WAVE ABOUT is a phrase that describes a type of movement. The crossword solutions BRANDISH, FLOURISH, and WAGGLE all refer to this type of movement. BRANDISH is an action of waving or shaking something in a threatening manner. FLOURISH is an action of waving or shaking something in a showy or impressive way. WAGGLE is an action of moving something back and forth or side to side. All three words describe the same type of movement, but with different connotations.