How does a tropical storm become a hurricane?

Histogram of Hurricane Florence 2018

Changes in the estimated average wind speed classify the weather events over the sea as a tropical depression, a tropical storm, or a hurricane (tropical cyclone). The Saffir-Simpson scale is used to allow proper classification.
The attached curve reveals no abnormality when a tropical storm becomes a hurricane.
However, satellite images show a significant change when a hurricane occurs. An eye appears and is clearly visible from space. The system is highly ordered but much more dangerous because a hurricane is a mobile thermal engine above the ocean, with a huge motive power.
The goal of this blog is to try to clarify this apparent contradiction. What happens when a tropical storm turns into a hurricane? What are the relative influences of various parameters on the formation of a hurricane and on its regression to a tropical storm?
Lastly, we note that hurricane Florence may be downgraded to tropical storm. Other hurricanes behave the same way. This is an encouraging sign.