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The instability of a thin sheet of liquid moving in the same direction as an air stream is studied theoretically. It is found that instability occurs if the Weber number is less than a critical value related to the ratio of the air and liquid stream velocities. Also, the wavelength for maximum instability is found to be inversely proportional to this critical value.

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The quasianalytical (QA) approach is applied to the three-dimensional full potential equation to compute wing aerodynamic sensitivity coefficients in the transonic regime. Symbolic manipulation is used and is crucial in reducing the effort associated with obtaining sensitivity equations, and the large sensitivity system is solved using sparse solver routines such as the iterative conjugate gradient method. The results obtained are almost identical to those obtained by the finite difference (FD) approach and indicate that obtaining the sensitivity derivatives using the QA approach is more efficient than computing the derivatives by the FD method, especially as the number of design variables increases. It is concluded that the QA method is an efficient and accurate approach for obtaining transonic aerodynamic sensitivity coefficients in three dimensions.