Making a Randomised Field of Distortion

What I’m trying to make is quite difficult to explain, but the best example I can give is this :
We’re talking about a field which distorts anything behind it. Look at it like a portal - as long as you look through this field, it distorts whatever is behind it at a random interval of time. Either that, or a sphere that distorts everything inside it at a random interval. I am completely new to Unreal, so simplifying your answers would be beneficial for me! Thanks!

Download the features tour 2014 project on the learn tab. There are some examples of looking at the depth buffer , etc. in game through a portal.

This is more accurate (made by me in Photoshop) :
I’m looking to make something like this inside Unreal.

I would look at using either a post process material or a translucent material that reads the scene texture. Then you can apply whatever distortion you want using a texture mask and adding to the ScreenPosition as the UVs to the scene texture. And you can try using maybe a sine wave or a few of them added up to randomize the strength of the offset or even the texture tiling of your mask you end up using to create more randomness.

The main point is that you will need to apply this distortion manually as the built in refraction system is not going to be well suited for this kind of intense localized distortion. I suppose you could try accomplishing it using normal maps but I would expect it to be tricky to tweak.