I imported the file, eagle bowl?, and played with the design, I made the bowl a little narrower on the top, and 3 rings appeared above the feature ring. With a little more wallthickness you can make the design.
Well, here's a different approach to the grain. In bowls 99% of all turnings is side grain, but with pens i often have end grain, depending of the (segmented) design.
The tools i use in the first place is a spindle gauge crown pro-pm half inch. Then i have made 6 or 8 scrapers from old...
Far from a ready vase, still gluing and turning but i can't resist. Until now 6840 segments (95 rows 72 segments) glued and ready to turn the last row. it will be 7848 pieces (109 rows) for the umbrella stand. I thought of sharing it already.