wave

To move freely back and forth or up and down in the air, as branches in the wind.

To make a signal with an up-and-down or back-and-forth movement of the hand or an object held in the hand.

To have an undulating or wavy form; curve or curl.

To cause to move back and forth or up and down, either once or repeatedly.

To move or swing as in giving a signal: synonym: flourish.