Create a plane.
Sub divide the plane so you have a decent amount of verticies.
Then put the plane in edit mode.
Select all the verticies in one column and create a hook for them.
Now you have a way to move a row of verticies using standard animation techniques.
Repeat this for all the rows, only make the even rows go up while the odd rows go down.
Because Turbulent displace is based upon perlin noise, you might be able to take that approach as well.
Also a lattice approach might achieve that effect.