Unmanned aerial vehicles (UAVs) are reaching offshore. In this work, we formulate the novel problem of a marine locomotive quadrotor UAV, which manipulates the surge velocity of a floating buoy by means of a cable. The proposed robotic system can have a variety of novel applications for UAVs where their high speed and maneuverability, as well as their ease of deployment and wide field of vision, give them a superior advantage. In addition, the major limitation of limited flight time of quadrotor UAVs is typically addressed through an umbilical power cable, which naturally integrates with the proposed system. A detailed high-fidelity dynamic model is presented for the buoy, UAV, and water environment. In addition, a stable control system design is proposed to manipulate the surge velocity of the buoy within certain constraints that keep the buoy in contact with the water surface. Polar coordinates are used in the controller design process since they outperform traditional Cartesian-based velocity controllers when it comes to ensuring correlated effects on the tracking performance, where each control channel independently affects one control parameter. The system model and controller design are validated in numerical simulation under different wave scenarios.