How to create a sine wave that conforms to an irregular shape and maintains curved crest and trough

As the subject line indicates, I'm trying to create a sine wave that will conform to an irregular shape and maintain a curved crest and trough. Also I don't want the lines of the wave to cross each other. I tried creating a wavy line (used the zig zag effect) and Object > Envelope Distort > Make with Top Object, but that created sharp points at the crest and trough and also crossed the line of the wave. I've drawn some amazing art to demonstrate what I'm trying to achieve. The picture uploaded in portrait and it's meant to be in landscape, but I'm sure you get the gist. I know that I can do this manually with the pen tool, but I'm hoping that there's a faster way as I'll be making the lines very dense. TIA.