Wave-number-based assessment of the doubly asymptotic approximation. I. Frequency domain wet surface impedance

The doubly asymptotic approximation (DAA) is a canonical relationship for the interaction between surface normal velocity and pressure. Its validity for a slender hemicapped cylinder is examined by formulating a frequency domain version of DAA using the global basis functions employed in the wave-number-based formulation of the surface variational principle [K. Wu and J. H. Ginsberg, ASME J. Vib. Acoust. 120, 392-400 (1998)]. The wet surface impedance matrix, which relates the spectral representation of normal velocity to a corresponding representation of pressure, is obtained according to a second-order version of DAA and according to the surface variational principle. Comparison and interpretation of the results reveals that DAA fails to account for highlights associated with transition from supersonic to subsonic surface waves as the surface wavelength decreases with frequency held constant.