Distorting a plane? Best method?

I'm interested in creating an aurora borealis effect for mobile, as in this tutorial. https://www.youtube.com/watch?v=SNP5QqAQqn4

I'd like to add some undulation to the plane on which the texture is moving. I'm wondering about the best method (lowest system overhead) for doing that on mobile. Should I arrange it as a skeletal mesh with bone animations? As a cloth sim with Alembic? As a displacement map with a procedural texture? Some other method?

It needs to be a pretty slow, cycling undulation, probably repeating unless the procedural texture method is the best. Any tips on what is best practice in this case for mobile much appreciated! Nick J