The Collaborative International Dictionary of English v.0.48:

Wave \Wave\, v. i. [imp. & p. p. Waved; p. pr. & vb. n.
   Waving.] [OE. waven, AS. wafian to waver, to hesitate, to
   wonder; akin to w[ae]fre wavering, restless, MHG. wabern to
   be in motion, Icel. vafra to hover about; cf. Icel. v[=a]fa
   to vibrate. Cf. Waft, Waver.]
   [1913 Webster]
   1. To play loosely; to move like a wave, one way and the
      other; to float; to flutter; to undulate.
      [1913 Webster]

            His purple robes waved careless to the winds.
                                                  --Trumbull.
      [1913 Webster]

            Where the flags of three nations has successively
            waved.                                --Hawthorne.
      [1913 Webster]

   2. To be moved to and fro as a signal. --B. Jonson.
      [1913 Webster]

   3. To fluctuate; to waver; to be in an unsettled state; to
      vacillate. [Obs.]
      [1913 Webster]

            He waved indifferently 'twixt doing them neither
            good nor harm.                        --Shak.
      [1913 Webster]

WordNet (r) 3.0 (2006):

waving
    n 1: the act of signaling by a movement of the hand [syn:
         wave, waving, wafture]

Moby Thesaurus II by Grady Ward, 1.0:

42 Moby Thesaurus words for "waving":
   ambages, anfractuosity, brandish, brandishing, circuitousness,
   circumambages, circumbendibus, circumlocution, circumvolution,
   convolution, crinkle, crinkling, flaunt, flaunting, flexuosity,
   flexuousness, flourish, flourishing, intorsion, involution,
   meander, meandering, rivulation, shaking, sinuation, sinuosity,
   sinuousness, slinkiness, snakiness, torsion, tortility, tortuosity,
   tortuousness, turning, twisting, undulant, undulating, undulation,
   undulatory, wave, wave motion, winding