Refer to figure. 
The Intertropical Convergence Zone (ITCZ) is a broad zone of air mass sometimes called the heat equator.

Here, the prevailing trade winds of the North and South Hemispheres collide.

Due to intense solar heating near the equator, the warm, moist air is forced up into the atmosphere.

As the air rises, it cools, causing persistent bands of showers and storms around the Earth’s midsection. these convective storms are known to produce intense rainfall, severe turbulence, severe icing, hail, lightning and windshear.

The rising air mass finally subsides in what is known as the horse latitudes (between 30° - 40°N), where the air moves downward toward Earth’s surface, forming a high pressure surface region with clear, warm weather.

Storms within the ITCZ will often go as high as 50 - 60 000 ft, so cannot be escaped upwards by commercial jet aircraft, and must be avoided using lateral deviations. 

Note: There can be a tropical jetstream flowing from East to West over the Equator region in the Indian Ocean and Central Africa, however, it is usually <100kts, and much lighter than all other jet streams. It would also likely be higher than FL390 due to the very high tropopause in that region.