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"fluctuate severely" is a correct and usable phrase in written English.
You can use it to describe a situation in which there are sudden and extreme changes in something that typically remains relatively stable. For example, "The weather during our camping trip seemed to fluctuate severely between scorching hot and freezing cold."
Exact(3)
In Studies in the Economics of Overhead Costs (1923), Clark developed his theory of the acceleration principle that investment demand can fluctuate severely if consumer demand fluctuations exhaust existing productive capacity.
When RSSI readings fluctuate severely, even sliding window filters fail to estimate the true value.
Potassium levels can fluctuate severely during the treatment of DKA, because insulin decreases potassium levels in the blood by redistributing it into cells.
Similar(55)
When the background noise fluctuates severely, the performance of the proposed algorithm using energy detection becomes unacceptable.
The load fluctuates severely in winter with a large peak from 16:00 to 21 00, whereas the load profile in summer is much more flat and smooth.
There are dangers, however, that investors, and particularly retirees, need to evaluate carefully: Dividends aren't as steady as bond yields, and the value of a stock is likely to fluctuate much more severely than that of a high-quality bond.
Mr. Bethune said even a month of ongoing conflict would severely hurt his airline and the rest of the industry, as oil prices fluctuate and passengers shy away from the skies.
Markets fluctuate.
Markets do fluctuate.
"Things fluctuate," Mr. Di Rita said.
The last two fluctuate.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com