Squat Interaction & Current, now being an Engineer these are not my areas of speciality, merely that they exist and their fundamentals -
ie Squat, travelling over shallow waters will drag the vessel down.
Interaction, a moving vessel moving near another staitonary or moving object will draw closer together, commonly seen near Major ports when someone isnt looking where they're going and narrowly avoiding collision (Seen it before in singapore on more than 1 Occasion).
For those that don't quite understand the physics of this & squat, think aircraft wings, when air flows over the surface of the top of the wing it creates a lower pressure and therfore lift, same with cutting through water & you drag a volume of water alongside the hull causing a low pressure area, to close and it will suck the other vessels together, or suck you down in the case of squat, that's why wooden sailing vessels cambered in as the sides went up, to counteract this when boarding another vessel.
Currents - Self Explanatory.
Hog - Larger Vessels in Ballast condition, yes they do bend, would be bad if they didnt, in this case like an arched bridge.
Sag - Larger Vessels in Loaded Condition, Think like a whale that's had to much to eat, your middle portion sags down.
Understandably all of these are hard to simulate, alot depending on the design of structure and hull, but the squat & Interaction could be simplified as an equation of speed attraction (like a magnet strength increasing to nearby objects) and distance from the vessel to give a basic feel of the effect.
