White smoke is normally unburned diesel or water/coolant.
At the slip, especially on a calm day, it is usually easy to tell one from the other. Water vapor tends to float away. Diesel tends to linger. Diesel may slick the water. Water does not. Water vapor usually has no real smell. If it has any smell, it is a sweetness, which is bad, as it is antifreeze. Diesel has a distinct miserable taste, smell, and even eye feel if there is enough.
Underway, it is harder to tell unburned diesel from water vapor as one is moving away from it, spreading it out. But, if one does see it linger, it is unburned diesel.
Blackness in smoke is partially burned diesel. It is the result of the engine not getting enough oxygen to fully burn the fuel. In a diesel this can be normal while accelerating as the fuel is supplied first, then the RPMs go up, getting in more air. So, there isn't enough air until the RPMs catch the fuel.
If there is a turbo (and I think you may have twin turbos!) , and it isnt working, at the point of the fuel curve where it should be pushing in more air, if it doesn't, smoke with grey up and turn black. It is also caused by overloading as it prevents the engines from developing the RPMs to match the fuel curve, so not enough air gets in.
Overloading can be caused by a dirty bottom, fouled props, over propping, or an engine that just isn't generating as much compression as when it was new so can't handle the same load, or a turbo not boosting.
Blue smoke looks a lot like black smoke. It is a blue black. It is from motor oil in the exhaust. If it is sudden or a short ramp up to the problem in a turbo engine, it could be a turbo leaking. It could also be something worse. If it increased slowly over time, it could just be age....aging rings or valve seals. Depending on how bad, it could be like some grey hair -- nothing more than a sign of midlife. This usually isn't super load sensitive. Rings tend to improve as things warm up and seal better. Valve seals might, or might be more intermittent.
Grey smoke tends to be a mix of white smoke and black or blue smoke.
If the engine is losing oil....that is another sign of an oil leak. If it is losing coolant, a coolant loop leak, often a head gasket. If the oil is milky, that might be water getting in, such as from a cooler or head gasket leak. If oil is getting thinned out, especially if fuel is getting in, that is a sign of fuel getting in, such as worn rings and excessive blow by.
Since the smoke being reported as grey and under load under way, I'm more concerned about the black component that the white component, if for no other reason that white smoke underway that doesn't occur at the slip is almost always steam -- underfunded fuel tends to get better underway, or at least more spread out.
So, focusing on the black part of the grey. Get the diver to clean the bottom and check the props. Check the oil level and character. Check the coolant level and character. At the slip with the engine running, pull the valve cover oil fill and feel for excessive blow by. If, and only if, you know how to do it confidently and safely, pull the coolant cap and look for exhaust gas leaks. Check the turbos to make sure they spin freely. While underway get someone in the cabin or engine room close enough to hear the engines well. Is any turbo making crazy noises? Compare unfamiliar things like the sound and blow by from one engine to the other.
There is obviously a ton of other places to look, but I'd suggest starting here...it is free stuff to check...and then reporting back. With more info you'll get more ideas from the peanut gallery!
Good luck!
