To Bob and Ted: many thanks for all the technical informations you have added here. Beside, the photo is not very élégante.

BOB,,, when a main engine is under a certain rpm or stopped a auxillary charger is running (our ship it kicks in under 82 rpm) in order to supply a certain continues stream of air to the engine. However on those Navy Ships, as they often have high rpm engines the set up may be different.

The turbocharger is a turbine air pump driven by the exhaust gases from the engine. At low revolutions and low engine load, the turbocharger doesn’t need to ram as much air into the combustion chambers as it does when the engine is working at full load or maximum revs. When the engine (be it main or auxiliary) is called upon to quickly increase power and/or revolutions, it may take the turbocharger a short while to ‘catch-up’ and supply the right amount of air for complete (smokeless) combustion.

It is actually a little more than usually, but nevertheless most probably as Bob mentioned, too much fuel and not enough air. We having those problems sometimes when discharging with all cranes and then 2-3 cranes starting a heavy load at the same time. Then the governor of the auxillary engine can not adjust quick enough to the required needed power and for a short moment one sees the (in german "Heizer-Gruss) black smoke for a moment like 4-5 sec. But this waqs like or 25-35 sec seems to be also bad adjustment .

The main cause of black smoke from a diesel engine (marine or in a road vehicle) is imbalance in the air:fuel ratio. This means that either there is shortage of air or the fuel supplied to injectors is not being treated properly or there is too much of it.
Just as when you put the accelerator to the floor in a stationary, diesel-engined truck or car, the turbocharger may not be able, at low engine revolutions, to supply enough air to the fuel being injected for complete combustion to take place and the result will be black smoke from the exhaust.
From what Ted says about this being a regular occurrence when the ship gets under way, I would guess this is the reason for the black smoke. He's giving it too much 'boot'!

OMG!!! Bad quality of the coke???

No idea, just saw it by chance. But everytime they leave they smoke like that. I watched one for a while and when on higher speed outbound the smoke stopped. Guess it is only during slow and maneuvering times.

BMW motors?

That is a lot of smoke... burning off buildup in the engines?