Resolution and structure of the wall pressure field beneath a turbulent boundary layer

Abstract

The power spectrum of the wall pressure that would be measured by a transducer of vanishingly small size and the corrections to the power spectra measured by finite-size transducers are determined from the spectra measured by four transducers of different diameters. The root-mean-square wall pressure measured by a transducer of vanishingly small size is $\sqrt {p^2}| \tau_w = 2 \cdot 66$, approximately 13% higher than the root-mean-square pressure measured by the transducer used in the earlier investigations of Willmarth & Wooldridge (1962). Corrections to the power spectrum measured by a finite-size transducer are computed using the theory of Uberoi & Kovasznay (1952, 1953). The computations require information about the correlation of the wall pressure for very small spatial separation of the transducers. Unfortunately, these measurements have never been made. Corcos's (1964) similarity of the cross-spectral density is assumed to represent the missing information, but the computed corrections fail at high frequencies because the similarity expression is not valid when the spatial separation is small. The range of validity of the similarity is determined, and the average radial derivative of the cross-spectral density is inferred from the measured power spectra.