The captain was flying the airplane with his right hand resting on the power controls. As the airplane turned onto final approach, it encountered turbulence of sufficient intensity that the captain's feet came off the rudder pedals. He felt a 'click' in his hand and 'there was an instantaneous propeller overspeed.' The engine was eventually secured by closing the fuel shutoff valve and an uneventful no flap landing was made. Post incident examination disclosed both air ground circuit breakers were open. The left engine was found to be functionally destroyed. A readout of the digital flight data recorder disclosed the maximum left and right propeller RPM values attained were 150.49% and 120.4%, respectively. Vertical acceleration values ranged from .647 to 1.26 G's, and longitudinal acceleration values ranged from .037 to .096 G's. The right engine torque peaked at 37%, while the left engine torque remained at 0%. Right engine fuel flow was 16% to 19% lower than left engine fuel flow, and propeller imbalance values for the left engine was approximately 50% higher than those recorded for the right engine.