Second-order theory for flow past oscillating foils.

A second-order theory for the lifting problem was developed for foils performing harmonic oscillations either in plunging or pitching modes. The second-order problem is obtained by systematic expansions of the variables involved. By a suitable definition of the second-order acceleration potential, the second-order problem is reduced to a form similar to that of the first-order problem. The method used for the first-order problem was applied for the solution of the second-order problem with some modifications. Numerical results were obtained for a symmetric Joukowsky foil oscillating in plunging or pitching mode. These results are compared with existing results on the effect of finite thickness of the foil, and to some recent results obtained by numerically solving the full nonlinear problem. (Author)