In Flags of our Fathers, why are the Navy doing these beautiful formations before the war is going to begin with the Japanese?
These are landing craft holding troops to storm the beaches.
It takes time to load each craft with troops and this is managed one or two at a time...usually one per side of the troop-carrying 'mothership'
However, you want all the craft to land at the same time so as each craft is loaded it enters a 'holding pattern' waiting for the rest of the craft to be loaded.
When the last craft is loaded and the circle 'complete'...all the craft can head towards the landing point together, usually in a line.
I found this which appears to be an extract of guidance for these types of operations..
15-11. Landing craft are formed into groups of six to eight boats. These groups of boats are called waves. The number of craft in each wave depends on the landing plan. The convoy commander is on the lead boat in the convoy. Control craft are stationed on the port and starboard flanks; salvage and maintenance boats are in the rear.
15-12. When a boat in a scheduled wave is loaded, it is given a paddle with two numbers on it--the first indicating the number of the wave, and the second, the boat's position in the wave.
15-13. After loading, a boat proceeds to the rendezvous area, falls in with its wave, and commences to circle slowly. The first wave of landing craft circles clockwise, and so on. Moving out of the rendezvous area, the boats proceed in a column and, when clear of the transport area, form into a wedge with odd-numbered boats to starboard and even-numbered boats to port of the boat carrying the wave commander. Before crossing the LOD, the boats are formed in line abreast. The distance between boats is usually 50 yards.