That’s funny. I was thinking “Jacobs ladder” as I was reading the post and then saw the image.
Unfortunately there is no Force motion blur like there is in Flame. But there are other ways.
Compound blur takes a grayscale image and blurs the underlying image by the amount specified by the grayscale map. This way the entire image need not blur just parts of it and by different amounts.
Echo will take past frames and blend them together – combine that with a density mask and you have have different parts of the image that have more echos than others.
Directional Blur (or Motion blur depending on the version of AE you have) can smear the image on specific angles – again, combined with soft edge masks you can get larger smears in only parts of the image.
You can use Particular to emit particles from different parts of the image and the image can be applied back to those particles – get enough of the right type of particles and it can produce some really cool smeary effects.
If you are animating things you can increase the default motion blur to crazy levels (Comp settings, advanced tab)
You can generate a motion blur data element and then throw that at something like RealSmart Motion blur and it will smear the image based on the element (its a color element with R,G,B denoting different directions of blur – in 3D no less!)