Here is an example file for my method of doing ring clouds.
To start with, make a cloud layer that has a high amount of warp. You'll end up with places in the clouds that look like holes as the warped perlin makes swirly patterns. Use a Transform Shader to position a swirl to where ever you want. Note that transforming in the y direction (assuming it's near [0,0,0]) may help in positiong the swirl pattern.
Next we will create the mask using another fractal. We could use an image to mask the cloud, but this method keeps the solution all in the .tgd file. The downside is that positioning the mask can be a little fiddly, and we are at the mercy of circular shapes only. Note that you can use the Noise Stretch XYZ to make the shape more or less circular.
We now multiply the swirly clouds with the mask using a Merge Shader. Finally we clamp the output between 0 and 1.
The example file has a small and large example of the ring clouds.
Enjoy!
(If anyone can tell me how to use the Link Inline Image feature properly, I would be most helpful!)