The ultimate goal is to develop a theory for a supercavitating propeller advancing with a constant speed and with a constant rate of rotation. The average flow at infinity is at rest but it contains periodic disturbances. The blade section is allowed to vibrate. However, the propeller case leads to unwieldy mathematics. Consequently, the main aim of this paper is to investigate the mathematical and physical aspects of the problem as follows. A lifting- line theory is developed for an unsteady supercavitating hydrofoil with a constant speed of advance as a singular perturbation problem. Secondly the flow field of an accelerating supercavitating flow past a thin two-dimensional plate is treated. The disturbances, which simulate the wake field, are thus defined in such a way that both the linearized Euler and continuity equations are satisfied. Finally, this second problem is adopted as the inner solution for a singular perturbation problem. When all this has been completed the extension to the propeller cases involves only lengthy algebra. The present emphasis is on the formulation of the problem, and correspondingly no calculated results are available.

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