A simple model for the experimentally observed instability of the vortex ring to azimuthal bending waves of wavelength comparable with the core size is presented. Short-wave instabilities are discussed for both the vortex ring and the vortex pair. Instability for both the ring and the pair is predicted to occur whenever the self-induced rotation of waves on the filament passes through zero. Although this does not occur for the first radial bending mode of a vortex filament, it is shown to be possible for bending modes with a more complex radial structure with at least one node at some radius within the core. The previous work of Widnall & Sullivan (1973) is discussed and their experimental results are compared with the predictions of the analysis presented here.

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A boundary element method is formulated in terms of time-averaged energy and intensity variables. The approach is applicable to high modal density fields but is not restricted to the usual low-absorption, diffuse, and quasiuniform assumptions. A broadband acoustic energy/intensity source is the basic building block for the method. A directivity pattern for the source is derived to account for local spatial correlation effects and to model specular reflections approximately. A distribution of infinitesimal, uncorrelated, directional sources is used to model the boundaries of an enclosure. These sources are discretized in terms of boundary elements. A system of equations results from applying boundary conditions in terms of incident, reflected, and absorbed intensity. The unknown source power for each element is determined from this system of equations. A two-dimensional model problem is used to demonstrate and verify the method. Exact numerical solutions were also obtained for this model problem. The results show that spatially varying mean-square pressure levels are accurately predicted at very low computational cost.

Analytical/numerical matching ͑ANM͒ is a hybrid scheme combining a low-resolution global numerical solution with a high-resolution local solution to form a composite solution. ANM is applied to a harmonically oscillating body to calculate the radiated acoustic field and the associated fluid loading. The approach utilizes overlapping smoothed dipoles, and local corrections to calculate the dipole strength distribution along the surface of the body. A smoothing length scale is introduced that is larger than the smallest physical scale, and smaller than the largest physical scale. The global low-resolution solution is calculated numerically using smoothed dipole solutions to the wave equation, and converges quickly. Local corrections are done with high-resolution local analytical solutions. The global numerical solution is asymptotically matched to the local analytical solutions via a matching solution. The matching solution cancels the global solution in the near field, and cancels the local solution in the far field. The method is very robust, offering insensitivity to node location. ANM provides high-resolution calculations from low-resolution numerics with analytical corrections, while avoiding the usual subtleties involving singular integral equations, and their numerical implementation. The method is applied to calculate the radiated acoustic field and surface pressure of various flat plate configurations in two dimensions. An oscillating rigid flat plate, a forced elastic flat plate, plane-wave diffraction, and mechanical impedance calculations are addressed.

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Free-wake analyses of helicopter rotor wakes in hover using time stepping have been shown to encounter instabilities which preclude convergence to valid free-vortex solutions for rotor-wake geometries. Previous work has demonstrated that these convergence difficultiescan he overcome by implementing a new free-wake analysis method based on the use of influence coefficients. The present paper reviews this approach and documents its incorporation into a hover performance analysis called Evaluation of Hover Performance using Influence Coefficients (EHPIC). The technical principles underlying the EHPIC code are described with emphasis on steps taken to develop the single-filament wake models used in previous work into a multifilament wake valid for realistic hover performance predictions. of the wake model to a lifting surface loads analysis is described, and sample problems are solved that illustrate the robustness of the method. Performance calculations are also undertaken for hover to illustrate the utility of EHPIC in the analysis of rotorcraft performance.

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