Is there a spiral modifier? Is is there a modifier that rotates vertices according to their distance from an axis. If for example, it was applied on the z axis, then from the top the vertices would spiral around the center, with the furthest ones out rotating more and the inner ones rotating less. A bit like what you do when you stir a bowl of cake mixture. I've tried the twist modifier, but it rotates either end in opposite directions.

Edit
I worked out how to show what I want in Sverchok.



When given a cube as an input it produces this:



I hope that demonstrates what I want to do. Basically rotate all vertices according to their distance from the central axis. Seems like a simple type of thing, I wouldn't have thought you'd need an add-on like Sverchok to do it.

I may end up using Sverchok, but it's a whole 'nother learning curve on top of the Blender learning curve. And I want the effect to animate, I'm not sure is Sverchok can do that.
Vertices can be rotated around an axis into a "spiral" shape using the Screw modifier.

Here I start with just a plane and an empty object with plain axis:



Then, I add the Screw modifier and use the Empty object as the AxisObject (i.e. the object that the vertices will "spiral" around):



The iterations control how many revolutions the vertices will make, the screw parameter controls the distance between "rungs" of the spiral shall we say (I believe there is an engineering term for it), the steps and render steps act like a subdivision surface modifier, smoothing out the "spiral" and the angle parameter controls how many degrees in 1 iterations (i.e. with 180 degrees as the angle 2 iterations will be required to form a complete circle). 

Here I have set the "spiral" to 6 iterations of angle 360 degrees with a screw measurement of 2.5 and a steps count of 256:



For this case i had to apply the modifier and then recalculate the normals so that the model now has lighter shading:



You can use this modifier with many different shapes to create various end results, I suggest experimentation to find the optimal shape for what you want to achieve.