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How air pass from cold sector to warm sector?

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We know that warm and cold air mass don't mix together because of different densities. Why cold air draw by wind pass from cold sector, to warm sector through front, how is it possible? Is the low pressure system always run from east to west below 30 degree and from west to east between 30 and 60 and from east to west above 60 and why?

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Im not exactly sure how to answer the first a little too broken for me but the second is fairly simple its because of the cells in those regions 0 to ~30 is the hadley cell, ~30 to ~60 is the ferrel cell, and ~60 to the pole is the polar cell with their associated atmospheric wind patterns.

 

It wont be an abrupt change across these regions for things west to east or east to west. Circulation around a high is clockwise in the northern hemisphere and low pressure counter clockwise and flow gets diverted to the right due to Coriolis effect. This does not mean localized will get diverted to the right but overall there is a general right turn to flow.

As for the first question may just to reword it unless someone else has an idea.

Earth_Global_Circulation.jpg

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