Here is the Beaufort from the 1st of May to the 18th of September (according to AMSR2 3.1k UHH). An earlier post showed the situation from January 1st to mid-July at five day intervals. It retains the original sea ice concentration color key which is critical to analysis. To show at 700 pixel width would quadruple file size to 22MB, not workable for the forum but an option after downloading (set mode to RGB and interpolation to 'none').
Note local eddies and lack of any effective Gyre from mid-season on. Import of ice from the CAA largely ceased as did export from Beaufort to Chukchi, contrary to textbook bromides.
In discussing the Beaufort Gyre, there's a potential for confusion between motion of floes and motion of surface water that has gotten worse in recent years. When floes are sparse, the effect of wind is much more pronounced and little is learned about surface currents.
Wind induced motion cannot really be predicted from reanalysis because it depends on floe freeboard lip, surface roughness and hydrodynamic drag.
Floe tracking is not essential to ocean current detection: "OSCAR global ocean surface mixed layer velocities are calculated from satellite-sensed sea surface height gradients, ocean vector winds, and sea surface temperature fields using geostrophy, Ekman, and thermal wind dynamics... modeling of the momentum transfer both within and across the boundaries of the turbulent mixed layer. http://www.esr.org/oscar_index.html
This is available at nullschool along with wind power density but it would be difficult to partition floe motion between the two with oscar not specialized to the Arctic Ocean, only recalculated at five day intervals, and limited to ice free areas.
Our interest is more in transport of recalcitrant ice to regions more favorable to melt. From the animation frames, it would be feasible to estimate how much thick multi-year ice moved from the CAB to melt in the Beaufort, as part of a larger project that considered export to the CAA, Nares, Fram and Barents front. Matching seasonal time series (animations) of these regions can be carved out of the same 141 MB master file (tomorrow).
These latter process export melt thermodynamics along with the ice. This year seemed quite odd, but perhaps it was just weather rather than the new normal.
Below the animation, there's an idealized average view of annual ice drift vectors from Woods Hole. There is also a mooring (to the sea floor) in the Beaufort that does not move with the ice.