For those who may not have access to the online OED, here the beginning of the entry for the noun "gyre."  I agree that "gyre" is a good candidate!  (OED = Oxford English Dictionary; and the pronunciation given is the "jire" one.)

gyre, n.

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Keywords: 
Quotations: 
Forms:  Also 16 gire.
Etymology:  < Latin gȳrus, < Greek γῦρος ring, circle. Compare giro n.1
poet. and literary.
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 1. A turning round, revolution, whirl; a circular or spiral turn.

1566   T. Drant tr. Horace Medicinable Morall sig. Bij,   Fashions..Which..do cum, And goe in circled gyre.
1590   Spenser Faerie Queene ii. v. sig. Q5,   To ward, Or strike, or hurtle rownd in warlike gyre.
1604   B. Jonson Particular Entertainm. at Althrope 107   Pardon Lady this wild straine,..Elues, apply your Gyre againe.
1608   Bp. J. Hall Epist. II. iv. iii. 137   Other Artizans doe but practise, we still learn; others run still in the same gyre, to wearinesse..our choice is infinite.
c1620   T. Robinson Mary Magdalene (1899) i. xciv. 786   Like to ye top, yt in his gyre doth spin.
1649   J. Bulwer Pathomyotomia ii. i. 71   In all these we may easily maintaine the gyre or circumaction of the Head.
1669   W. Simpson Hydrol. Chymica 78   Whirling them in oblique gyres.
1814   H. F. Cary tr. Dante Vision I. xvii. 73   Be thy wheeling gyres Of ample circuit, easy thy descent.
1829   R. Southey Inscriptions Caledonian Canal ii, in A. Cunningham Anniversary 195   The glede Wheeling between the mountains in mid air, Eastward or westward as his gyre inclines.
1856   E. B. Browning Aurora Leigh iv. 176   Graduating up in a spiral line Of still expanding and ascending gyres.
1920   W. B. Yeats Michael Robartes 34   All our scientific, democratic, fact-accumulating, heterogeneous civilization belongs to the outward gyre.
1928   W. B. Yeats Coll. Poems (1950) 217   O sages standing in God's holy fire... Come from the holy fire, perne in a gyre.
1929   W. B. Yeats Let. (1954) 764,   I believe I shall have a poetical re-birth for as I write about my cones and gyres all sorts of images come before me.
1930   R. Campbell Adamastor 98   A serpent..With lifted crest and radiant gyre Revolving into wheels of fire.
1948   C. Day Lewis Poems 1943–7 64   Earth-souls doomed in their gyres to unwind Some tragic love-tangle.
1962   Listener 20 Dec. 1047/2   It is deeply satisfying both as riddle and as poem. The poet evokes an atmosphere of mystery within the frame of the eternal gyre.
On Oct 30, 2015, at 5:36 PM, JD Erskine iDance via Callers wrote:

On 2015-10-30 1408, John Sweeney via Callers wrote:
Pleas could you clarify how you intend to pronounce "gyre"?

I have been saying "gyre" with a hard "g" as in "give" or "gimble".

But if it is related to "gyrate" then maybe people are using a soft "g" and
making it sound like "jire".

Which do you use?  Thanks.
snip

Happy dancing,
John

My paper Oxford Concise appears to have it as a soft or "j" consonant (from the Greek, guros, or ring.)

On-line, so obviously up to date, it appears it may be either

gyre - definition of gyre in English from the Oxford dictionary
http://www.oxforddictionaries.com/definition/english/gyre
Here they place the origin with both Greek and Latin.

I know of it as movement or place of movement within a body of water.

Most folks I've heard pronounce it as in gyrfalcon, gyrate, gyro (gyro compass), jive, java ;)

TTFN, John
- geographer, mariner
--
J.D. Erskine
Victoria, BC

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