Firstly, let me make it clear that I'm not a meteorologist so I can't give you a definitive answer to your questions. However I can offer some very basic principles regarding jet streams. Jet streams form whenever two sections of the atmosphere of different temperature are adjacent to each other. This occurs on a global scale at the lateral boundaries of the tropical cell, the mid-latitude cell and the polar cell.
For simplicity, let's assume that the sea level pressure is the same for each cell. Again,
for simplicity let's imagine each cell extending to the limit of the atmosphere where the pressure can be considered to be zero. The warmer cell will have a greater vertical extent that the cooler cell. So at the level of zero in the mid-latitude cell, the warmer tropical cell will still have more air above and therefore have a higher pressure at that level.
This produces a horizontal pressure gradient from the warm air towards the cooler air. An effect that was called the 'thermal wind effect' when I was studying meteorology. As air attempts to flow under the influence of that pressure gradient, the Corioli's effect causes it to swing to the left in the southern hemisphere and to the right in the northern hemisphere producing very strong westerly wind at high level. The diagram shows that there is no horizontal pressure gradient at sea-level but an ever increasing pressure gradient as height increases. The jet streams are found at the boundary between the convective cells in either hemisphere. The effect is even greater in the northern hemisphere where the greater land mass produces more extreme variation in temperature between the cells.
By the way, it is true that the air temperature at the tropical tropopause is colder than that at the polar tropopause, but the tropical tropopause is about twice the height of the polar tropopause.
In the case of the tropical cyclone, it is not the circulation of the wind that is producing the low pressure in the centre of the system, it is the low pressure in the centre of the system that is producing the circulation. At the equator, the Corioli's effect is in the process of changing from acting to the left to acting to the right. So at the equator, there is no Corioli's effect and high or low pressure areas are short-lived because air tends to flow directly into a low and directly out of a high. At about 15 degrees south latitude there is a strong enough Corioli's effect to deflect the air flowing into a low. Also over the warm ocean at these latitudes, there is a massive amount of water vapour releasing latent heat as it condenses. This heat adds to the convection making the air rise faster and causing the pressure to drop further. This release of latent heat is what is maintaining the very low pressure in the centre of the system.
If you can get your hands on a copy of the Bureau's publication called 'General Meteorology', you will find more detailed mathematical presentations of these effects.
It's a pleasure to know the students like you have such a healthy interest in these topics.
Bob
