The movie Twister makes a good example. But the characters in the film are storm chasers, who are attempting to place their new, innovative device inside the cyclone to solve the mystery of what causes a tornado. Other mysteries have a supernatural problem at their core. The X-Files is a popular mystery show right along those lines. Each episode faces some new problem that looks to have a preternatural source whether it is UFOs or other types of extra-terrestrials, ghosts, vampires, or even just witchcraft or the occult.
Mysteries are usually very intricate.
There are multiple clues, plot twists, perhaps even fake clues, called red-herrings. Clues are a necessary part in any mystery, if it is expected to be solved. When the clues are missing, it cannot be resolved. Such are the cases of John F. Kennedy and the young Jon Benet Ramsey. There was not enough clues or evidence to form a proven conclusion, and so their cases were left open.