Lathe chisels and gouges, which one?

I have a pretty good set of chisels with a couple bowl gouges parting tool, spindle gouge and a skew.
I’m going to make some bowls and I need a good tool to hollow out the bowl. It seems everything I have wants to be thrown to the outside of the bowl when I turn it and I cant get it smooth. I think one of the problems is the dry walnut I’m using. I’ve heard it’s much easier to turn green wood.

So can you recommend a good tool to hollow out the bowls? I need to know what it’s called so I can look around at several brands before I buy.

-- Failure does not stop me, it makes me try harder..... because I'm crazy.