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To be tempestuous is to be violent and turbulent.
The adjective tempestuous comes from the word  tempest, which denotes  a storm. According this  the adjective tempestuous is used to describe anything stormy or volatile, blustery, squally, wild, turbulent.
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The correct answer is violent; turbulent

To be tempestuous is to exhibit behavior that is violent, turbulent, frenzied and intense. An example of tempestuous in a sentence is, "His tempestuous streak is likely to get him in trouble at work". Alternatively, 
tempestuous can be used to describe non-human characteristics as well. For instance it can be used as follows: "The tempestuous storm makes me afraid to step out."