Hi there !
Maybe try this one…
Draw a mask with the pen tool to create the path you want the smoke to follow.
Copy and paste to a new solid.
Apply the stroke effect to the mask. Effect> Render> Stroke
App. Settings : Brush size 9
Brush hardness 60 %
Spacing 80 %
Animate the end of the stroke
Add some Fast blur to it Blurrines 10 for only the horizontal pixels
Add a new solid to the comp
Add some Fractal noise , animate the evolution, let’s say 10 evolutions.
Precompose this layer.
Go back to the stroke layer.
Add a displacement map. Set the fractalnoise comp to be the Displacement map layer. Use Luminance
Horizontal displ. 8
Vertical Displ. 1
Adjust the mask (the smoke trail) to your liking.
This might need some more adjustments and experimentation but I hope it will help you getting started.
Best Regards