The Collaborative International Dictionary of English v.0.48:

Gyre \Gyre\ (j[imac]r), n. [L. gyrus, Gr. gy^ros, cf. gyro`s
   round.]
   A circular motion, or a circle described by a moving body; a
   turn or revolution; a circuit.
   [1913 Webster]

         Quick and more quick he spins in giddy gyres. --Dryden.
   [1913 Webster]

         Still expanding and ascending gyres.     --Mrs.
                                                  Browning.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Gyre \Gyre\, v. t. & i. [Cf. OF. gyrer, girer. See Gyrate.]
   To turn round; to gyrate. [Obs.] --Bp. Hall. --Drayton.
   [1913 Webster]

WordNet (r) 3.0 (2006):

gyre
    n 1: a round shape formed by a series of concentric circles (as
         formed by leaves or flower petals) [syn: coil, whorl,
         roll, curl, curlicue, ringlet, gyre, scroll]

Moby Thesaurus II by Grady Ward, 1.0:

141 Moby Thesaurus words for "gyre":
   Baba Yaga, Charybdis, Lilith, afreet, barghest, cacodemon, circle,
   circling, circuit, circuiteer, circuition, circuitousness,
   circuitry, circularity, circulate, circulation, circumambience,
   circumambiency, circumambulate, circumambulation, circumflexion,
   circumlocution, circummigrate, circummigration, circumnavigate,
   circumnavigation, circumrotate, circumvent, circumvolute,
   circumvolution, cirrus, close the circle, coil, come full circle,
   compass, corkscrew, crank, curl, curlicue, cycle, daeva, demon,
   describe a circle, deviance, deviancy, deviation, devil,
   deviousness, digression, dizzy round, dybbuk, eddy, encircle,
   encompass, evil genius, evil spirit, evolute, excursion, excursus,
   fiend, fiend from hell, flank, genie, genius, ghoul, girdle,
   girdle the globe, go about, go around, go round, go the round,
   gurge, gyrate, gyration, gyring, helix, hellion, incubus,
   indirection, involute, jinni, jinniyeh, kink, lamia, lap,
   maelstrom, make a circuit, meandering, orbit, orbiting, pirouette,
   pivot, purl, rakshasa, rat race, reel, revolve, ringlet, roll,
   rotate, rotation, round, roundaboutness, rounding, satan, screw,
   scroll, shedu, skirt, spin, spiral, spiraling, succubus, surge,
   surround, swing, swirl, swivel, tendril, the undead, turn,
   turn a pirouette, turn around, turn round, turning, twirl, twist,
   vampire, volute, volution, vortex, wamble, wheel, wheeling, whirl,
   whirligig, whirlpool, whirlwind, whorl, wind, yogini