Just to synch this up this forum with whole-ocean animations over at the 2016 melt season forum #1254... Note three of our posters have discovered palette image squeezing on WorldView (open tiny little icon next to layer's 'X'). This improves color separation as a variant on grayscale contrast adjustment that wipneus is using above. This does not degrade the data in any way nor add non-invertible aesthetic enhancements.
The blowtorch in the latter frames corresponded to an influx of warm air on nullschool but the relevant blackbody emitter is the ice surface, not intervening air.
Ice of the entire Arctic Ocean is incapable of coherent rotation. Where would the center of rotation be and how would a constant radius deal with fixed islands? The innermost island will always be limiting. (The North Pole itself is way off center.) When an irresistible force meets an immovable object, something has to give and that is the ice, not the island.
Over the years, I have watched Banks Island serve for weeks as limiting factor for the Beaufort Gyre, then seen a transition to Prince Patrick, then shoreline cracks out to Greenland (but no associated coherent rotation). This latter has been moderate compared to recent years as noted by wipneus, though the Gyre itself looks more torn up. (We have a great many spring 2013 BG animations stored on site, Neven linked to them recently.)
The center of Gyre rotation remained rather stable this year, associated with a surprisingly stable high pressure persistent winds. However here was a surprising shift in floe motion west of Banks about five days ago as the winds shifted. It is quite remarkable how such a massive object can be jerked around by a little wind. The floe has to have an edge, surface roughness or ridge for the wind to get a grip.
Neven located a monthly mean wind vector product that doubles fairly well as the mean center of rotation of the Beaufort Gyre. Academics would go with the wind stress curl here.
http://tinyurl.com/z97ckwyI don't know that anyone has ever determined the radius and center of the maximal possible rotating object in the Arctic Ocean. That would take some thought on choice of a non-misleading projection (or purchase of two globes, one to be cut into caps of increasing radius and placed on the other).
Next up: make the cap gradually smaller to construct the overall translation/rotation footprint. Do this for each point in the Arctic Ocean, indeed all the world's oceans over geologic time, throw in lunar and martian basins, save as a humongous netCDF file that no one will ever open and write the ultimate academic paper that no one will ever read.
On the technical side, measuring rotation centers gets into Euler's fixed point theorem, much used in plate tectonics with hot spot coordinate systems to measure convection-driven drift of continents which from our perspective are just bigger floes with a more viscous connection to mantle than ice to ocean water.