Ocean workflow reccurent problem

Hi. I am frequently working with oceans and I need an advice that help me to avoid this problem:

When doing oceans for info-graphics I usually need to show the sides of the ocean. The sides need to be flat and the top surface well…the ocean. Like this:

As you can see in the example. One mesh with two materials and the render on the right. You can appreciate some weird artifacts that I imagine they come from having a displacement on the top and not having it on the sides…I imagine blender or any other software can not figure it out what to do there.

I really need advice on how to finally get rid of this problem. I might be wrong but it seems to me that the two material workflow in one mesh is not the way to go.

I am thinking if the way to go is to model only the top surface (yellow contour) apply the displacement and bake it…After that extrude the mesh and then I will achieve the wave feeling without conflict with the sides.

If this is the right way to go I will need to research the baking option…never made bake in my life.
Guess its not that difficult.

The reason why I am asking here is to know any other alternative to achieve this kind of surfaces with a displacement on top and non displacement on the sides.

Here is a print screen of the mesh

And the material just in case:

Thank you, and please if somebody in the forum knows about what I am talking about and have a smart workaround I would really really appreciate it .