The term 'wave wildly' can be summarized by two crossword solutions: GESTICULATE (11 letters) and FLAIL (5 letters). GESTICULATE is a verb meaning to make gestures, often with the hands, to emphasize a point or express an emotion. FLAIL is a verb meaning to move one's arms and legs around wildly, usually in an attempt to hit something. Both words describe the action of waving one's arms and legs around in an uncontrolled manner.