Make a horizontal square pattern and change it to circular with Filter > Distort > Polar coordinates > to Polar
A coarse example:
A 1800 px wide image, some rectangular areas are filled, the becoming mid part is on the top. The becoming edge is grey. It's useful to have multiple layers but I worked in one layer (=no easy edits)
It's many ways to make a random looking zigzag but i made a selection and applied Filter > Distort > Waves:
Beware: The selection should not contain black nor grey. The result of the Waves:
The image is squeezed with Image > Resize to exact 600 x 600 pixel square. It was not originally square to have more room to make the pattern. Then conversion to polar coordinates is applied:
Cut the wanted piece into use.
Have more color stripes in separate layers. It makes a possibility to scale and rotate them. Only one color (the rest is tansparency) per layer gives the greatest freedom for making a good composition.
Manual drawing before changing to polar coordinates is surely an useful idea. It's much easier with vertical only strokes. You can paint something and smudge it with a smudge brush with vertical strokes. It's useful to keep different colors in different layers to avoid dirty looking mixes and to be able to fix errors easily. Try artistic filters to get more painted like strokes.
The pattern idea is not mine, its a plagiate of one of your examples.
After polar transformation it's this. It's more plausible as a painting than the previous waves version.
Photoshop has some noise based filters which can create complex patterns with very little effort. In the next image the basic vertical strokes are made with Render > Fibers + Accented brush strokes filter before conversion to polar:
Near the edge the pattern is faded with a feathered circular selection. There was a grey background which is also clipped with a circular selection before merging the layers.