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I want to use a vector map in the node graph to displace/distort a 2d texture map, where X and Y values denote 2d direction and Z denotes strength.

i.e. Suppose I have two noise texture maps from two texture nodes. I'd like the first to displace/distort the second to "push" or "smear" the resultant texture information.

To visualize, imagine you're using a Noise node and using the distortion attribute. Now imagine I want to do that to a another texture node based on some other node. Like this:

enter image description here

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Use a Vector Math node combined with your Noise (or any) texture to warp the vectors:

VectorWarp

As I mentioned above, you can use other textures as well to create different effects. You can also get better control over the "distortion amount" by using a MixRGB node to mix the texture with white before it connects to the Vector Math Node :

VectorWarp2

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