For this question, I was inspired by the following image of the "Jupiter Abyss":
Please do not take the image too seriously, as I only did my best to mock up what I'm looking for (which is why there are only a few storms instead of hundreds). In reality, I want the storms to get deeper towards the center, making light harder to reach there, which gives the impression of a whirlpool-like dark or black storm.
EDIT: The storms wouldn't need to be persistent. They can form and dissipate, I'm just looking for them to look like tons of giant black dots from space.