wave warp effect - How can I adjust the speed gradually?

You could always precomp the assets and the effect, trim the layer to desired length, right click time/ freeze on last frame. Then easy ease the newly created keyframe. Done 🙂

You can use a timewarp effect or adjust the height parameter to straighten it gradually

Pre-compose your Wave Warp layer moving all attributes to the new comp. Add Time remapping to the pre-comp and adjust the speed curve in the graph editor so it looks like this.

That project has wave warp animating only wave height, but then the playback speed goes from no time passes or zero seconds per second of realtime to 5 seconds per second of realtime or 5 times faster than normal. 

I know it's late, but it works if you move the "phase" keyframe instead of wave speed. Just move the phase to wherever you want and play with the "easy-ease".

Some effects simply cannot be animated in the manner you want, especialyl ones that auto-animate like Wave Warp. It messes with their internal math. You have to think of something else like creating a static wave and animating iot with a Motion Tile effect or using Displacement Map with a custom map.

Mylenium