"heavy storm" is correct and usable in written English. You could use it when describing a large, powerful storm containing lots of precipitation, such as rain or snow. For example: "The heavy storm blew through town, leaving a few feet of snow in its wake.".
It sounded like a heavy storm.
The boat capsized because of the heavy storm".
Before then, he needed three pumps after a heavy storm.
Anticipating heavy storm surges, their protectors provided hay, and the ponies retreated to the hills.
One heavy storm can cause ageing urban sewerage systems to overflow.
There it was even more like being in a heavy storm.
The story begins at nightfall on a dirt road in southern Portugal during a heavy storm.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK