How to achieve a 3D warp field effect in blender (2.81)

Question

I'm after a way to create an effect such that when an object is placed inside the volume the verticies are displaced based on the localised field value (thinking of it like a density field in physics where the local distance between atoms decreases as density value of a region increases)?

The current model I would like to use it on is spiral column that I need to gradually flare out at the top and displace randomly along its length in order to create a solid tornado funnel - but I'm sure I could come up with lots of uses once I know how to do it.

Answer 1

Thanks to the comments I finally found out about the Lattice modifier system which when you take away the physics speak is exactly what I was thinking of when I posted the original question - below is a proof of concept 'Tornado Susan' using the stock Susan model with a lattice modifier applied to flare the top and give the length a bit of a flick And the Lattice Modifier that was applied is shown below which takes no time using proportional editing