In the photos you selected, the photographer is shooting up at the bow from the eye level of the bulbous bow. The angle creates an optical illusion. The ship’s profile on page 5 of the pamphlet posted above by ombugge shows a more accurate representation.
This is a more obvious example of the effects of the photographers POV and use of a wide angle lens:
I would imagine the shape of that bow is aimed entirely at reducing fuel usage and improving performance in the vessels intended role of long-haul ocean towing, although it does seem to be pretty large compared to the rest of the vessel.
The fendering is likely there so that the ship can come against either vessels in distress to render aid/fight fires or rig/connect/disconnect towing lines. The protrusion of that bulbous bow pretty much rules out coming in from a 90 degree angle so I assume it would approach from an oblique angle and be tied off while operations were underway.
During towing the bulbous bow doesn’t make much difference to fuel consumption, or speed.
(At, say max. 6 kts.)
But a tug of this type and for the the purpose of salvage and long distance towing will spen much of her time free running to get to where the action is, or the tow starts.
That bow fender is typical for the purpose of pushing against the flat side of a casualty, maybe for transferring personnel, passing over light salvage gear, or to steady a casualty etc.
These are DP2 vessels, so they would be able to hold station, even while using the FiFi monitors, or passing towline, which is normally done by shooting a line, pass a messenger and eventually pulling the towline across. (Stern towards the casualty)
PS> Waiting for someone to find and post a GA-drawing in profile.
The apparent length of the bulbous bow changes depending on the photo, @Lee_Shore’s explanation that it’s lens distortion makes the most sense.
In this screen shot there’s a line hanging off the bow.
In the drawing above (coming from the report in post #19) I measured that the bulbous bow is about one meter behind the bow fendering.
(overall length of the ship = 80.1 meter)
I served on the Tamaroa in the 1980s the USCG operated 6 in this class.
Cherokee wmec-165
Tamaroa wmec-166
Ute wmec-76
Lipan wmec-85
Chilula wmec-153
Avoyel wmec-150
Here’s a better Wikipedia article than the one I posted last Perspective distortion
With regards to the fendering:
Is the fendering mounted this way to increase the clearance on the bulb?