The research of Hoese (1985) suggests that Sea Mullet use this second category of movements to fill the pharyngobranchial organ (an area at the back of the throat) with air.
The trapped air is believed to allow the fish to remain active in water of low oxygen concentration for about five minutes.
Several interesting lines of evidence support this theory. The number of jumps is correlated with the concentration of oxygen in the water. The less oxygen, the more jumps.
Secondly, Sea Mullet feed during the day often in bottom sediments that have low oxygen concentrations. Jumping occurs much more commonly during the day. Sea Mullet rarely jump at night.
via Science Dump.