Hmm... it looks like you're going to want to use the Distort -> Displacement map effect. The tricky part will be creating the displacement map to get the desired effect here.
What I would do is create a new comp that will serve as the displacement map (same dimensions and duration as the video). Create a solid in that comp and add a Noise & Grain -> Turbulent Noise effect to it. Scale the noise (in the effect, not the layer) so it's pretty high-frequency (small-looking), then add a levels effect to a new adjustment layer at the top of the layer stack, and set the output white level to 0.5 (or 128... or 32768 depending on what bit-depth you're working in). This is because the displacement map effect goes in both directions (ie values >0.5 go in one direction, and values <0.5 go in the other) and since all of the displacement shown above seems to go in one direction, we need to limit the color range there, hence the levels. Then, add a directional blur effect to the noise layer, under the turbulent noise effect, set it to 90 degrees, and crank it up!
Now, go back to your main composition (with the footage) and add a displacement map effect to the footage. Add the displacement map comp you created earlier into the main comp, and reference it in the effect. Also, hide the DM (tired of writing out "displacement map") layer, so it doesn't show up: we only want it to be used by the effect, not actually be seen.
Now, set the vertical max displacement to 0, and play around with the max horizontal displacement. Should look fine, except its all over the image. It seems in the reference photo that you want to limit it to one half of the frame.
To do that, go back into your DM comp, and add another layer. Add a gradient ramp just under the adjustment layer, but above the turbulent noise layer, set it's blend mode to add. Then change the colors of the gradient to Black and white (those should the defaults, come to think of it). Adjust the start and end positions to make the turbulent noise appear to taper off.
This isn't exactly what they did, but it's a quick solution that gets it pretty close.
You can also do this with masks and scale on a duplicate layer. There are a lot of ways to accomplish this kind of distortion. The key to the effect is to use at least two copies of your footage. Animate a mask to separate the part of the image that remains intact and distort the bottom copy.
It does work and it looks great! Thanks for the help Still wondering how they thought of the effect but with this method i can get it pretty close.