Physical Water in Game-engine?

Hello,
I have been working on a few game projects that I would like to add water to. But a specific kind. I see it video games a lot, where you can jump into the water and dive into it’s depths. I was wondering if anyone could share how this Air-to-underwater process could be done. Basically, what I want to know is, how can I give the effect that the character has actually been submerged in water?

Well, I think it is quite simple. Just add a blue effect to the screen via an overlay scene or the likes and have the player controls flip over to water mode. So you can swim and dive instead of walking. How you do all of that is up to you and your game. FPS?

I know how to set up controls and animations for this, I just need to know how the scene set up should be to get it working properly. It’s Third-Person Adventure Fantasy. Minimal realism.