There are lots of ways to portray a sense of annual rings, or bark, and this is my version. I keep the caving quite light so as not to distract from the main action.
Don't make the grooves too deep, or too many, and offset the centre for a little more interest. And do enjoy it; it's a relief from the breath-holding, picky work we've been doing on the bird.
Oh yes, and don't forget to leave a little wood for the beetle!