"fluctuate violently" is a correct phrase in written English.
You could use it in a written document to describe a situation in which something rapidly changes in intensity or degree. For example, "The stock market has been known to fluctuate violently over the course of a single day."
Saudi leaders were frightened: heavily dependent on imports, they had seen the price of rice and wheat, their dietary staples, fluctuate violently on the world market over the previous three years, at one point doubling in just a few months.
Celebrity clothing brands are particularly volatile, because their success is closely tied to one person whose popularity can fluctuate violently.
The crucial supposition for a representative model is that iron fluxes in the body are (approximately) balanced and cellular pools do not fluctuate violently during the experimental period.
Claudel died in 1955, aged 86, and his reputation has fluctuated violently ever since.
Food price markets are fluctuating violently because of extreme weather events.
Gold has, of course, been a status symbol and a signifier of wealth since it was minted for coinage in the 7th century BC, and as a commodity its value has always fluctuated violently, depending on the economic environment.
During the "tequila effect" period following Mexico's 1994 devaluation, EMBI returns fluctuated violently and did not really settle back down for nine months, until the fall of 1995.
Winds fluctuated violently and changed direction, preventing the ship from remaining stabilized despite being within safe operating limits.
Period I, when the cutting distance is less than half of the size of the abrasive particle, the friction coefficient fluctuates violently in certain range due to surface effect of the material; while in period II, all the friction coefficients fluctuate in very small range, and the friction coefficients remains steady state at different angles.
With her hair scraped back from a plain-pretty face sometimes dominated by black-rimmed glasses, Ms. Bush is believably either vibrant or desolate as Catherine contends none too successfully with her violently fluctuating emotions.
The FI increases with the increase in rock brittleness while the PN decreases, which suggests that the cutting force fluctuates more violently but less frequently during cutting rocks with large brittleness.
