How to create ripple effects in Illustrator.

I feel this should be a simple task but cannot find a satisfactory solution.

I want to create a water ripple effect automatically. After much experimenting I have settled on the Warp Tool but this creates sharp points instead of rounded points. Trying to convert sharp points to rounded creates horrendous results. What I am hoping is there is a way of 'brushing' over a graphic and creating wavy lines. I feel it should be the warp tool but can I force it to create rounded points only?

I am attaching a graphic of a stylised moon on water to demonstrate. The left graphic is what happens with the warp tool. The right graphic is more what I want.