Here are some more cleaning videos, but they are all hangar cleaning.
Engine cleaning at the gate is very unlikely due to environmental reasons.
Unscheduled water wash takes place when performance is affected or stalls/surges have happened. Scheduled water wash with detergents is to clean compressor/turbine blades and coking residues at the nozzles and also reduces fuel consumption. Washing intervals depend on company programmes, engine types and manufacturer recommendations.
I hope this helps!
Easaman