Since you need only about 10 frames for something like that, you could do the smoke in Photoshop as a long soft vertical band, wave distorted, then animate it in AE to move upward while keeping the origin point in the same horizontal location frame by frame. If you already make it repeatable in Photoshop, you just have to match up the beginning and end positions so that it looks continuous. You can use a track matte to mask off the bottom part.
If you want to avoid keyframing, a simple solution is to make a shape layer of a lumpy white line, lower the opacity, Fast Blur it a little and put a Wave Warp or two on it, like this:
I have a larger warp (height 10, width 120) going at 0.6 speed and a smaller warp (height 2, width 30) going at 1.0 speed so they're a bit out of phase.
If you want to prevent the bottom of the smoke from moving, you can precompose the shape layer and in the precomp move the bottom of the smoke to the bottom of the comp and then set the Wave Warp pinning to "Bottom Edge."