Tropical waves are perturbations within the low/mid level easterly trade winds just north of the equator. Ahead of the wave axis, winds turn a bit more northerly (NE) and behind the wave axis, winds turn a bit more southerly (SE). This shift in direction causes convergence, and thus rising motion. If there’s enough moisture and instability, the waves will produce thunderstorm activity.
This satellite image from September 2018 shows a series of tropical waves stretching from East Africa all the way into the Western Atlantic. Four of the waves are in fairly typical form, with disorganized shower and thunderstorm activity along their SW-NE oriented axes. The wave over the Central Atlantic has developed into a tropical cyclone (Hurricane Florence) while the easternmost wave over South Sudan is just beginning to develop.
So how do tropical waves develop? The answer lies in a feature known as the African Easterly Jet.
Here’s the ECMWF’s forecast for winds at about 10,000 feet a few days before the satellite image shown above. The African Easterly Jet is clearly visible as a region of brisk easterly winds along the boundary between the extremely hot Saharan desert and the relatively cooler coastal rainforests farther south. This temperature gradient is responsible for that jet, which shifts north or south with the seasons. Like any jet stream, the AEJ wobbles slightly north or south as it moves generally from east to west. These wobbles can come from interaction with the higher terrain of Eastern Africa, the development of persistent thunderstorm activity, or just the instability inherent to the boundary between two different airmasses.
Through thunderstorm activity, these wobbles eventually manifest themselves as troughs of surface low pressure embedded within the near-surface easterly trade winds, and tropical waves are born. As these waves move west off the African continent, they often lose most of their thunderstorm activity as even the tropical Atlantic waters aren’t nearly as warm as the land heated by the strong tropical sun. However, if conditions are right, that thunderstorm activity can persist over the ocean. If the storms become organized enough, the system can be classified as a tropical cyclone.
Many Atlantic tropical cyclones can trace their roots to tropical waves emerging off the African coast, though the vast majority of tropical waves never develop into tropical cyclones.