This is a tutorial for partially submerged object with an open face such as a crate or a boat.
This uses the boolean modifier to create a hole on the water the shape of the displaced object. The boolean modifier need an object with volume to work. I tried with a plane object but it doesn’t seem to work.
First add two cubes. Resize one of the cube as shown on picture 1. Rename the cube “water” and the other cube “box”.
Duplicate the box [Shift]+[D]. Resize it slightly bigger than the original box. Rename it boxfield. Parent boxfield to box. See picture 2.
Select water and goto Edit Buttons [F9]. Add boolean modifier. Select Union and type boxfield for object. See picture 3 and 4.
Hide boxfield to another layer [M]. Delete the top face of the box. Add your textures. Animate and enjoy. See picture 5.
See my YouTube example.