Perhaps have a plasterer come in and put another layer of plaster over the swirls. Same with the walls. Sometimes, painting it can "fill in" the swirl marks a little bit and help. I just did this in a room in my house with swirls. However, the grooves on the swirls were very minimal. I painted the ceiling with two coats of flat ceiling paint...all by hand so it really got in the groves. A neck and back ache later, they definitely look better, but could probably use one more coat to eliminate the look. I won't have an entirely "flat" ceiling, but it will eliminate the swirls.

Best of luck, keep us posted!

If this is anything like a "popcorn" effect ceiling, you may be able to spray it with a wallpaper sprayer, saturate it, and scrape it off with a trowel or scraper. ?????

Now, the swirl pattern is usually done by mudding the ceiling and taking a trowel or other object and just manually swiping it over the wet compound and letting it dry. It was originally done to cover imperfections on old plaster ceilings, and it 'caught on' and most new homes here had them and still do.....done on drywall. I think contractors like to do them, because it takes the work away from having to do a very even skim coat and sanding it to make a perfect surface for paint.

I have sanded the swirls down on those dudes in one house I owned. I actually like to work plaster and drywall finish and have been in the process of finishing off walls in my old house over the years my husband had slapped wallpaper on, because he was time constrained to move in and it was the easiest finish to put up and cover minor imperfections on the plaster. My God, the rooms were so 'busy' with all the different patterns, it got to me.

I have never had a popcorn ceiling, but they look like nightmares as far as collecting dirt and grime in the crevices. I think most of them are blown on with a special applicator.

If you do sand the ceilings or walls to remove swirl texturing, you would want to know the composition of the wall as to lead or other dangerous material in the plaster or finish..... and proceed accordingly, and also want to use very good respiratory protection.