  A recipe is presented for interpreting non-invasively the transport processes
at work during relaxation of a cylindrical, superfluid-filled vessel, after it
is accelerated impulsively and then allowed to respond to the viscous torque
exerted by the contained fluid. The recipe exploits a recently published
analytic solution for Ekman pumping in a two-component superfluid, which treats
the back-reaction self-consistently in arbitrary geometry for the first time.
The applicability of the recipe to He II, 3He, 3He-4He mixtures and
Bose-Einstein condensates is assessed, and the effects of turbulence discussed.
