets to be warmer than descending moist air when falling through the same distance.
So how does the air get back to the ground? Well, the only way to go is sideways, so it sets off on a long journey across the upper atmosphere towards the pole. Except it never gets there. Thanks to the Earth’s rapid rate of daily rotation the dry air is forced to track eastwards and eventually, in the Horse Latitudes it cannot go any further pole-ward, and so it is forced to descend.
On forced descent the dry air will maintain a clear atmosphere, and so sunlight will be able to reach the ground more easily. At the surface the descended air creates a zone of high pressure before it sets off back to the equator as the surface Trade Winds. On crossing over the ocean, the Trade Winds pick up moisture from the water by forced evaporation of moving air, and eventually the now moisture rich air arrives back at the equator. Here in the Doldrums, it is now ready for the next daily passage of the solar zenith. It is then set off on its journey once again and forever through the cycle strokes of the giant Hadley cell convection machine.