Yes, an expanding square spiral search pattern is what you would expect for a blue water search around a vague search datum point, but the recorded track pattern as seen on AIS looks to me much more like a contact investigation track.
Not sure what you mean, but we dont search the way that was show on AIS. They are spending too much time stopping/slowing down for the turns, and the optimum search is in a straight line, especially at the depths they are working at.
This is a basic towed array search pattern that we use to optimize area:
The fish is towed, so anything over about 4 kts will cause it to cavitate, (or the harmonics in the umbilical) and degrade the measurements.