Select an empty, tab into edit mode, select its corresponding vertex on the wave surface mesh, and hit CTRL-H to add a hook modifier. Duplicate the bezier and its empties for however many wave controllers you need Once the 2d animation is satisfactory create a 2d mesh with 1 vertex per control point
Create 1 empty per bezier controller and selecting each empty and tabbing into object mode, parent each empty to its corresponding bezier control point. First hand animate a 2d bezier curve animation of a crashing wave cross section This was difficult enough to figure out that I will leave this guide here for future reference
