Knackered turbo, ie crack causing water from the water cooling on it to enter the exhaust, so fault is on the turbine(exhaust) side, you don't see it as it has evaporated, once the engine/turbo/exhaust is up to temperature, you could try temporarily disconnect the water cooling, and bypass then take for a drive taking it easy and see the result.
I assume it is a KKK turbo ?
tabetha