Photoshop :: Progressive Distort>wave Effect

I want to add progressive blur to a pic from left to right, I can do so on several layers with masks, and add more and more blur on each one.

I would like a similar effect, but with the wave filter.
For example, a straight horizontal line at the left that slowly starts waving in larger and larger amplitudes.
(the final idea is a bit more complicated, but I only want to get some initial help so that I can figure out the rest myself).
In fact: several other filters from the distort group behave the same way: apply more intense filtering to a next layer, and the beginning/end and curve doesn't fit anymore.