I've been seeing this distortion treatment popping up everywhere lately and was curious if anyone knew how or could point to some resources? I've tried a google search but can't find anything relevant. I've also tried the flag/wave effects in Illustrator but it looks like a cheap recreation.
On Photoshop: text layer, could be with transparent or white background:
Make a PSD file the same size as the text layer with a B&W gradient (50% gray is static, black and white will be displaced right and left):
For the gradient use guides on the part of the text you want to get the distortion
Back to the text layer, Menu Filter > Distort > Displace, after click on OK, the program will ask the file for the distortion, is the PSD gradient file.
I would just use the Warp Tool (Shift+R)
Take some text and select it all (make sure it's converted to outlines)and then using the warp tool, just brush across it (hold down Shift to make it go straight)
You can adjust the intensity of the tool by double clicking (I ad mine pretty high)
Play around with where you brush with the warp tool (how many times etc.) until you get the desired effect.
After playing with the settings etc. for a couple minutes, this is what I achieved:
Here is an old answer which also applies to this question.
The Envelope Method
You can accomplish some of the desired goal here using Illustrator's Envelope Distort. First, create your text. Next, make a rectangle and then using the Mesh Tool (U) click in the middle to turn this rectangle into a mesh. You can edit the mesh points to create some waves. Then make sure your text and mesh are both selected and use Menu > Object > Envelope > Make with Top Object to warp the text to the mesh. This works with objects that do not curve around to show a back side. Yet, this can too be approximated by doing more work and slicing your text into front/back pieces and warping them both to connect in the same place in a visually-acceptable way.
This shows a basic text wave distortion with top mesh object. https://i.stack.imgur.com/pqt09.png