The Dudh Kosi has been called the "Relentless river of Everest" because it's on the main trail to Everest Base Camp and so thousands of trekkers and mountaineers have walked along part of it and also of course, because of kayaking films and books. This is a convenient but misleading label as it's only one of its tributaries, The Imja Khola that actually starts from the Khumbu Glacier. This in itself is only one of four glaciers that start on the mountain; the other three drain to tributaries of the Arun, a much more powerful river, that has a perhaps stronger claim to be the ever of Everest.
This is steep river: the majority of the upper river has a gradient of up to 12 m/km (600 ft a mile) flowing in a deep gorge with the trail a long way above. Namche Bazar the gradient is more reasonable and further downstream, south or the main trekking route, the gradient again becomes less steep making for some good kayaking down to near Rasuwa where the river becomes almost flat for the 32 km to it's confluence with the Sun Kosi.
The Dudh Kosi has seen several huge floods that have scoured out the river bed and washed away the usual rounded, water-worn boulders: leaving instead jagged social debris all the way down the river- hence the derogatory but perhaps apt description 'rock-infested ditch" that has been coined by those who have kayaked. These floods have mainly been caused by 'GLOFs' - glacial lake outburst foods. One in August 1985 had a flow of 11,600 cumecs, 17 times the average in August. A ten meter high tidal wave of water, mud and debris crushed homes, swept away bridges, removed whole fields, and gouged out a new river: those who had kayaked the river in 1976 didn't recognize it when they turned ten years later.